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    Plan détaillé Texte intégral Introduction The origin and provenance of the manuscript The shape of the science album: comparanda for Madrid Mss/9605 A macroscopic view of Mss/9605 (1). The computistical core A microscopic view of Madrid Mss/9605: the portfolio of cosmographical diagrams The macroscopic view of Madrid Mss/9605 Conclusion Appendix: Summary of Contents of Madrid, Mss/9605 Illustrations Bibliographie Notes de bas de page Auteur

    Lumières du Nord

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    Table des matières

    Mss/9605: An Eleventh-Century “Science Album”

    Faith Wallis

    p. 19-72

    Texte intégral Bibliographie Notes de bas de page Auteur

    Texte intégral

    Introduction

    1Manuscript Mss/9605 of the Biblioteca nacional de España is an example of a type of manuscript book produced between the 9th and the early 13th centuries for monastic and clerical libraries. We can call these manuscripts “science albums”. They appeared in the wake of the diffusion of Bede’s De temporum ratione (725) on the Continent by Insular missionaries and visitors, and as a consequence of the Carolingian promotion of computus as a critical element in the reform of clerical education. De temporum ratione provided an encyclopedic framework, as well as technical arguments, for the management of the Roman solar calendar and for the Alexandrian-Dionysian formulae for calculating Easter. This encyclopedic framework drew cosmology, mathematics, astronomy and medicine into the orbit of computus. The Carolingian project, on the other hand, ensured the proliferation of manuscripts devoted to presenting computus within this expanded framework. The Carolingian period, as well as the turn of the 11th century, mark two moments within the history of computus when efforts to unify, simplify, but also “totalize” the reach of this science reshaped its manuscript vehicles1.

    2“Science albums” are compiled according to a certain formula, but with considerable latitude in the choice and arrangement of the contents. They comprise a core of computistica (typically a Roman calendar with the tables required to translate its dates into days of the week and days of the lunar month, as well as a Paschal table and dependent materials) along with additional material on one or more allied topics such as astronomy, cosmology and mathematics, medicine, history, geography, and prognostics. Treatises, shorter tracts and extracts, formulae (argumenta), lists, tables and diagrams are arranged paratactically, like pictures in an album, without an explicit structure. Science albums are instructional; hence their computistica differs from computus tables found in a liturgical manuscript, in that they are not for immediate reference2.

    3A study of Mss/9605 is appropriate within the present collection, because this volume is richly decorated with framed tables, diagrams and schemata. Computus is centred on two tables, namely the Roman solar calendar and the Paschal tables; but the impetus to distill all computistical knowledge into graphic form reached its apogee in the decades when Mss/9605 was created, largely through the influence of Abbo of Fleury (d. 1004). Abbo’s highly visual approach to computus is strongly evident in this manuscript, and in other 11th century manuscripts made in the territory of modern France. However, Mss/9605 and its comparanda embed Abbonian diagrams and tables within a more conservative structure of texts. To facilitate my analysis of the main graphic component of Mss/9605 – the portfolio of cosmographical and computistical figurae – and to situate it within its global manuscript context, a summary of the contents of the manuscript is provided in the Appendix to this article. I shall refer to particular items in the codex by the reference number assigned in this summary.

    4Mss/9605 comprises 117 numbered folios, and measures 28 x 19 cm3. Where the content is text, it is for the most part in two columns. The binding is dark green cloth over boards. At the top inside of the front cover are the Biblioteca nacional’s labels, one with the modern shelfmark 9605, and an older one with the shelfmark Ee. 40, the latter both on a printed label and underneath in a handwritten notice4. In the middle of this front pastedown is an eighteen-century ex-libris that reads “Ex fundatione R.P. Ioachimi Fauchet Bolennensis Societ. Iesu, ab anno 1644”. I shall return to this ex-libris later. On the outermost medieval leaf (ir) is written in a 12th or early 13th century hand “Liber compotus”. There are two foliations: an older one in ink on the top left-hand corner, starting with this cover leaf, and a modern one in pencil, starting with 1 on the first written folio. When this modern foliation took place is not clear, but it should be noted that the folio numbers in a some published discussions of this manuscript are in error by one page5. This study cites the folios according to the current modern numeration. The gatherings are mostly of eight folios, with some variations6. The manuscript is executed in a neat late-Caroline script by a single scribe. There are a number of striking decorated initials, notably the I(anuarius) on fol. 19r (foliage and interlace, red and blue), the A(nni) on fol. 57ra (red and blue interlace, with bird-head finials), the A(pud) on 97ra (red interlace, with animal-head finials), P(ericulosum) 104r (red and cream interlace), and Q(uia) on 113r, at the beginning of the second part of Claudius of Turin’s Chronicon (red, blue and pale green interlace). Smaller interlace capitals appear on fols. 61ra and 64rb. Foliage capitals are found on fols. 64vb, 66rb, 67vb, 69ra, 72ra, and 112v. Paragraph capitals are in red (occasionally black), some with beading or flourishing.

    5The last item in the codex (no. 116), a summary of the Sixth Age of the World, furnishes a date for its completion, and the name of its compiler or scribe: This date of 1026 is also indicated as the annus praesens in a group of computistical formulae (argumenta) found between fols. 25r-26r (no. 35).

    Ad quibus annis [i. e. AD 854] usque ad presentem annum in quo nostra deuenit aetas uidelicet quo felix adalax comitissa dormiuit in pace colliguntur anni CLXXII. Qui in summa collecti a natiuitate Christi Millesimum uicesimum sextum, presentem annum efficiunt in quo iste libellus conscriptus est a quodam fragili monacho Arnulfo nomine.

    The origin and provenance of the manuscript

    6Prior to the summary description by Paul Ewald and the fuller treatment by Alfred Cordoliani, this manuscript was known mainly through the account provided by its late-18th century owner Joseph-Louis-Dominique de Cambis, Marquis de Velleron (1706-1772), who resided in Avignon. The 1770 Catalogue raisonné of his manuscript collection contains the earliest and most extensive description of Mss/96057. Cambis also provides a detailed, but somewhat problematic reconstruction of the volume’s provenance. He states that in 1693 it was in the library of the Avignon jurist Antoine Calvet of Villeneuve-les-Avignon, where it was consulted by the Maurist Dom Jean Martianay for his work on the Vulgate and Septuagint chronologies8. Cambis mentions that Martianay compared the Calvet volume to one at Saint-Père in Chartres. After Antoine Calvet’s death in 1694, his son sold part of his father’s library, including Mss/9605, which came into the possession of Archdeacon Pierre-François de Pertuis of Avignon9. When in Pertuis’s library, it was examined in 1716 by the Oratorian liturgical scholar Pierre Le Brun (1661-1729). After Pertuis’ death in 172210, it was allegedly acquired by the archbishop of Avignon for a projected public library at the Benedictine Collège de Saint-Martial. After the archbishop’s death in 1742, this project collapsed. Cambis claims that it was at this juncture that he purchased the volume from the Benedictines, but without specifying a date. What he unaccountably fails to mention is that at some point the Jesuits of Avignon owned Mss/9605. Their library was endowed by the Jesuit Joachim Fauchet of Bollène (1606-1650), and it is this library’s ex-libris label, “Ex fundatione R.P. Ioachimi Fauchet Bolennensis Societ. Iesu, ab anno 1644”, that is pasted on the inside of the front cover11. The Order was expelled from Avignon in 1768, and their College was taken over by Benedictines of Saint-Martial in February 1769. In May of that year, the library was sold to one “Sieur Fréchier, rue de la Grande-Carreterie”, who sold the individual volumes to various bibliophiles12. Without question, Cambis obtained Mss/9605 by this route. Thus Cambis is technically correct that he acquired the book from the Benedictines of Saint-Martial, but a significant intermediate chapter in its history is omitted. Why he omitted this information in not clear. He seems to have had a certain animus against the Jesuits – he excuses the presence of “astrology” in his manuscript by pointing out that a recent Jesuit manual of mathematics makes similar “ridiculous” claims13 – but whatever the motive, the erasure of the Jesuit chapter casts some doubt on his account of Mss/9605’s provenance, including his assumption that Antoine Calvet acquired it directly from the monastery of Saint-André.

    7This last point is very important to Cambis, for he is concerned to prove that his manuscript is the autograph of Arnulf, scholasticus of the abbey of Saint-André in Villeneuve-les-Avignon in the late 10th century, and that Arnulf was an exceptional scholar who composed much of the material in Mss/9605 for the instruction of his students. Cambis’ information on Arnulf comes from Mabillon’s Annales ordinis sancti Benedicti, sub anno 1026. Mabillon ascribed to Arnulf a chronology which numbered 5325 years from the Creation to the birth of Christ, 853 years to the death of Charles the Bald, and 1026 years to the present. This short chronology is indeed found on fols. 116-117 of Mss/9605 (no. 112), where it is introduced as “Excerptum ex cronica sancti Ysidori”. The summary of the first five world ages is derived from Etymologies 5.39, but the short notice on the sixth age is not, save for the final sentence. Mabillon14 and Cambis15 quote extensively from this, which is here reproduced in full.

    Octauianus LVI. Huius anno XLoIo Christus dominus nascitur. Si enim hos annos id est quadraginta et unum necnon et cainan annos CXXX quos alii scriptores computant superioribus annis addere uolueris colliguntur ab inicio mundi usque ad Christum secundum hanc supputationem anni V CCC XXV. A natiuitate uero domini nostri Ihesu Christi secundum carnem usque ad annum quadragesimum regni gloriosissimi karoli filii piissimi imperatoris Hludouuici supputantur anni DCCCL(erasure?)IIII. A quibus annis usque ad presentem annum in quo nostra deuenit aetas uidelicet quo felix adalax comitissa dormiuit in pace, colliguntur anni CLXXII. Qui in summa collecti a natiuitate Christi Millesimum uicesimum sextum presentem annum efficiunt in quo iste libellus conscriptus est a quodam fragili monacho Arnulfo nomine. Residuum sextae aetatis tempus Deo soli cognitum est.
    (Octavian 56 years, in whose 40th year Christ the Lord is born. If one wishes to add those 41 years, as well as the 130 years of Cainan which other writers compute, to the above years [i.e. 5154 to the death of Julius Caesar] the total from the beginning of the world until Christ according to this reckoning is 5325 years. From the birth of our Lord Jesus Christ according to the flesh up to the fortieth year of the reign of the most glorious Charles, son of the most pious Emperor Louis, 854 years are reckoned. From these years up to the present year, which is our own time, in which the fortunate Countess Adelaide rested in peace, 172 years are reckoned. Added all together, they make 1026 years from the birth of Christ until the present year, in which this book was written down by a certain frail monk named Arnulf. The time remaining to the Sixth Age is known to God alone.)

    8The “130 years of Cainin” refers to Bede’s remarks in De temporum ratione 66 concerning the Septuagint text of Genesis. The Septuagint inserted an extra generation between Arpachshad and Shelah (Genesis 11:12), and ascribed it to Cainan. This generation was dropped by Eusebius’s, and hence Jerome’s, world chronicle, but the excess 130 years from the Septuagint reckoning were retained in their calculation of the length of the Second World Age16. The Adelaide in question is Adelaide or Blanche of Anjou, daughter of Fulk of Anjou and wife of Guillaume I, count of Provence. She died in Avignon in 1026, and was a benefactor of religious houses, including Saint-André17.

    9Arnulf’s exemplar for this summary chronology contained a text composed in 854, and Arnulf brought the text up to date by adding his own colophon and date. Why he omitted Isidore’s sixth age is not clear, but fol. 117v is both the end of a page and the end of a gathering so it might have been a matter of space.

    10That Mss/9605 was made in and for Saint-André in Avignon is supported not only by the reference to the Countess Adelaide, but also by entries in the martyrology on fols. 27v-37v commemorating local and regional saints. Cambis notes against 26 April “Dedicatio ecclesie sancti Andree”, the dedication of church of Saint-André in Avignon; 17 June, the translation of St Veredeme, bishop of Avignon; 2 September “Avenione sancti Agricoli episcopi”; 27 November “Sancti siffredi” i.e. St Siffrein bishop of Carpentras18. There are, to be sure, numerous other saints from other cities in France and Spain,19 to say nothing of saints from Crete, Naples, Alexandria, Britain, Messina, “Africa”, and of course Rome, for this is a pedagogical and not a liturgical document. Nonetheless, the strong representation of saints from south-eastern France is noteworthy.

    11It is highly likely that the manuscript cited by Mabillon is the same manuscript cited by Cambis, but also probable that Mabillon was working from a report of its contents, and not from first-hand inspection. Mabillon ascribed to Arnulf the following:

    1. “breve Martyrologium seu Kalendarium Sanctorum per annum” (cf. Mss/9605 no. 37).
    2. “libellum de ponderibus et mensuris”, beginning “duodecim unciae libram viginti solidos contentem efficient” (there are notes on weights and measures in Mss/9605 no. 3, but not this one).
    3. A tract “De recipiendis vel non recipiendis Auctoribus secundum edictum de Urbe Roma” which, he observes, is in fact the Gelasian decretal (cf. Mss/9605 no. 12).
    4. Two short tracts, one on the solstice and the other “de die Obitus ac Passionis Domini Nostri Jesu-Christi”. These are not easy to identify with any of the material in Mss/9605, though the Gelasian decretal is preceded by a short note on the spiritual significance of the (old Roman) dates of the winter and summer solstices (no. 12) and followed by a short tract discussing the problem of the resurrection of the dead at the time of Christ’s passion (no. 13).

    12Mabillon does not say where he obtained his information on Arnulf’s works; but he was likely relying on a summary or transcript from an informant in Avignon. Cambis, however, does not entertain that theory, for he is anxious to prove that Arnulf was famous throughout France, and that he was the author of many more works than just the few items Mabillon ascribed to him. He therefore posits that Mabillon saw not one but two “imperfect” manuscripts of Arnulf’s works in the library of Saint-Germain-des-Prés. The first was a sibling of the volume he owned, while the second contained “les autres écrits d’Arnoul” without specification. There is indeed an 11th century manuscript from Saint-Germain-des-Prés which contains many of the same computistical materials found in Mss/9605: Paris BnF Latin 12117 (described below). However, Cambis’s “imperfect” manuscript of Arnulf cannot be BnF Latin 11217, because this manuscript does not match Cambis’s description of the contents of the “imperfect manuscript”20. Cambis thus maintains that his manuscript is Arnulf’s autograph21. It is this which underpins his hypothesis that Antoine Calvet acquired the volume directly from Saint-André.

    The shape of the science album: comparanda for Madrid Mss/9605

    13Impressed by the range and detail of the materials in his manuscript – and perhaps also with a view to inflating its value – Cambis spared no effort to elevate Arnulf to the stature of a major intellectual and teacher. Thus it was with some embarrassment that he admitted that Arnulf’s date of 854 in his colophon corresponded not to the fortieth, but to the fourteenth year of the reign of Charles the Bald22. Cambis also fails to mention another error in the dating clause on fol. 117v, namely in the total number of years from creation to the birth of Christ, 5145 + 41 + 130 totals 5316, not 5325. More seriously, Cambis’s assumptions about Arnulf reveal a lack of awareness that his manuscript was a representative of a genre, and that this genre, by its very nature, was essentially a formula for a compilation of materials of diverse kinds, and from different sources. Hence from copy to copy, individual elements can be re-ordered, interpolated, or subtracted.

    14Cambis’s oversight continues to infect studies of computus. From pioneers like Cordoliani to the recent monumental study of Arno Borst, Schriften zur Komputistik im Frankenreich von 721 bis 81823, computus has been approached as if its literature were in the form of canonized treatises. That these “treatises” almost never appear whole and entire in any manuscript is ascribed to “later” manuscripts reproducing only excerpts of the “original” work. Thus, Cordoliani posits that fols. 19-55 of Mss/9605 contain a recueil that when “complete” contained 15 chapters. When elements of this ideal text are not present in Mss/9605, they are described as “missing”24. Similarly Borst’s description of this manuscript assumes that its contents are “excerpts” from idealized “textbooks” of the Carolingian period – few if any of which actually appear in any manuscript in the synthetic form represented in Borst’s editions25. This obscures an essential characteristic of the manuscript evidence, which is that computus was almost always conveyed in albums assembled deliberately and by design from an open treasury of texts, formulae, tables, and lists.

    15The character of Mss/9605 as a representative of this science album genre comes into focus when it is set beside others of its kind made in the same region and at the same time. Some of these manuscripts are strongly influenced by the teaching of Abbo of Fleury. However, it also reflects pre-Abbonian and non-Abbonian traditions of computus texts and tables, as indeed do Abbonian manuscripts. The following manuscripts will serve as a representative, though not comprehensive, set of comparanda.

     

    (A) Berlin. Staatsbibliothek Preussicher Kulturbesitz, Ms Phillipps 1833 (132)

    s. X ex. or XI in. Fleury.

    Digital facsimile: <http://digital.staatsbibliothek-berlin.de/werkansicht?PPN=PPN83017379X&PHYSID=PHYS_0012&DMDID=DMDLOG_0005>

    Edition: Abbo Floriacensis 2019.

    Abbo of Fleury’s science album26, assembled by himself or more likely his students and followers. It comprises a Carolingian-type array of excepts and tables; Abbo’s commentary on the Calculus of Victorius of Aquitaine; Abbo’s distinctive calendar and accompanying tables for determining the weekday or age of the Moon on a given date; Abbo’s Ephemerida (an intricate calendar coded as an acrostic poem); Abbo’s portfolio of astronomical diagrams27; Abbo’s tracts on the correction of the annus domini and Paschal tables28.

     

    (D) Dijon. Bibliothèque municipale, Ms 44829

    s. XI med. Burgundy or north-eastern France. Owned by St-Bénigne, Dijon, from 1061.

    Digital facsimile: <http://patrimoine.bm-dijon.fr/pleade/img-viewer/MS00448/viewer.html?ns=FR212316101_MS00448_000_01_PS.jpg>

    Extensive compilation of tracts, notes, and argumenta on computus; Isidore, De natura rerum; Paschal tables with annals; star catalogues (ps-Bede, Hyginus); Abbonian album of cosmological and astronomical texts and figurae; extensive album of computus tables, ending with a calendar; carmina figurata and prognostica; Helperic, De computo; Bede, De temporum ratione, De natura rerum, De temporibus.

     

    (L) London, British Library, Ms Sloane 26330

    s. XI. Southeast France, probably Lyon.

    Description and digital facsimile: <http://www.bl.uk/manuscripts/FullDisplay.aspx?Source=BrowseScribes&letter=A&ref=Sloane_MS_263>

    Helperic, De computo; computus tracts, argumenta and poetry; calendar with Abbonian and non-Abbonian tables; cosmological and astronomical diagrams. acephalus star catalogue.

     

    (P1) Paris, Bibliothèque nationale de France, Ms Latin 7299A31

    s. XI or XII. South-western France.

    Digital facsimile: <https://gallica.bnf.fr/ark:/12148/btv1b10544628b>

    Calendars with computus tables and Paschal tables (several suites, some repeating); prognostica; suite of cosmology-astronomy figurae; Bede, De natura rerum and Isidore of Seville, Etymologiae book 3; a text on astrological magic and divination melts imperceptibly into a suite of computistical argumenta, notes, definitions and poems.

     

    (P2) Paris, Bibliothèque nationale de France, Ms Latin 7361 pt. 1 (fols. 1-56v)32

    s. XI, probably 1098. Germany, perhaps lower Rhine region.

    Digital facsimile: <https://gallica.bnf.fr/ark:/12148/btv1b10546173z>

    Computus tables and poetry; Paschal tables for 1026-1101; Helperic, De computo; didactic dialogue on computus; summary chronicle of world-ages to annus mundi 4761 (AD 808); Adalbold of Utrecht’s commentary on Boethius’ “O qui perpetua”.

     

    (P3) Paris, Bibliothèque nationale de France, Ms Latin 7419

    s. XI ex. or XII in. Eastern France.

    Digital facsimile: <https://gallica.bnf.fr/ark:/12148/btv1b52506007j>

    Computus texts and tables; Abbonian solar calendar; calendar tables; portfolio of computistical and astrronomical diagrams and tables; Helperic, De computo; tracts on divisions of time; extended Ratio calculi; suite of computistical poetry.

     

    (P4) Paris, Bibliothèque nationale de France, Ms Latin 1211733

    ca. 1060-1063. Saint-Germain-des-Prés34.

    Digital facsimile: <https://gallica.bnf.fr/ark:/12148/btv1b10542293s>

    Poems on weights and measures, and on computus; ps.-Clementine Recognitiones; games or riddles; tabular world-chronicle based on Bede with lists of rulers of Italy and France; Paschal tables with annals; astronomica (Hyginus, star catalogue); Helperic, De computo; Abbonian computus with his Ephemerida, calendar, and distinctive tables, as well as tracts and poems; excerpts from Pliny and Macrobius on measurement of cosmos.

     

    (V1) Vatican City, Biblioteca Apostolica Vaticana, Ms Reg. lat. 309 pt. 2 (fols. 121-156)35

    s. XI Saint-Denis.

    Digital facsimile: <https://digi.vatlib.it/view/MSS_Reg.lat.309>

    Abbonian computus.

     

    (V2) Vatican City, Biblioteca Apostolica Vaticana, Ms Lat. 1263

    s. XI. Saint-Mesmin-de-Micy.

    Description and digital facsimile: <https://digi.vatlib.it/view/Reg.lat.1263>

    The first part of this manuscript (fols. 1-80v) is a loosely structured album of tracts, tables, calendar and Paschal tables, and notes on computus, pre-Abbonian in character. An Abbonian computus follows on fols. 81r-102r.

     

    (V3) Vatican City, Biblioteca Apostolica Vaticana, Ms Rossi 24736

    s. XI. France, perhaps Saint-Chaffre du Monastier (near Le Puy), Haute-Loire.

    Digital facsimile: <https://digi.vatlib.it/view/MSS_Ross.247>

    Abbonian computus embedded inside a monumental compilation of pre-Abbonian character, including Bede De natura rerum, De temporibus and De temporum ratione.

    A macroscopic view of Mss/9605 (1). The computistical core

    16As a “science album”, Mss/9605 comprises a computistical core (fols. 1-88r, nos. 2-59) and two scientific extensions: first, a cosmography in the form of a portfolio of diagrams (fols. 88v-97v, nos. 60-82) and secondly, materials on chronology and history (fols. 104v-117v, no. 108-117). These extensions are conceptual outgrowths of computus: cosmography reveals the astronomical and physical setting of time, and chronology and history its role in the drama of salvation. Hence while they follow the computistical core, they are also linked to one another by a computistical-chronological bridge (fols. 97r-103v, no. 83-107).

    17Most of the comparanda manuscripts exhibit the same pattern of computistical core and para-computistical extensions.

    • A: cosmography in the form of diagrams and maps; mathematics.
    • D: cosmography in the form of Isidore of Seville’s De natura rerum, portfolio of diagrams; astronomy (star-catalogues).
    • L: cosmography in the form of diagrams; astronomy (star-catalogue).
    • P1: cosmography in the form of Bede’s De natura rerum and diagrams; astronomy; astrology.
    • P2: cosmology in the form of Adalbold of Utrecht’s commentary on the cosmogony of Boethius’ “O qui perpetua”; history in the form of summary version of Bede’s Chronica minora ending in 808 (annus mundi 4761), as in Madrid.
    • P3: cosmography in the form of diagrams.
    • P4: chronology and history; astronomy (texts, including extracts from Martianus Capella and Abbo’s astronomical tracts, and diagrams).
    • V1: purely Abbonian computus with no scientific extensions, but bound with a Carolingian copy of the 7-book “Aachen Textbook of Computus”37 and a copy of Bede’s De natura rerum.
    • V2: cosmography in the form of diagrams.
    • V3: cosmography in the form of Bede’s De natura rerum.

    18The portfolios of cosmographical diagrams in A, D, L, P1, P3 and V2 are highly similar to the diagrams in Madrid Mss/9605; these will be discussed in greater detail below. What is important for an initial macroscopic perspective on Madrid Mss/9605 is the dominance of cosmology, astronomy and history in this group of science albums, and the absence of materials found in other albums, such as medicine, music and divination or prognostication38. Madrid and its kindred, in short, represent a cosmological-historical sub-type of science album. My microscopic view of the portfolio of diagrams, which is the particular focus of interest of the present volume, will thus be embedded into a macroscopic survey of the materials which precede and follow this portfolio.

    19Madrid Mss/9605’s computistical core is anchored by two substantial texts: the De computo of Helperic of Grandval (fl. 900) (no. 2) and the anonymous De ratione temporum uel de compoto annuali (no. 59). De computo39 was apparently composed in 903; this is the annus praesens found in ch. 23, which contains the argumentum or formula for finding the current annus domini. Madrid’s text records this year; it also renders the author’s name as “Helpericus”, and includes two prefaces, one addressed to abbot Asper of Saint-Germain in Auxerre, and the second a prologue explaining how the author came to write this work at his students’ request. Many manuscripts of this work, however, alter the annus praesens, omit the letter to Asper, or deform the author’s name to Chilpericus, Albericus, Heiricus, or Heriricus40. Abbo of Fleury is alleged to have produced a revised edition of Helperic with the annus praesens of 978 and some modifications of the text. However, none of our comparanda has this particular version41. Moreover, the most authoritative manuscript of Abbo’s computus (A) does not contain Helperic at all (though it is likely Abbo used Helperic in his teaching), while a contemporary Abbo manuscript from Fleury, now Bern, Burgerbibliothek 250, contains only a few excerpts. In sum, the influences shaping a science album like Mss/9605 were not confined to the pages of manuscripts, but also included traditions of instruction.

    20Helperic is followed by a suite of computus-related texts and diagrams. A text on weights and measures (no. 3) evokes the theme of mensuration, setting the measurement of time within a wider intellectual framework. A rubric for a missing text on weather prognostication (no. 4) links computus’ role as a key to future dates for important events with the larger theme of foreseeing time to come. These are followed by a suite of diagrams (nos. 5-10) illustrating the cosmological context of time-reckoning: a diagram, based on Pliny’s Historia naturalis 3.44, of the apogees (absides) of the planets (no. 5); a rectangular representation of each planet’s latitude, or course in relation to its angle to the ecliptic (no. 6);42 a rota divided into wedges showing the geographical direction of sunrise and the length of daylight in each month (no. 8), and a rota of the twelve winds, with the cardinal directions inscribed on the outer rim (no. 9), supplemented by a marginal text on the names of the winds (no. 10). This particular array is not found in any of our comparanda, though D fols. 72v-73r contains other Plinian astronomical diagrams and two elaborate wind-roses (75r-v). The Plinian latitudes schema was elaborated by Abbo and merged with another diagram showing the interplanetary intervals and their equivalent musical tones (A f. 38v, Abbo Floriacensis 2019, p. 59). Madrid’s version, however, is conservatively Carolingian.

    21One item within this suite which stands out is the table on the lower half of fol. 12v (no. 7) for finding the position of the moon within the zodiac in relation to the day of the lunar month. This table is graphically striking, as it writes the names of the zodiac signs into mandorla-shaped cells, in a decorative pattern of alternating diagonals. The alternative form of this table inscribes the names of the signs diagonally across each square cell of the table to form a lattice pattern43. This version is found in no. 41. Both forms appear in our comparanda: the mandorla variant in P1 fol. 49r and P4 fol. 161v, and the lattice version in A fol. 39r (Abbo Floriacensis 2019, p. 63), P3 fol. 18v, and V1 fol. 141r. V3, like Madrid, has both versions. This highlights an important feature of science albums, namely deliberate redundancies, and a taste for visually agreeable variant versions of the same table. Whether for didactic or symbolic reasons – or more likely both – these manuscripts delighted in making the same statement in as many ways as could be imagined.

    22On fols. 13v-16v another cluster of material mixes computus with theology. The Gelasian canon of approved Patristic texts (no. 12) shows the attractive force exerted by computus on other kinds of material that could be conveyed in list form, but it also implies a parallel between the authoritative library of theology and the authoritative rules for Easter, supposedly endorsed by the Council of Nicaea. This is followed by a question (no. 13) concerning the appearance of the “resurrected” dead at the time of Christ’s resurrection (Matthew 27:52-53) – doubtless reeled into our manuscript by the theme of Easter. Four texts on fol. 16r seem to be cues for sermons,44 reminding us that science albums could also serve as notebooks or repositories for all kinds of clerical erudition. In the midst of this religious material is the Tabula Dionysii (no. 15), an old Carolingian table showing the concurrents (weekdays of 24 March) for each year of the 532-year Great Paschal Cycle45. The Tabula is customized for a particular cycle – in this case, the one beginning in 1064 – because it also flags the indictions or fifteen-year Roman administrative dating cycles, and these do not repeat after 532 years. Abbo, as was his wont, modified the Tabula to include a sequence of key-letters for the dates of Easter and other moveable feasts. This version is found in A fol. 34v (Abbo Floriacensis 2019, p. 38-39), P4 fol. 172r, V1 fol. 153 and V2 fol. 96v. Madrid’s conservative format is found in D fol. 82r, L fols. 42v-43r, P2 fol. 8v and V2 fol. 86v. V2 contains both versions, once again exemplifying the phenomenon of redundancy with variation.

    23The anthology of computus poetry on fols. 17r-18v corresponds to comparable anthologies in D fols. 193-195, L fols. 21v-23r, P2 fols. 4v-6r, P3 fols. 52v-53v and 54v-56v (containing some of the same poems as Madrid, in the same order), and P4 fols. 171v, 174v-176r, 177r46. Poetry is an ancient tool of computus pedagogy – Bede inserts Ausonius’ poem on the zodiac signs “Respicis Apriles Aries Phrixeae kalendas” (Madrid no. 30) into ch. 16 of De temporum ratione47. The Madrid suite includes a verse exposition of the Roman months, mnemonics on their length and internal divisions into nones, ides and kalends, and versified formulae for the monthly solar regulars (numbers which, when added to the annual concurrent, indicate the weekday on the kalends of the month), and lunar regulars (numbers which when added to the annual lunar epact or age of the moon on 22 March, indicate the age of the moon on the kalends). These are followed by part of a widely copied series of five poems of nineteen lines each, giving the calendar terminus for each of the moveable feasts (Septuagesima, Quadragesima, Easter, Rogations and Pentecost) along with a key-number for locating the weekday of the terminus. Madrid has three of the five (nos. 24-26). The most famous of these was the Easter mnemonic “Nonae aprilis norunt quinos”, first recorded in Hrabanus Maurus’ De computo ch. 84 and found in innumerable computus manuscripts, often accompanied by the text found later in Madrid (no. 58) claiming that the poem was delivered by an angel to Pachomius, the father of cenobitic monasticism48. No. 27 is an extended verse summary of basic calendar data, beginning “Annus solis continetur quottuor temporibus”49. This poem is found in D fol. 194r, L fols. 21v-22v, and P2 fols. 4v-5v and 54v-55r. The remainder of the poetry anthology comprises a mnemonic for the eight columns of the Paschal table (no. 28), two poems on the signs of the zodiac (nos. 29-30), a poem on the winds (no. 31), and a mnemonic on lucky and unlucky days (no. 32).

    24On fols. 19r-24v of Madrid Mss/9605 we encounter an expanded version of a collection of lists of basic computus data called the Ratio calculi or computus Grecorum siue Latinorum50. The core of the Ratio calculi is found on fol. 19r (no. 33): these are lists of (1) divisions of Roman months with number of days; (2) solar regulars; (3) lunar regulars; (4) sequence of leap years; (4) epacts. The material is laid out in three columns, framed by elaborated decorated architectural columns. Following this is a series of eleven pages (no. 34) all laid out in a uniform format of decorated architectural arcades. These contain the termini and key-numbers for the moveable feasts, and an extended suite of multiplication tables for numbers often used in computus calculations: 4-13, 15 (for indictions), 19 (for the lunar cycle), 28 (for the solar cycle), 30, 59 (the number of days in two lunar months of 29.5 days – easier to calculate with than a fraction), and 60. This entire ensemble is found in D fols. 2-28 and 62r-v, L fols. 29r-34r, and P3 fols. 41v-47r. Only P3 is not laid out in decorated display tables.

    25What follows is unique to Madrid Mss/9605: a collection of formulae or argumenta based on the annus praesens of 1026, that is, the year in which the manuscript was written (no. 35)51. The annus praesens is explored from every computistical angle: its equivalent annus mundi, its induction, concurrent, position within the 19-year cycle and so forth. Occasionally the text takes on a question-and-answer format (25v-26r).

    26A new section of the manuscript opens with Abbo of Fleury’s distinctive version of the Roman solar calendar (no. 37). Abbo modified a formula for presenting the calendar that dates back to the Roman Republic, namely as a vertical list of dates, flanked to the right by indications of the character of the days (e.g. if it were one of the nundinae or market days) and to the left by key letters or key numbers to translate the date into a weekday or a day of the lunar month. Christian calendars retained the architecture of the classical prototype, but substituted the martyrology for the civic market or law-court days. In the case of Mss/9605, the martyrology is mostly Roman, but with some entries specific to Avignon and its region52. The key-letter columns are (reading out from the date-column): 1) litterae punctatae (three alphabets, the second with a dot before the letter and the third with a dot after, for finding the day of the lunar month); (2) the numbers 1-7 repeated (a form of “Dominical number”) for finding the weekday, and (3) A-O letter series for finding the position of the moon in the zodiac. What is distinctively Abbonian is the right-hand page of each opening, which contains a table for the age of the moon on the kalends of each calendar month through the 19-year cycle. This calendar in Abbo’s premier manuscript, A fols. 23r-28v, has even more key-letter series, but the first three are the same as in Madrid. However, it omits a martyrology. So do P1 fols. 7v-19r, P3 7419 fols. 2v-8v and 49v-41r, P4 fols. 149v-160r and V1 fols. 128v-140r53. A version with martyrology and the same headnotes as Madrid is found in P1 fols. 39r-44v54.

    27Following the calendar are the necessary tables for customizing the dates to the lunations of any given year, using its key-letters: (1) the Pagina regularis for the A-O series (no. 38); (2) the litterae punctatae tables with Bede’s explanation (nos. 29-40); (3) another lunar-zodiac table like no. 7 above, but in “lattice” format (no. 41 – essentially an alternative to the A-O table); (4) Abbo’s alternative to the litterae punctate table using the key-letter series A-V with intervening spaces (no. 42), used in his Ephemerida – a text not included in Mss/960555; (5) and a duplicate litterae punctatae table but with a different layout (no. 43). As the comparanda listed in the Appendix indicate, four of these these tables (nos. 38, 41, 42 and 43) were found in A; the major difference is that no. 8 lacks Abbo’s distinctive graphic enhancement, namely the extension of the four sides of the table to form a cross shape56. Interestingly, this Abbonian style of A-O table appears below accompanying a non-Abbonian calendar (no. 48). In sum, Madrid and its siblings could adopt Abbo’s formula for the calendar and its accompanying tables, but did not feel obliged to imitate all his stylistic innovations, or maintain the integrity of his portfolio of tables.

    28A second, very minimalist calendar (no. 44) is presented in twelve columns across four pages without martyrology or textual enhancements, but in a decorated frame of architectural columns and capitals. To the left of the dates are (1) Golden Numbers (year of 19-year cycle when new moons fall on the date in question); (2) the AEIOV lunar-month letter sequence; (3) Dominical letters; (4) the A-K lunar-month key letter sequence; (5) litterae punctatae; (6) a reprise of the Dominical letters, but with only As marked); (7) the A-O lunar zodiac sequence; (8) the A-V lunar month sequence. As with the first calendar, this is followed by an array of tables for customizing the calendar data. These comprise yet another alternative presentation of the litterae punctatae table (no. 45); the Dominical Letter tables with the “Ratio septizodii” canon; Abbo’s re-organized table for the A-K lunar letters, modified so that the letters align in decorative diagonals (no. 47); Abbo’s cross-shaped pagina regularis (no. 48); and Abbo’s AEIOV table (no. 49). These last tables often appear in paired versions in Abbonian manuscripts like A and V1, but not consistently. Again, Abbo’s computistical innovations seem separable from his graphic presentations.

    29On the other hand, a typically Abbonian key-letter sequence (A-K) could be paired with a stripped-down calendar (no. 50). While this does not appear in Ms A, it was perhaps inspired by no. 52, the Ludus compoti uenerabilis Bedae, which replicates the skeletal calendar in no. 44, but with additional computistical enhancements. The theme of “add-ons” continues with no. 32, a merger of the A-O lunar-zodiac table with a concurrent table for the great 532-year Paschal cycle (no. 52). The Ludus compoti is found in A, but oddly the other Abbonian manuscripts in our comparanda vary considerably from A and Madrid: V1 fols. 149v-150r is incomplete; V2 fol. 85v and P4 fol. 168r use the A-V and A-K key letter series.

    30No. 54 is a table for finding the dates of Paschal full moons and of Easter, using the Dominical letters. The odd ascription to Julian of Toledo is found nowhere else – the table is, in fact, Abbonian, as the comparanda indicate. The ascription may reflect the singular esteem in which Julian’s writings were held, notably in southern France, but this remains at the level of speculation57. Complementing this table is no. 55, which also uses the Dominical letters to show the dates of Quadragesima, Easter and Rogations as well as the age of the moon on Easter Sunday, paralleled by poems on the creation of the sun and moon.

    31The closing section of the computus core seems to reflect the opening section in reverse. It consists of argumenta and computistical poetry, the prose “Legend of Pachomius” that attached to the “Nonae aprilis” mnemonic. (no. 26), and finally, to mirror Helperic, an extended prose work on number and computus in the form of a master-student dialogue (no. 59). This apparently deliberate “book-end” structure is found in some other science albums58, though not in our comparanda.

    A microscopic view of Madrid Mss/9605: the portfolio of cosmographical diagrams

    32The dossier of computistical and cosmographical diagrams on fols. 88v-97r is the most visually striking part of Madrid Mss/9605. As mentioned above, dossiers of this kind are fairly common in the comparanda manuscripts, notably A, D, L, P1, P3 and V2. This table shows which items in Madrid find parallels or near-parallels (indicated by ≈) in these codices:

    Madrid Mss/9605ADLP1P2P3P4V1
    60. Text explaining the rotae in nos. 65, 76, and 66.46r13v
    61. Rota showing length of day.
    62. Rota of Egyptian months.
    63. Rota of termini of moveable feasts.
    64. Luna in her chariot.
    65. Rota showing age of the moon on the kalends of each month through the 19-year cycle.≈35r≈ 15r≈ 163r
    66. Pair of syzygiae elementorum38v46v14r≈76r
    67. Horologium 1.
    68. Pair of rotae showing the length of moonlight and distance relative to the sun of the moon on each day of the lunar month.
    69. Litterae punctatae table.
    70. Diagram of cardinal directions and dissemination of the word of God.
    71. Solstice diagram with rectangular earth.74r35r≈ 9r
    72. Rota of planets and their zodiac signs.
    73. Rota showing rising and setting of zodiac signs.45v53v13r
    74. Rota of visibility of zodiac signs.45v13r
    75. Rota of concurrents through 28-year cycle, with number years from the present when the same concurrents will obtain.35v26v-27r11v51v-53r
    76. Rota of weekday of kalends of the month through the 28 year cycle.35v
    77. Tidal rota with OT map and winds.35v74v48r16r
    78. Abbo of Fleury’s horologium with two smaller rotae affixed to upper rim, showing length of moonlight for each day of the month and the relationship of the months to the zodiac signs.38v≈73r48v-49r17r≈7v
    79. Explanatory texts for no. 78.

    33L and P3 closely resemble one another and are clearly derived from Abbo of Fleury’s “teaching portfolio” of images, as represented in A59. Madrid contains a number of diagrams from this collection, but also several not contained in Abbonian manuscripts, and some which are unique, at least within the group of manuscripts studied here. There is some evidence that Madrid’s compiler made a deliberate selection from materials in more than one exemplar. For example, the texts in no. 50 imply that at some stage in the transmission, no. 75 originally followed on no. 65 (“Subsequens uero rota…”). However, no. 66 does indeed appear on the fifth page (“Vta pagina”), counted inclusively, from no. 60, but the equivalent texts in L and P3 do not contain this clause; thus, the text in Madrid was edited at some point to indicate the location of no. 66.

    34A distinctive theme seems to be guiding the selection and arrangement of the items in this dossier, which we might call “the harmonies of the physical and spiritual universe”. This theme is expressed in the dominance of rotae. Rotae are neither new nor unusual as frames for representing computistical, cosmological and astronomical information. But an argument can be made that in the Madrid manuscript, the rota-form appears in particularly exaggerated and unusual ways. It is as if the compiler wished to emphasize this form as a symbol of unity and cyclic reiteration, and not for the ends of pedagogy or reference. The rota also serves to link computistical content to a graphic form – the circle – which evokes the spherical universe of the cosmologists60. Secondly, the theme of concordia is enunciated in no. 60 (3), the explanation of the syzygiae elementorum; it also re-surfaces explicitly in the inscription in the hub of no. 67 (“Concordia mensuum [sic]”) in the tidal rota (no. 77 “Concordia maris et lunae”), and implicitly in no. 75, which illustrates a principle Bede called “the harmony of the recurring years”. Choice and arrangement of elements within a science album has been shown in other instances to be driven by ideas of a metaphysical nature – ideas which the paratactic nature of the album rarely articulates explicitly, but which can be “read” in the arrangement and character of the contents61. This, it seems, is also the case with Madrid Mss/9605.

    35The use of the rota as an expressive format for presenting information that does not require a circular frame is clearly illustrated in no. 61 (Fig. 1.1), which shows the length in hours, puncti, minutae etc. of each day of the week. The information is the same for each day, so it could be conveyed in a single sentence. But the repetition of the days and their presentation as a wheel evokes their similarity, as well as the cyclic character of the week. The same can be said for the rota of Egyptian months beside it (no. 62), since all Egyptian months are of the same length, namely thirty days. Below this pair is a rota showing the calendar termini of the moveable feasts (no. 63). This material is found elsewhere in Madrid Mss/9605 in table and list forms (nos. 34) which are considerably easier to consult than a rota, which can only be read by laboriously turning the codex around. But the rubric suggests that the point of this rota is not ease of reference, but the representation of the cyclic character of the data (“Hic est ciclus decemnouenalis”) and hence of the perfection, order and “harmony” of the Paschal reckoning62.

    36The expressive or symbolic nature of this dossier emerges clearly in nos. 64 and 65 (Fig. 1.2). No. 65 is a somewhat elaborated version of an Abbo of Fleury rota showing the age of the moon on the first day of each month through the 19-year cycle. Above is an image found only in Madrid Mss/9605: a personified Luna in a chariot drawn by two horses, one dark and one light, and carrying two torches. The meaning of these attributes is explained by the large nimbus around Luna: “Splendens sidereas depeluit luna tenebras (The shining Moon drives off the starry shadows)”. The two horses and the two torches represent the moon’s waxing – when she eclipses the stars by her increasing brightness – and her waning.

    37No. 66 (Fig. 1.3) is one of the oldest and most common forms of cosmological diagram, the “conjunction of the elements” (syzygia elementorum)63. Isidore of Seville popularized this figure as a way of representing, first, the relationship of the seasons to the primal qualities of hot, cold, wet and dry, and secondly, the overlapping qualities of the elements, seasons, and humours of the human body64. These two Isidorean figures were brought together by Abbo of Fleury65, and yoked to a horologium showing the equivalent length of day and night across pairs of months – for example, November and February have the same number of hours of daylight and night, as do October and March, September and April, and so forth. Madrid departs from the Abbonian model by representing the horologium as a rota rather than as a semicircular “sundial” with a “gnomon” (this form is found in no. 87), but it retains Abbo’s label “Concordia mensuum (sic)66”. The syzygiae are accompanied by a note referring the reader back to the description in no. 60, where the first syzygia is said to show the concordia of the seasons.

    38No. 68 is a visually stunning and highly original display of information within a rota format, across a double-page opening (Fig. 1.4). Though it finds no parallel in the other manuscripts, its attention to effective mise en page bespeaks Abbonian inspiration67. The two rotae both show the length of moonlight and relative distance of the moon from the sun along the zodiacal band. The one on fol. 90v is for the waxing moon, and the one on fol. 91r for the waning moon. The fifteen rings of the “waxing moon” rota are read outwards from the centre in ever-widening rings, while those of the “waning moon” rota are read inwards. Hence the disposition of the information mimics the increase and decrease of the moon’s visibility. Each ring contains a text detailing the duration of moonlight on that day, and the moon’s distance from the sun along the Zodiac, i.e. “Luna I quattuor punctis lucet. quattuor I IIII. Quattuor punctis lucet luna I et distat a sole similiter IIII punctis.” Once again, this information could be much more easily read if presented as a simple list or in a rectangular table, but the rota format dramatizes the cyclical quality of the lunar month. Adding to this sense of solemnity is the monumental majuscule script of the rubrics, and the hand in the middle of each rota, holding a ring inscribed with the initial letters of the months of the year and the corresponding sign of the zodiac. The hand and the ring recall images of the hand of God holding the crown over the head of Charles the Bald in the Vivian Bible, or over the head of the Emperor in the Lothar Gospels. But the Hand (of God) has a special resonance within the context of computus. The “Nonae aprilis” mnemonic was, according to legend, delivered from heaven to Pachomius, and representations of this story in manuscripts are sometimes illustrated by the dextera Domini emerging from the clouds of heaven68. Finally, the hand was used in computus pedagogy as a tool for basic mathematical calculation (as explained in Bede’s De temporum ratione ch. 1), and more specifically, as a “memory place” for the epacts and concurrents (De temporum ratione cg. 55). Some of the argumenta in Mss/9605 use hand-mnemonics (25v). In sum, the hand was a potent symbol of both the sacred origin of computus, and of its practice by human students.

    39Following an unusual litterae punctatae table, which is also spread across a two-page opening, is a diagram which seems to hold the exegetical clue to this entire ensemble (no. 70; Fig. 1.5). This is a representation of the world as a quadrilateral, divided orthogonally and diagonally into eight triangles, painted in alternating shades of dark blue, light blue, green-blue and yellow. In the middle of each side is the bust of a nimbed figure, rising out of a ring whose centre is the centre of the square. There is a smaller ring at the hub, inscribed: “Sensus spiritualis interius uoluens (The spiritual meaning, revolving inwardly).” The ring from which the busts emerge is inscribed: “Hystoria legis et prophetarum exterius in littera ab initio mundi usque in finem eius uelut rota uoluitur et propter IIII mundi partes et quattuor elementa quattuor facies habere dicuntur (The history of the Law and the Prophets, outwardly in written form, revolves like a wheel from the beginning of the world until its end, and because of the four parts of the world and the four elements, is said to have four faces).” On the frame of the square is inscribed: “Oriens euangelica predicatio. / Meridies apostolorum predicatio. / Occidens lex Moysi. / Septentrion prophete ueteris testamenti.” We might title this diagram “the cardinal directions and the dissemination of the word of God.” The artist seems to have been inspired by a type of diagram of the winds which divides a circular wind-rose into twelve segments, and personifies the four winds at the cardinal directions by human or winged figures, sometimes standing on a square hub69. But he also alludes to a type of schematic mappa mundi that overlays the mission-fields of the Apostles onto the three continents, radiating outwards from Jerusalem to the ends of the earth70. The sources of this exceptional diagram remain to be investigated. What we can say at the outset is that, like the other diagrams in this dossier, it fuses time (“ab initio mundi usque in finem”) with the physical cosmos (“propter III mundi partes et quattuor elementa”). Moreover, though at first glance it seems to be a square, it identifies itself as a rota – the “sensus spiritualis interius uolens” mirrored in the “Hystoria legis et prophetarum exterius” which “uelut rota uoluitur.”

    40This ambiguous mixture of rectilinear and circular is reflected in the diagram below the “dissemination of the word of God” figure (no. 71). This is a representation of arc of the sun’s journey across the sky at the solstices and equinoxes from an earthly observer’s perspective. East is at the top of the diagram, and Earth itself is a rectangle (“Mundus”) positioned on the horizontal diameter, but set off to the left. The circles on the east and west sides of earth’s frame represent the rising and setting points of the sun on (left to right) the summer solstice, the equinoxes, and the winter solstice. The arcs show the sun’s path on these days: rising and setting to the south of the equator at the winter solstice, on the equator at the equinoxes, and to the north on the summer solstice. Hence the winter solstice arc is small (to represent the short period of daylight) and the summer solstice arc the largest.

    41This is one of two ways of representing the solstices and equinoxes, the second being a schema of concentric circles, with a circular earth in the centre71. Two of our comparanda contain the Madrid version (D fol. 74r; P1 fol. 35r) while P2 fol. 9r contains the concentric schema with a circular earth. That the compiler of Madrid chose the square-earth version may not be accidental, as it echoes the square earth of the diagram above it.

    42The following page also presents two parallel diagrams, both rotae and both featuring the zodiac (Fig. 1.6). At the top of the page (no. 72) is a classic rota showing the concentric spheres of the planets and on the outermost sphere, the Zodiac. The rota in divided into twelve segments, one for each sign of the zodiac. The seven planets revolve around a central earth, staggered so that the Moon is in Cancer, Mercury in Virgo and Gemini, Venus in Libra and Taurus, Sun in Leo, Maris in Aries and Scorpio, Jupiter in Pisces and Sagittarius and Saturn in Aquarius and Capricorn. This makes a radiating pattern, with Saturn’s two signs adjacent, Jupiter’s separated by two signs, Mars’ by four, the Sun with only one sign, Venus’ signs separated by four, Mercury’s by two and the Moon with only one sign. This diagram ultimately originates in Macrobius’s Commentarium in Somnium Scipionis 1.31.3-7 and 24-27, and can either “stack” the names of the planets one atop another, or distribute them, as in the Madrid manuscript. The distributed form is closer to Macrobius’ text, which assigns the planets to the zodiac signs or houses in which they were located at the creation of the world72.

    43The rota beneath (no. 73) also concerns another sort of birth, namely the times of the rising of each sign of the zodiac. This is an unusual case of a text-diagram mixture. Together, they constitute an argumentum. If you wish to know what zodiac sign will be rising at any given hour, divide the number of hours that have passed from 1 October to the current hour of the current day by 24, and look up the remainder in the rota below. The rota is divided into twelve segments, each with the remainder from the above calculation and the resulting sign, e.g. “Si I aut II remanserint. oritur Libra.” This configuration is found in L fol. 45v, P1 fol. 53v, and P3 fol. 13r.

    44The presence of these two diagrams hints at a certain interest in astrology, notably the natal “houses” of the planets, and the ascension of the zodiac signs. As David Juste has shown, the roots of medieval western astrology reach well back into the Carolingian period73. But this is all we hear on the subject in the Madrid manuscript – P1 contains much more.

    45The configuration of vertically stacked rotae on fol. 93r is echoed on fol. 93v (Fig. 1.7), and the subject of no. 74 corresponds to no. 73. This rota shows the position of other zodiac signs in relation to the sign that is currently rising, e.g. “Aries oriente II horis occidit libra et centrum superioris zodiaci tunc Capricorum inferioris optinet Cancrum.”

    46The lower rota on the same page (no. 75), deals with a totally different matter, though one which relates to no. 76 on the facing page. This is a diagram which A and other Abbonian manuscripts call “de recursu concurrentium” or the “recurrence of the concurrents”. The rota is divided into 28 segments, marked with the concurrents through the solar cycle (leap years indicated above by a “B<issextus>”) and the number of years in the future when the same concurrents will recur below. The concurrent is a number representing the weekday of 24 March, which is used as a marker to calculate the weekday of any calendar date in that year. Since the solar year of 365 days is equal to 52 weeks plus one day, the concurrent advances by one each year; however, in leap years it will advance by two. Thus, the entire cycle will play out in 28 years, which is the product of the seven days of the week and the four years of the leap year cycle. In ch. 53 of De temporum ratione, Bede points out an interesting fact:

    The course of their cycle is such that whatever the concurrents are in leap year, they are the same five years earlier and six years later. Whatever they are in the first year after the leap year, they will be the same as those which occurred eleven years before, and those which will recur in six years. Those for the second year after the leap year are the same as those which occurred six years previously, and which will recur after eleven years. Those in the third year after leap year are the same as those which took place six years before, and which will revert after five years. And the regular pattern of this division applies to all the days of the revolving year74.

    A few pages later, in ch. 55, he elaborates this pattern:

    … every computist should remember that the same solar concurrents will follow in 30 years as will come in next year, and in 60 years from now as will come in four years, and in 120 years from now as will come in eight years, and in 150 years from now as in ten tears, and in the others in like manner. And if you want to know the concurrent for a year occurring at any interval, find out how many times 30 goes into that number [of years] and with this 30th part doubled, you will know the harmony of the revolving years. For instance, 10 times 30 is 300, and hence the same number of concurrents occur in 300 years from now as will occur 20 years from now. If there is a remainder, add it in. In a similar manner, the order of the concurrents can be projected into the past75.

    47The text which accompanies this rota in Madrid, and also in L fols. 26v-27r and P3 fols. 51v-53r (but not in A fol. 35v) frankly admits that this information is of no computistical use whatsoever, though is it an intriguing mental exercise:

    (Haec \scilicet inferioris/ figura ut uidetur mihi potius causa exercicii quam alicuius est reperta commodi. Nunc et plurimum obscuritatis et parum meo [meo] iudicio continet utillitatis. Hoc scilicet solummodo. ut nouerit calculator post aliquot a presenti annos que sunt future concurrentes. This diagram [that is, the one below] seems to me to be more for the sake of [mental] exercise than for finding anything of advantage. In my opinion, it contains a lot of that is obscure and very little that is of use, except for the calculator to learn what number of years in the future will have the same concurrent as the present year.)

    48That such a diagram would be included in this manuscript speaks to the fact that “mental exercise” involving “obscurity” was considered equally appropriate to the study of computus as practical advantage or usefulness. It aligns this diagram not only with the riddles, secret alphabets, games and other “mental exercises” found in science albums, but also with Abbo of Fleury’s exceptionally intricate and challenging Ephemerida – a suite of computus tables hidden inside a poem, and which can only be untangled by a “studiosus lector76”. Like this diagram, the Ephemerida is splendidly useless; everything in it can be found in a more simple and transparent form elsewhere, even within Abbo’s manuscripts. The point, however, is not accurate reference or novel information, but the intellectual and psychological effort expended on understanding the poem. Studying computus thus becomes equivalent to meditating on an obscure passage of scripture for the sake of devotion.

    49The final double-page opening of the portfolio (Fig. 1.8) of diagrams once again offers a visual symmetry, this time between two large rotae both of which have smaller circular appendices. The text on fols. 94r-v announces the figure on fol. 94v (no. 77) as an illustration of the “harmony” (concordia) of the moon and the ocean, a title borrowed from Bede’s De temporum ratione ch. 29, which it summarizes (“ut beda docet”). Bede’s innovative analysis of the relationship between the synodic lunar month and the pattern of spring and neap tides divided the month into four quarters: two straddling the peak of the spring tides (ledones) and two spanning the neap tides (malinae). The initial points of these four periods are signaled in the four small roundels budding off the main rota. The days of the lunar month are inscribed in the outermost ring, the word AQ<VA> on the middle ring, and the seven days of each ledo and malina occupy the third ring. This information could be displayed in a number of ways: as a rectangular table, or as a simple rota with the three rings. Abbo of Fleury, however, included an elaborated Carolingian version of the tidal rota in his portfolio (A fol. 35v), and it is this design which is replicated in the Madrid manuscript77. Madrid’s text is also very close to that in A. This rota sets the tides in a cosmic context by embedding an OT map with the three continents in the hub, surrounding it with a wind-rose in which the cardinal winds are highlighted to form a cross. In the Madrid manuscript, the wedges for these cardinal winds are coloured a deep green, which accentuates the cross but obscures the inscriptions. In effect, the tidal rota proper takes the place of the circumambient Ocean in the OT map, surrounding the oekumene. But it also makes a visible link between the globe of the earth and the celestial orbits of the heavens. All four cosmic elements – earth, air (the winds), water (the oceans) and fire (the planets) are “harmonized” in this diagram, as in the syzygia.

    50Facing this is a semi-circular “sundial” type horologium with an upper half added to form a rota with two smaller rotae attached to its upper rim (no. 78). These smaller rotae show (left) the length of moonlight for each day of the month and (right) the overlap of the solar months and the zodiac signs. This configuration – including the particular patterns on decorative segmenting in the smaller rotae – dates from the Carolingian period, but it was incorporated by Abbo into his dossier (A fol. 38v) and thence into other manuscripts inspired by it (L fols. 48v-49r; P3 fol. 17r)78. Explanatory texts for these three (no. 79) are found on fol. 95v. The entire suite closes with some short tracts addressing the themes illustrated in the diagrams: no. 80 deals with the divisions of the solar year; no. 81 with the movement of the sun and moon through the zodiac, and no. 82 with the visibility of the moon over the synodic lunar month.

    The macroscopic view of Madrid Mss/9605

    The computistical bridge (fols. 97r-103v)

    51Following the portfolio of diagrams in Madrid Mss/9605 is a group of texts which bridges the cosmographical and computistical themes of the portfolio to the next topic, chronology and history. This bridge is marked by the elaborately decorated initial of its first text, a didactic dialogue on the divisions of time, the parts of the body, and so forth (no. 83): “Apud grecos uero ab hornatu appellatur mundus cosmos…”. The two texts which follow are also found in a sequence with “Apud grecos” in L and P: a tract on the Jewish feasts of the Old Testament (no. 84), and an incomplete version of a treatise on the divisions of time (no. 85). A suite of computistical argumenta comes next (nos. 86-100), ending with an extract from Helperic on the origin of the epacts amongst the Egyptians (no. 101), and a suite of notes and argumenta on the reckoning of Easter and its dependent feasts (no. 102).

    52The Old Testament feasts and the historical note on the epacts hint at a shift in the direction of this material towards historical time. This impression grows stronger with the tract on the wonders of the ancient world (no. 103) and the eight signs of the impending Last Judgement (no. 104). A tract on the beginning of the year amongst various ancient peoples leads the reader into the next section of the manuscript, on chronology.

    The chronological materials (fols. 104r-117v)

    53The chronological finale of Madrid Mss/9605 opens with a spectacularly graphic representation of world history, the Chronicon of Claudius of Turin (d. ca. 827). Claudius was a Spaniard who made Lyon his home, and later was attached to the court of Louis the Pious when he was King of Aquitaine. He became bishop of Turin in 816, and though later accused of heresy for his views on religious images, seems to have retained his reputation as a scholar.

    54The Chronicle is in two parts. The second (which Michael Allen calls the “reckoning section” – fols. 113r-116r in Mss/9605) is a survey of the Six World Ages as presented in Bede’s De temporum ratione. Rather than attending to historical events, it is entirely oriented towards establishing chronology. The first or “display section” (fols. 104r-112r) “consists of a series of recto-verso openings used as frames for a left-to-right progression of inscribed genealogical roundels accompanied by discursive exposition.” The whole is prefaced by a letter-preface to the priest Ado79.

    55The Madrid manuscript is one of three witnesses to this work. Paris BnF Latin 5001 fols. 1r-8v (eastern France, s. IX) contains only the reckoning section, but Monza, Biblioteca capitolare c-9/69 fols. 19r-86v, has both, and “shares the relatively large physical size and the effort to safeguard layout of the Monza codex80”. It is interesting to note that in Monza, Claudius’ Chronicon has been absorbed as “liber tertius” of a multi-part compilation of didactic materials from the writings of Isidore of Seville, but also incorporating computistical, astronomical and chronological materials81”.

    56Madrid Mss/9605 contains the whole Chronicon as a self-standing work, but separates it into two parts (fols. 103r-111r and 112r-116v) articulated by rubrics which are peculiar to this Ms: “Explicit prima aedicio Claudii de sex aetatibus” (fol. 111v) and “Claudius iterum Adoni presbitero sermonem dirigit in Christo (fol. 112r).” Between the two is a tract on the calendar date of Christ’s Passion (no. 109). This addition is pertinent to both Claudius’ work, and the debates over computus at the time Madrid Mss/9605 was written. Claudius is quite dependent on Bede, using his revised annus mundi chronology and quoting him frequently. However, on one issue he departs from Bede. Claudius concludes that not only the creation of Adam, but also the Passion occurred on 23 March82. Bede pointedly refused to commit himself on the date of the historic Passion (cf. De temporum ratione ch. 47 and 62)83, because he was well aware that no annus Domini within the years of Christ’s mission could produce a Friday luna 14 on that date. Abbo of Fleury and a number of other “reform computists” of the 10th and 11th centuries set out to rectify Dionysius’ chronology84.

    57The striking mise en page of the “display section” of Claudius’ Chronicon was deeply appreciated by the designers of Madrid Mss/9605, who took considerable care in presenting the double-page openings with their intricately branching genealogies85. Within the overall “ecosystem” of Madrid Mss/9605, this “display section” is also of interest because, like the cosmological-computistical portfolio, it is dominated by circular forms. The world ages and the names of the patriarchs and kings in the genealogies of Old Testament history are enclosed in roundels that are arrayed across the pages as horizontal, vertical and diagonal chains, sometimes interlocking. The motif of the interlocking chain of roundels is also displayed in the list of the embolisms at the foot of the litterae punctatae table in the portfolio (no. 69). Circles visually link chronology to computus and cosmology as a single expression of the unity of creation with salvation-history and the rites of the Church. Like computus, world-history in the Middle Ages developed its own ingenious graphic devices to enable sequential and referential reading; a comparative study of these two types of devices is an important desideratum86.

    58Madrid Mss/9605 closes with two summary chronologies of the Six World Ages. Both the first – here mis-ascribed once again to Julian of Toledo (no. 111) – and the second, a paraphrase of Isidore of Seville’s Etymologiae 5.29-1-25 (no. 112), are combinations of discursive texts and tabular lists. The latter omits the Sixth Age, and replaces it with Arnulf’s summary, discussed above. It ends, however, with Isidore’s comment that “residuum sextae aetatis tempus Deo soli cognitum est” – a fitting explicit for this ambitious album of time-reckoning and the cosmos.

    Conclusion

    59Madrid Mss/9605 is in every respect a typical “science album”. Upon a scaffolding of computus, it hangs an array of materials on cosmology and history, and orders the elements of the compilation to create a meaningful sequence of topics, even in the absence of the explicit signposts one would find in a discursive text. Without such a signposting structure, the reader is left to discover the contents of the album page by page, beginning at the beginning. I have endeavored to replicate that diachronic experience of the book here, in order to show how the portfolio of diagrams – undoubtedly the most significant part of the volume from the point of view of illustration – fits into this unfolding narration. For the medieval reader, after all, the portfolio of diagrams was inseparable from the computus tables and texts which precede it, and the Chronicon of Claudius of Turin which follows. They all referred to a single domain of erudition, an encyclopedia of science parallel to and linked into the study of Scripture, as envisioned by Bede87; they all required a particular kind of mental skill, an ability to navigate within non-syntactic webs of words, numbers and geometric shapes, as well as the ability to read prose and poetry, and the reckon with numbers.

    60At the same time, Madrid Mss/9605 is unique. Its configuration of contents is not replicated in any other manuscript, though parts of it can be found in sections of the volumes we have chosen as comparanda. Its compiler made deliberate choices within a vast treasury of texts, tables and images, and positioned each element intentionally. So did the compilers of Dijon (Bibliothèque municipale, Ms 448), of Berlin (Staatsbibliothek Preussicher Kulturbesitz, Ms Phillipps 1833), or of London (British Library, Ms Sloane 263), but not in the same way. As we continue to unpack the riches of science albums of the 11th century, we will surely learn more about the local teaching traditions and intellectual interests that guided these choices.

    Appendix: Summary of Contents of Madrid, Mss/9605

    61Key to comparanda:

    • (A) Berlin, Staatsbibliothek Preussicher Kulturbesitz, Ms Phillipps 1833 (132)
    • (D) Dijon, Bibliothèque municipale, Ms 448
    • (L) London, British Library, Ms Sloane 263
    • (P1) Paris, Bibliothèque nationale de France, MS Latin 7299A
    • (P2) Paris, Bibliothèque nationale de France, MS Latin 7361 pt. 1 (fols. 1-56v)
    • (P3) Paris, Bibliothèque nationale de France, MS Latin 7419
    • (P4) Paris, Bibliothèque nationale de France, MS Latin 12117
    • (V1) Vatican City, Biblioteca Apostolica Vaticana, MS Reg. lat. 309, pt. 2 (fols. 121-156)
    • (V2) Vatican City. Biblioteca Apostolica Vaticana, MS Reg. lat. 1263
    • (V3) Vatican City. Biblioteca Apostolica Vaticana, MS Rossi 247
    ref. no.fol.Contents
    1irVolume title (s. XII ex or XII in.): liber compotus
    ivblank
    21ra-10vaHelperic of Granval, De computo. (rubric) Incipit prephatio in libro Helperici doctoris. (text) Domino patri sanctissimo nomine quidem aspro… The annus praesens in ch. 23 (fol. 6rb) is 903. Includes both prefaces.
    Cambis 1770, p. 591-596. Cordoliani 1955, p. 437-439. Clavis scriptorum 2010, p. 426. Not included in the list of manuscripts in Traube 1909-1920, v. 3, p. 128-153.
    Comparanda: D fols. 94r-107v; L fols. 1r-13v; P2 fols. 9v-38v; P3 fols. 20r-31r.
    310va-11vbText on weights and measures. (rubric) De mensuris et ponderibus. (text) Mensura est iuxta hysidorum. quicquid pondere capacitate… Due leuue siue miliarii tres. apud germanos unam restam efficiunt. (rubric) De ponderibus. (text) Ponderum pars minima calculus est… Libre maximum talentum est. (rubic) De mensuris in liquidis. (text) Mensurarum in liquidis coclear est… Duo chori: chulleum. quod sunt modia L.
    Cambis 1770, p. 596-599. Cordoliani 1955, p. 438-439.
    411vbRubric for a text on weather prognostication. (rubric) De presagiis tempestatum. Praesagia solis.
    Cambis 1770, p. 599.
    512rText and circular graph showing apogees of planets and the signs of the zodiac in which they occur. (rubric) De absidibus earum. (text) Absida grecum est. quod est latine circulus… ut subjecta figura demonstrat. The source of the information is Pliny, 2.13.61-65: see King 1969, p. 113. Cambis 1770, p. 599. Cordoliani 1955, p. 438-439.
    Bibliography: Eastwood 1988, p. 265-280, with illustrations of fols. 12r-v on p. 277-278. See also Eastwood 1987, p. 141-172 esp. p. 155 and Eastwood 2007, ch. 3 and p. 357-358.
    612v(top) Rectangular diagram showing planetary latitudes, as described in Pliny Historia naturalis 2.13.66-67. Discussed by Eastwood (see above)
    Comparanda: A fol. 38r (Abbo Floriacensis 2019, p. 59).
    712v(bottom) Table correlating day of lunar month to position of moon in zodiac.
    Cordoliani 1955, p. 438-439. Illustrated in Eastwood 1988, p. 278.
    Comparanda: P1 fol. 49r; P4 fol. 161v; V3 fol. 28r.
    813r(top) Unusual rota divided into twelve wedges like a wind-diagram, and containing texts indicating the geographic direction of sunrise (sometimes expressed as the direction of the wind) in each month and the legth of daylight, e.g. “Aprili mense oritur solis in partibus meridie. currit horas XII. Mai mense oritur sol ad eurum. currit horas XIII…”
    913r(bottom) Rota divided into twelve wedges, inscribed with names of the twelve winds; cardinal directions on outer rim.
    Not one of the types described by Obrist 1997, p. 33-84.
    1013r-vText on twelve winds, with etymologies of their names (text) Subsolanus uentus orientis contrarius fauonio. Ideo dictus quod sub sole oriatur. Vulturnus uentus contrarius affrico. a dextera parte subsolani. Ideo nominatus eo quod in alter perflando habeat potestatem quasi uultur in alto uolans…
    Not listed by Obrist, “Wind Diagrams.”.
    1113vaText on solstices (the old Roman ones, i.e. 25 December and 24 June) and their religious significance. (rubric) Incipit argumentum solsticiale. (text) Primum solsticium est VIII kl. ianuarii qua dies natus est dominus ihesus christi… Quia sic baptizatus est VIII idus ianuarii II feria et passus est ut superius diximus VIII kl. aprilis.
    Cambis 1770, p. 599-600. Cordoliani 1955, p. 438-439.
    1213va-15raGelasian canon of authoritative Biblical and Patristic texts. (rubric) Incipit decretale aeditum ab urbe Roma de recipiendis siue non recipiendis auctoribus. (text) Post propheticas et euuangelicas atque apostolicas disciplinas… sub anathematis indissolubili uinculo. in aeternum confitemur esse damnata. Amen. Explicit.
    Cambis 1770, p. 600-603. Cordoliani 1955, p. 439.
    Cf. edition by Dobschütz 1912.
    1315ra-bQuestion concerning the resurrection of the dead at the time of Christ’s resurrection; contains references to Rufinus of Aquileia and to Jerome… (text) Plures reor esse annos quod iugiter querebatis quod sancta scriptura de eis qui cum Christo resurrexerunt dicat. An ipsum habuerint pro futura resurrectione. et celos ascenderint. an quomodo?… Illam sine dubio ingressi fuissent ciuitatem celeste.
    Cambis 1770, p. 603.
    1415vBlank, but at the bottom is a Greek alphabet with the names of the letters and their numerical values. See next item.
    Cambis 1770, p. 603, who refers to this as “Algèbre numérale ou vulgaire.”
    1516rTable of concurrents (Tabula Dionysii) through 532-year great Paschal cycle, customized for cycle beginning with 1064. Years numbered in Greek notation. Beginning of indictions flagged in green, leap years with red colon. Columns on left indicate dates of termini on the five moveable feasts. Epacts are listed on bottom row. NB no Paschal key letters as found in Abbonian Mss like A fol. 54v (Abbo Floriacensis 2019, p. 123), P4 fol. 172v and V1 fol. 153r.
    Cordoliani 1955, p. 439-440.
    Cf. edition in Migne 1850, p. 735-736.
    Comparanda: D fol. 82r; L fols. 42v-43r; P2 fol. 8v; V2 fol. 86v.
    1616vFour texts, all in left hand side of the page:
    (1) Turbabuntur a facie eius patres orphanorum et iudices uiduarum; hoc est scribae et pharisei quibus ab ipsu domino dictum est. Vae uobis pharisei hypocritae: qui comeditis qui comeditis domos uiduarum longa oratione orantes.
    (2) Dixit dominus ex basan conuertam. conuertam in profundum maris. Basan interpretatur pinguis siue confusio… Pes domini tinctus est sanguine. quia corpus quod assumere dignatus est: per crucem et passionem ab impiis cruentatum est.
    (3) Et meditatus sum nocte cum corde meo. exercitabr et scobebam spiritum meum. Pre ecercitatione: septuaginta decantationem uel meditationem transtulerunt… a sarculo demonstrauit.
    (4) Quia comederit iacob. Iacob secundum litteram populum iudeorum dicit agentibus consumptum. Secundum anagogen uero populum fidelium ab impiis in persecutione deuoratum.
    Cordoliani 1955, p. 440.
    1717raQuatrains on the 12 months of the year, acephalous (missing leaves?). (text)
    <AUG> Latona genitum quem prehibent echatem.
    SEP Surgentes acinos uarias et persecat uuas…
    Cambis 1770, p. 603.
    1817ra(rubric) Versus Bede Presbyteri de XII Mensibus. (text)
    Martius octimber maius quoque iulius atque…
    Romano ianus iulum september habebit.
    Cordoliani 1955, p. 440.
    Comparanda: L fol. 21v; P3 fol. 55v.
    1917r-bMnemonic poem on the monthly solar regulars for each month of the year. (rubric) Item uersus de regularibus XII mensium. (Text)
    Ianus et octimber binis regulantur habenis…
    His regularibus ostenduntur rite kalende.
    Cordoliani 1955, p. 440-441.
    Bibliography: Schaller and Könsgen 1977, no. 9786.
    Comparanda: S fol. 21v; P3 fol. 1r; P4 fol. 55v.
    2017rbMnemonic poem on monthly lunar regulars. (rubric) Versus de regularibus ad lunam inueniendam. (text)
    September semper ter quinis atque octimber habenis…
    Altiuago rutilans transcurrit culmine caeli.
    Cordoliani 1955, p. 441
    Schaller and Könsgen 1977, no. 14907; Walther 1963; no. 17542.
    Cf. edition by Van Wijk 1936, p. 119-120.
    Comparanda: P3 fol. 55v; P4 fol. 117r.
    2117rbMnemonic poem for monthly solar regulars. (rubric) Versus de regularis ad kalendas inueniendas. (Text)
    Marcius ut proprias demonstret rite kalendas.
    Quinta de feria quinque sibi sociat…
    Februus inueniet senos at solis epactis.
    Sedes attribuit martius exoriens.
    Cordoliani 1955, p. 441.
    Schaller and Könsgen 1977, no. 9356.
    Comparanda: L fol. 21v; P3 fol. 55v.
    2217rbPoem on the Roman names for the weekdays. (rubric) Versus de septimane diebus. (Text)
    Prima dies phoebi sacrato lumine fulget…
    Emicat alma dies saturno septima summo.
    Cordoliani 1955, p. 441-442. Schaller and Könsgen 1977, no. 12488; Walther 1963, no. 14566.
    Cf. editions in Baehrens 1883, no. 58.6, p. 353-354 and Riese 1870, no. 488, p. 38.
    2317rbMnemonic on the annual lunar epact for each year of the 19-year cycle.
    (rubric) Item uersus eiusdem ad lunam inueniendam. (text)
    Nullae. undenae. uiesbinae.
    Ternae. quater denae. uicenae quinae…
    Vicenae senae. septus. decunae bisse.
    Cordoliani 1955, p. 442, who knows of no other example.
    2417rb-vaMnemonic poem modelled on “Nonae aprilis” (no. 26) indicating calendar terminus of Septuagesima for each year of the 19-year cycle, plus the key-number for locating the weekday of the terminus. (rubric) Argumentum sextuagesimale. (Text)
    Kalende februi: quinos exquirunt V…
    Idus februi: perfodiunt ternos. III.
    Cordoliani 1955, p. 442
    Schaller and Könsgen 1977, no. 8602; Walther 1963, no. 10035a.
    Comparanda: P3 fol. 56r.
    2517vaAnalogous mnemonic poem for Quadragesima. (rubric) Argumentum quadragesimale. (Text) Octauo martis: kalendae quinae. V…
    Pridie nonas martis. in ternas. III
    Cordoliani 1955, p. 442-443
    Schaller and Könsgen 1977, no. 11148;
    cf. edition by Dümmler 1884, p. 423; Strecker 1923, p. 671.
    Comparanda: P3 fols. 56r-v.
    2617va-bMnemonic poem indicating calendar terminus of Easter for each year of the 19-year cycle, plus the key-number for locating the weekday of the terminus. No rubric. Text:
    None aprilis. norunt quinos. V…
    Quindene constant: tribus adeptis. III
    Cordoliani 1955, p. 443
    Schaller and Könsgen 1977; no. 10525.
    Cf. edition by Strecker 1923, p. 670-671.
    Comparanda: P3 fol. 56v.
    2717vb-18raVerse mnemonic for basic computus data. (text)
    Annus solis continetur. quattuor temporibus
    Ac deinde ad impletur duodenis mensibus…
    Quorum nobis non est nota numeri peritia
    Altum caelum qui creauit terras atque aequora.
    Doxa regum per aeterna deo soli secula. Amen.
    Cordoliani 1955, p. 433.
    Schaller and Könsgen 1977, no. 853; Walther 1963, no. 1271.
    Cf. edition by Strecker 1923, p. 682.
    Comparanda: D fol. 194r; L fols. 21v-22v; P2 fols. 4v-5v; P3 fols. 54v-55r
    2818raMnemonic poem for the contents of the eight columns of the Paschal table. (text)
    Linea Christe tuos primae quae continet annos…
    Aetatem lunae monstrat nouissimus ordo.
    Cordoliani 1955, p. 444-445.
    Schaller and Könsgen 1977, no. 8931; Walther 1963, no. 10329.
    Cf. edition by Henel (Heinrich), Studien zum altenglischen Computus, Leipzig: Tauschnitz (Beiträge zur englischen Philologie 26), 1934, p. 9, n. 26.
    Comparanda: P2 fol. 6r.
    2918ra-bPoem on the signs of the zodiac.
    (rubric) Versus de duodecim signis. (Text)
    Primus adest aries obscuros lumine lambens…
    Ex in squamiferi. serpentes ludere pisces.
    Cordoliani 1955, p. 445.
    Schaller and Könsgen 1977, no. 12525.
    Cf. edition by Strecker 1923, p. 698.
    3018rbAusonius Ecloga 16 on the signs of the zodiac. (rubric) Item uersus de duodecim signis. (Text).
    Respice apriles aries frixee kalendas…
    Procedunt duplices in martia tempora pisces.
    Cordoliani 1955, p. 445.
    Cf. edition by Sextus Prete 1978, p. 108-109.
    3118rbPoem on the winds. (Text)
    Quatuor a quadro consurgunt limite uenti…
    Argenstenque grai uocant cognomine dictum.
    Schaller and Könsgen 1977, no. 13113; Walther 1963, no. 15281.
    Cf. edition in Meyer (Heinrich), Anthologia veterum Latinorum epigrammatum et poematum, Leipzig, 1835, 2, no. 1056; Riese 1870, p. 323.
    3218vaPoem by Ausonius on lucky and unlucky days. (Text)
    Est et non cuncta monosillaba nota frequentatur…
    Qualis uita hominum duo quam monosillaba uersant.
    Schaller and Könsgen 1977, no. 4582.
    Cf. edition by Schenkl 1883, p. 150-152.
    3319rTabular summary of computus data commonly known as Ratio calculi or Computus grecorum siue latinorum. The material is laid out in three columns, framed with elaborately decorated architectural columns: 1) divisions of Roman months with number of dats; (2) solar regulars; (3) lunar regulars; (4) sequence of leap years; (4) epacts (n.b. not as described in Cordoliani 1955, p. 447).
    (rubric) In nomine sanctae et indiuiduae trinitatis incipit conputatio Grecorum siue Latinorum. que a CCC decem et octo episcopis in Nicea ciuitate Bithiniae est aedita.
    Comparanda: see no. 34
    3419vA series of 11 pages all laid out in a uniform format of elaborately decorated architectural arcades, as a sort of continuation of the Ratio calculi.
    (1) The first column contains a running count of the number of days in the year: e.g. Ianuarius in Kl. .I. in non. .V. in idus .XIII. Februarius in kl. XXXII in non XXXVI….
    (2) the second column list the sequence of common and embolismic years in the ogdoad and hendencad, followed by a rather curious list of the epacts, beginning with 8, 19, 30 rather than 9, 20, 1…
    (3a) dates of termini for Septuagesima, Quadragesima, Easter, Rogations and Pentecost.
    (3b) Regulares et loquela digitorum – recte the claves terminorum (Cordoliani 1955, p. 447-448, n. 48).
    Comparanda: D fols. 2-28 and 62r-v; L fols. 29r-34r; P3 fols. 41v-47r.
    20rFrom left to right: (1) terminus of Septuagesima with regular
    (2) terminus of Quadragesima with regular
    (3) date of Paschal new moon
    Cambis 1770, p. 603-606.
    Cordoliani 1955, p. 448.
    20v(1) Paschal terminus with regular
    (2) terminus of Rogations with regular
    (3) terminus of Pentecost with regular.
    21r(1) (rubric) De termino Paschali. (text) Nonae aprilis norunt quinos… (see above no. 26)
    (2) list of the special regulars for the Paschal terminus, with two explanatory texts:
    Quisquis per hos uersiculos feriam termini paschalis nosse nititur… tota teria incunctanter in ipso termino inueniet.
    Si autem uis scire de regularibus ipsius cicle unde procedant… in quo idem euenerit terminus.
    (3) (rubric) Incipiunt aepactae id est adiectiones lunares. (Text) In primo decennouenali cicle VIII ponis. Post addas XI fiunt XVIIII. Addas XI fiunt XXX… (cf. Cordoliani 1955, p. 448 and note 51)
    Iam hic non addas XI sed XII fiunt simul XXXVIII. deduc XXX remanent VIII quos habet in capite et sic redis ad caput.
    21v-22rmultiplication tables for 4 through 9: the multiplicands are 1-9, 20-100, 200-1000.
    Cordoliani 1955, p. 448.
    Comparanda: D fols. 62r-v; L fols. 31r-34r.
    22v-23rmultiplication tables for 10-13m 15, 19.
    23v-24rmultiplication tables for 28, 30, 59 and 60, and on fols. 24r, 30 and 60 are repeated, with the last column blank.
    24vwords for numbers in Hebrew, Syriac and Egyptian.
    Cordoliani 1955, p. 448.
    3525rSuite of argumenta based on annus praesens of 1026, beginning with an unusual feria table for 532-year great Paschal cycle. (rubric left) Hae sunt ferie septimanarum annum deducentium secundum solis cursum. (rubric right) Haec item ratio decemnouenalis lunaris.
    The left column of the table shows the solar regulars and leap years for 19 years, beginning in a year which is a leap year with concurrent 4, i.e. the first year of the 532 years cycle.
    Text in middle column:
    Haec ratio solaris septimanaria quae per ferias ducens annum distinguitur usque ad XXVIII annos accedit… Sic usque in finem consumatur.
    Cordoliani 1955, p. 448.
    25rcolumn 2: (1) formula for finding annus mundi with annus praesens AM 4978, i.e. AD 1026. (rubric) Argumentum ad annum mundi inueniendum. (text) Si scire cupis annos ab initio mundi multiplica CCC XXX III quindecies… et hoc ordine deinceps seruato annos mundi sine errore reperies.
    (2) formula for finding indiction using annus mundi. (rubric) Ad indictionem. (text) Si uis scire quota sit indictio tene annos ab initio mundi… Si nichil remanserit XV erit.
    (3 columns 2-3) formula for finding the year within the 19-year cycle (i.e. Golden Number) and lunar cycle using annus mundi. (rubric) Ad ciclum decemnouenalem inueniendum. Si uis scire quotus sit ciclus decem nouenalis summe annos ab origine mundi… Si nichil remanserit XVIIII erit.
    Cordoliani 1955, p. 449, who remarks on the unusual character of this material.
    25r-25vcolumn 3: Formulae for epacts and concurrents. (Rubric) Ad epactam. (Text)
    Si nosse uis *notas* epactae collige annos ab exordio mundi et de his subtrahe III… Si concurentes inuenire cupis sume annos ab origine mundi quot fuerint. et eorum quartam partem semper adice. Ex his subtrahe I. …
    Si uis scire qualiter possum quotum in manu tua uel in mente tua compotum tenes… Sic semper in infinitum crescit an minuitur.
    Si uolueris in C annos seu amplius aut infra inuenire concurrentes. tene secundam iuncturam ubi illo anno in quo concurrentes habes …
    Cordoliani 1955, p. 449.
    25vColumns 1-: Argumentum for finding Paschal termini using a hand-mnemonic. (text) Si uis inuenire terminos paschales. uel etiam aepactas lunare tene memoriter quot aepactas habes in anno quo stas… Sed innumera huiuscemodi disciplinae sicut et ceterarum artium melius uiue uocis alloquio. quam stili signatis traduntur officia.
    Cordoliani 1955, p. 449.
    See similar argumentum on fol. 26r.
    Column 2. (1) Another formula for finding the annus mundi. (rubric) Secundum Hebreos. (text) Multiplica per XV CCCXXXIII fiunt IIII DCCC LXV. adde regulares IIII et indictionem presentis anni. idem VIIII fiunt IIII DCCCC LXXVIII. Istis anni ab initio mundi.
    (2) To find the position of the year within the 532-year cycle, using AD. (text) Si quis ciclum anni magni nosse desiderat. qui habet annos Dtos XXXa IIos. Sumat annos dominice incarnationis… quo uero remanserint tot sciat esse annos cicli magni. (3) To find year of solar cycle with annus praesens of 1026. (rubric) Ad ciclum solarem. (text) Anni ab incarnatione domini nostri ihesu christi I XXVI. his adde VIIII… Talis est ciclus solaris id est XXVI.
    (3) To find position of year in leap-year cycle with annus presens of 1026 (rubric) Ad bissextum. (text) Reposita summa anni ab incarnatione domini I XX VI… Secundus annus est post bissextum.
    Cordoliani 1955, p. 449.
    Column 3. (1) Formula for indiction using annus praesens of 1026. (rubric) Ad indictionem. Reposita summ anni ab incarnatione domini I XXVI. Adde III fiunt I XXVIIII… Talis est indictio id est VIIII.
    (2) Formula for concurrent using annus praesens of 1026. (rubric) Reposita summa anni ab incarnatione domini I XXVI adde quartam partem… Quintus est concurrens.
    (3) Generic formula for finding the weekday. (rubric) Ad feriam. (text) His [concurrentibus] add II regulares ianuarii mensis… non adicias sed unum.
    25v-26rFormula for finding position of the year within the 19-year cycle, based on annus praesens of 1026. (rubric) Ad ciclum decem nouenalem. (text) Reposita summa anni ab incarnatione domini I XXVI adde I fiunt I XXVII… Quare unum regularem iubes addere? Responsio. Quia quando incarnatione christi facta est. annus unus precesserat de ciclo debem nouenali.
    26rColumn 1. (1) Formula for finding position of the year within the lunar cycle, based on annus praesens 1026. (rubric) Ad ciclum lunarem. (text) Resposita summa anni ab incarnatione domini I XXVI. Subtrahe II… Interrogatio. Quare IIos regulares iubet subtrahere? Responsio. Quia quando incarnatio est christus. duo anni restabant de ciclo lunari.
    (2) Formula for finding epact based on annus praesens of 1026. (rubric) Ad epactam. (text) Reposita summa anni ab incarnatione domini I XXVI. Decemnouem L. DCCCL. saperis LXXVI. Decemnouem … His adde VIII talis est epacta romanorum id est VIII.
    Column 2. (1) Formula for finding Paschal terminus, using hand-mnemonic. (rubric) Argumentum ad terminum paschalem inueniendum. (text) Si quis memoriter non potest tenere terminum paschalem… Et si unum scierit omnia argumenta per hos repperiet articulos nisi in anno ultimo. bis dic quindecim.
    (2) On the new moon. (rubric) De cursu uel interlunio lunae. (text) Die quo renouatur luna non dicitur prima. Nam ea die quo extinguitur renouatur. Ideo non dicitur prima. sed XXXa… dicitur.
    (3) On the new moon. (rubric) De eadem re. (text) Interlunium lunae est tempus illud inter deficientem et nascentem… recedendo uidetur.
    Cordoliani 1955, p. 450.
    Column 3. Despite the rubric this argumentum is not about the saltus at all, but about how to calculate the distance of the moon from the sun along the ecliptic. (rubric) De ratione saltus lunae quantum distat longius a sole. (text) Si scire cupis luna prima quantus partes distat a sole… iterum transiliatur sic.
    26r-vCalculating the time of the moon’s first visibility. (rubric) Argumentum qua hora uel quo puncto luna accendatur. (text) Si uis scire qua hora uel quo puncto accendatur luna. seu aetas ipsius lunae mutatur.. Si autem totum numerum per LX partitur fueris. in duodecima hora et in V puncto lunae aetas commutatur.
    26v(Col. 1) (rubric) De eadem re. (text) Multiplica et ciclum lunarem. sexies ut puta II fiunt XII. Adde et numerum qui remanseris de superiori diuisione. idem XXXI fiunt XLIII. Adde et unum regularem. quot LX dimiseris tot regulares. Hoc numerum diuide per XXX. remanent XIIII. finit luna XIIIIa in VIII hora et in primo puncto.
    (Col. 1-2) Formula for finding the zodiac sign of the moon’s first visibility. (rubric) Argumentum in quo signo luna accendatur uel moretur. (text) Si uis scire in quo signo uel in qua parte cuiuslibet signi luna uersetur uel accendatur… In XI parte aquarii est II luna.
    (Col. 3) Formula for hours of moonlight. (rubric) Argumentum quot horis luceat luna. (text) Si uis scire quot horis luceat luna in unaquaque nocte quota luna fuerit tot milia in calculo numerabis…computandi ratio.
    27rblank
    3727v-37vAbbo of Fleury’s astronomical Calendar (missing December, i.e. the middle bifolium of this gathering). Each month covers a double-page opening. On the left-hand page is the calendar proper, with martyrology (some entries are from a metrical martyrology). Cordoliani 1955, p. 453 notes that there are a number of saints “propres à l’Espagne” (Barcelona, Valencia, Cordoba) but also s. France (Lyon, Arles…). Cambis 1770, p. 607-609, notes against 26 April “Dedicatio Ecclesiae sancti Andree” as the dedication of church of St-André in Avignon; 17 June Translation of St Veredeme, bishop of Avignon; 2 September “Avenione sancti Agricoli episcopi”; 27 November St Siffren of Carpentras. The key-letters, reading right to left from the date-column, are (1) litterae punctatae, (2) the numbers 1-7 repeated (a form of “Dominical number”), (3) A-O lunar-zodiac letter series (cf. fol. 38r for corresponding table). Note that Abbo’s special suite of key-numbers for the 35 possible dates of Easter (as found in A fols. 23v-24v) are not included. There is the conventional etymological headnote (that for January partially transcribed by Cordoliani 1955, p. 451). At the foot of each page are the hours of day and night, and the relevant verse from two calender poems, both describing the presiding divinity or “genius” of each month: (1) Primas romanas ordiris iane kalendas (ascribed to Ausonius; cf. edition by Schenkl 1962) and (2) Dira patet iani Romanis ianua bellis (cf. edition by Baehrens 1883, no. 11); Riese 1870, 258 (no. 394).
    On the top of each right-hand page is a note on the Egyptian and Latin names of the month, the solar and lunar regulars, the number of days in the lunation of that month, and the zodiac sign in which the month. The relevant verses from “Respice Aprilis Ares frixae kalendas…” (see above, no. 30) are at the foot of the page from March onward; from January onwards, “Hic uersus omnis lunaris sit tibi abba” and “Graiorum noscis qui numerum in titulis.” Most of the page is taken up by Abbo’s table showing the age of the Moon on the kalends of the month through the 19-year cycle, expressed in Greek notation. At the foot of each table is a note the locations of the embolisms. A date key is in the left-hand margin. To the left of this is a column indicating the position of the moon in the zodiac.
    Cambis 1770, p. 606-610. Cordoliani 1955, p. 450-453 (reproduces March page in fig. 2).
    Comparanda: A fols. 23r-28v (Abbo Floriacensis 2019, p. 5-17); S fols. 34r-38r; P1 fols. 7v-19r; P3 fols. 2v-8v and 49v-41r; P4 fols. 149v-160r; V1 fols. 128v-140r (P1 and V1 with same headnotes for each month as Madrid Mss/9650).
    3838rPagina regularis for A-O lunar-zodiac letter series found in the calendar. (rubric) Cursus lunae per duodecim signa. At the foot of the page are two tables showing litterae punctatae for new and full moon in full and hollow months.
    Cambis 1770, p. 610-611. Cordoliani 1955, p. 454.
    cf.
    ed. in Migne 1850, p. 757-758.
    Comparanda: A fol. 31v (Abbo Floriacensis 2019, p. 29); P1 fol. 50r; P4 fols. 160v-161r.
    3938v(1) Extract from Bede, De temporum ratione c. 33 on the litterae punctatae table (cf. calendar and fol. 38r) (rubric) De cursu lunae si quis computare non potest. (text) Si quis adeo deses uel hebes est… provuidit antiquitas.
    (2) Text on embolisms. (rubric) De embolismis IIIbus. (text) Sunt autem anni tres circuli decemnouenalis in quibus idem argumentum lunae stabilitatem sui tenoris conseruare nequit…. Septima III no. mar. initium sumit.
    Cordoliani 1955, p. 454.
    4039r-41rLitterae punctatae tables, in their “deconstructed” version. Instead of a single table with columns for each year (as in no. 42 below), there is one table for each year of the 19-year cycle, with the three alphabets and the corresponding age of the moon in three columns.
    Cordoliani 1955, p. 454-455 (his explanation of this table is erroneous).
    Comparanda: P4 fols. 165r-166v; V1 fols. 145r-147r.
    4141vTop: lunar-zodiac table in “lattice” format (see no. 7 above).
    Bottom: Three lists: (1) “Epactae romanorum”: epacts of each year in 19-year cycle, with monthly epacts (beginning in January = 1) underneath. (2) “Epactae Egyptiorum”: with monthly epacts beginning in September. (3) “Item regulares Bedae”: Bede’s monthly regulars, beginning in January.
    Cordoliani 1955, p. 455.
    Comparanda: A fol. 39r (Abbo Floriacensis 2019, p. 63); P3 fol. 18v; V1 fol. 141r; V3 fol. 51v.
    4242rAbbonian A-V lunar letters table. Years of 19-year cycle in Greek notation.
    Cordoliani 1955, p. 455.
    Comparanda: A fol. 30v (Abbo Floriacensis 2019, p. 24-25); P1 fols. 5v-6r; P4 fol. 163v.
    4342vSynthetic litterae punctatae table. Numbers for days of lunation are in Greek numerals. “A”s are in red.
    Cf. ed. in Migne 1850, p. 755-756.
    Comparanda: A fol. 29r (Abbo Floriacensis 2019, p. 20-21); P1 fols. 6v-7r and 29r; P4 fol. 154v; V1 fol. 145r; V3 fol. 52r (letters highlighted to form cross).
    4443r-44vCalendar in twelve columns spread across four pages. Each month is separated from the next by an architectural column with decorated capital. Reading right to left: (1) Calendar dates, (2) Golden numbers, (3) AEIOV lunar letter sequence, (4) A-K lunar letter sequence, (5) Dominical letters, (6) litterae punctatae (7) A in every 8th space (i.e. Dominical letters), (8) A-O lunar-zodiac letter sequence for pagina regularis, (9) A-V lunar letter sequence.
    Cordoliani 1955, p. 455-456.
    Comparandum: P1 fols. 1r-3v.
    4545rSynthetic Litterae punctatae table of 30 columns and 19 x 2 rows (cf. n. 43, but re-reoriented 90 degrees). The first row for each year applies to the “full” lunar months of 30 days, the second to the “hollow” months of 29 days. Number key for years of 19-year cycle and days of lunation are in Greek notation. “A”s are in red. (text) (transcribed in Cordoliani 1955, p. 456): (1) Incipit ordo solaris anni cum litteris a sancto iheronimo super positis ad explorandam septimane diem et ad lune aetatem inuestigandam quottidie per XVIIII annos. (2) Me legat annales uult qui consocere causas. (3) Tempora qui uaria qui simul astra poli.
    Cordoliani 1955, p. 456 notes that text (1) usually accompanies the A-V series.
    Comparanda: A fol. 31r (Abbo Floriacensis 2019, p. 26-27); P1 fols. 6v-7r (separated into two tables, one for full and one for hollow lunations) and 50v (as in Madrid); P4 fol. 166v; V1 fol. 147v; V2 fol. 81v.
    4645vAbbonian Dominical letter tables of the type commonly called Ratio septizodii. The main table is in 7 columns for each weekday (starting with F VII, i.e. Saturday), and 28 rows for the years of the solar cycle. Leap-years are flagged. The lettering is in red, and the dominical letters are doubled in black for leap years. There is a reduced version of the table for 1 January. (text) Littere huius laterculi qui uocatur ratio septi zodii… per XXVIII annis reuoluitur.
    cf. ed. in Migne 1850, p. 819.
    Comparanda: A fol. 29r (Abbo Floriacensis 2019, p. 18-19) has the same rubric; but Madrid is missing A’s text; L fol 42r; P1 fols. 17v and 49v; P4 fol. 167v; V1 fols. 148v-149r; V2 fol. 81r; V3 fol. 30r.
    4746rAbbonian A-K lunar letter table with extended bottom margin showing the dates of the embolisms (see below no. 51). (rubric) Argumentum quota sit luna. On the right margin, the numbers 1-30 have been inscribed next to the rows, though the rows do not in fact represent a sequential list of the days of the lunation.
    Cordoliani 1955, p. 467.
    Comparanda: A fol. 32v (Abbo Floriacensis 2019, p. 32) with same rubric as in Madrid; S fol. 40r; P4 fols. 162v-163r; V3 fol. 49r.
    4846vCross-shaped Abbonian pagina regularis with names of zodiac signs in Greek. The wing extending from the upper margin, labelled “Cursus lune per XII signa”, shows the sequence of common and embolismic years through the 19-year cycle, with the years numbered in Greek notation. The lower wing indicates the litterae punctatae for new and full moons of full and hollow months through the 19-year cycle.
    Cordoliani 1955, p. 467.
    Comparanda: A fol. 31v (Abbo Floriacensis 2019, p. 29); S fol. 40v; V3 fol. 27r.
    4947rAbbonian AEIOV lunar letter table, with numbers in Greek notation. Embolisms are listed in lower wing.
    Cordoliani 1955, p. 457.
    Cf. Ed. in Migne 1850, p. 802.
    Comparanda: A fol. 34 (Abbo Floriacensis 2019, p. 37; doubled version); D fol. 84 (doubled, but not in Abbonian form); L37v; P1 fol. 16v; P4 fol. 162r (doubled); V1 fols. 141v-142r (doubled); V2 fol. 83v; V3 fols. 24v and 51r.
    5047vA-K lunar letter table laid out in 12 columns – i.e. a reduced version of the calendar, with the days numbered in Greek letters and the A-K sequence in red.
    Cordoliani 1955, p. 457.
    Comparanda: P1 fol. 48v; P3 fol. 19r; V1 fol. 148r; V2 fol. 91v.
    5148rA-K table (cf. no. 47), again with an “Abbonian” extension from the bottom of the table containing the embolisms on the bottom. Dates of lunar month on the left margin are in Greek notation.
    Cordoliani 1955, p. 457.
    Comparanda: A fols. 32r-v (Abbo Floriacensis 2019); S fol. 28r; P1 fol. 48r (non-Abbonian); V1 fols. 142v-143r; V2 fols. 82v-83r and 92v; V3 fol. 25r.
    5248v-49rThe table called Ludus compoti uenerabilis Bedae, which is a condensed calendar (cf. no. 44). Each month-column includes only the dates, the A-V lunar letters sequence, the As of the Dominical Letter sequence, and the A-O lunar-zodiac letter sequence. Each month heading contains (1) solar regular in Greek notation, (2) age of moon on kalends of year 1 in Greek notation, (3) lunar regular in Greek notation. (rubric) Incipit ludus compoti uenerabilis Bedae presbiteri.
    Cordoliani 1955, p. 457.
    Comparanda: A fol. 42v-43r (Abbo Floriacensis 2019, p. 80-81); variant versions in P4 fol. 168r; V1 fols. 149v-150r and V2 fol. 85r.
    5349v-50rA-0 lunar zodiac table merged with a concurrents table, for the great Paschal cycle 532-1063. Greek alphabet with Roman numerical values in upper margin. Zodiac signs in left margin. Year numbers are in Greek notation, as is the cumulative count of years of the cycle in the right margin. On the lower half of the page is a table showing the ages of the moon on 1 January, the epacts, years of the solar cycle, first visibility of first lunation of the year, termini of Quadragesima, Easter and Rogations.
    Cordoliani 1955, p. 458.
    Comparanda: P1 fol. 47r; P4 fols. 170r-171r (functions separated into two tables); V1 fols. 150v-152r; V2 fols. 92v-93r.
    50v-51rIdentical table for 1576-2127.
    51v-52rIdentical table, with years not filled in.
    52v-53rTable of similar format for 532-1063, but for concurrents (in Greek notation) and Dominical Letters. The supplementary table on the bottom shows the epacts, years of the lunar cycle, first visibility of first lunation of the year, terminus of Quadragesima, first visibility of Paschal moon, terminus of Easter, and terminus of Rogations.
    Cordoliani 1955, p. 458.
    Comparanda: D fol. 81v; P4 fols.168v-169r; fols. 170v-171r.
    5453v-54rTables to find the dates of the Paschal full moon and of Easter, with the age of the moon on Easter, using the Dominical letters. The suite consists of a table of seven columns labelled Feriae A, B etc., and 19 rows. The mis-ascription to Julian of Toledo in the rubric is not found in any other examples; the table is in fact Abbonian. (rubric) Ratio Paschalis probato a sanctissimo uiro domno Iuliano Toletanae sedis. metropolitano episcopo aedita.
    Cambis 1770, p. 611; Cordoliani 1955, p. 458.
    Comparanda: A fols. 40v-41r (Abbo Floriacensis 2019, p. 71-72); L fol. 43v; P4 fol. 172v; V1 fols. 154v-156v; V2 fols. 84v-85r.
    5554v-56vTables for 19 years of Paschal cycle and 7 days of Dominical letter cycle showing, in each cell, the dates of Quadragesima, Easter and Rogations and the age of the moon on Easter day. On fol. 56v right hand is the following text: Ab inicitio sunt anni usque ad partum uirginis quinque millia ducenti XC. ex his septem subtrahit per quindenos iam partiti. tres ex ipsis remanerit. (i.e. Christ was born in AM 5290; subtract 7 [5283] and divide by 15; three will remain). At the foot of each page are a verse from a poem on creation of Sun: (text) Fecit deus lumen uerum inter caelos medium prima hora sui cursu uenit ad mercurium. totum mundum clara luce erat magnum. gaudium – and a poem on creation of moon: (text) Fecit deus lumen magnum subtus caelos lunium. prima hora luce sua fuit quarta decima totam lux ipsa nocte nihil erant tenebrae. In addition, a formula for finding annus praesens from indiction. (text) Ordines indictionum diuide per quindecum. his autem regulare adice XIIIim presens anno apponatur ibidem indictio.
    Cordoliani 1955, p. 459.
    Comparanda: P4 fol. 173r; V2 fols. 87v-88v.
    5657ra-58vbCollection of computistical argumenta in verse, sometimes ascribed to Pacificus of Verona, for elements of computus, beginning with the contents of the columns of the Paschal table. Intermixed with notes in prose. (text) Anni domini notantur / in presenti linea / cum inserus mundo deus. / ad tollenda crimina / natus homo hic processit / notra ferens uiscera….
    Cambis 1770, p. 611-612; Cordoliani 1955, p. 459-469.
    Schaller and Könsgen 1977, no. 814
    Cf. editions by Robertini 1966, p. 33-65; Meersseman and Adda 1966, p. 138-144; Strecker 1923, p. 674-682 and MGH Poetae 8.1 (Addenda p. 207).
    Bibliography: Strecker 1911, p. 333.
    Comparanda: D fols. 188v-189v; P1 fols. 20-21; P3 fols. 52v-53v; P4 fols. 175v-176r; V3 fols. 6v-8r.
    5758vb-60vbArgumenta in prose of the Si uis scire… type. No rubrics until fol. 59vb.
    5861ra-72Argumenta and short computistical notes, including (fols. 69-70) a short summary of the Six World Ages (“Subputatio Eusebii Iheronimi”). Introduced by decorated 12-line interlace initial. This block of texts is found in other manuscripts with Breton, Irish and English affiliations: see Bisagni 2020 passim).
    (61ra-b) Argumenta qualiter termini inueniantur. De anno comuni et embolismo…
    (62ra) De epistolis grecorum. Legimus in epistolis grecorum…
    (70ra-71rb) Excerpta from Irish De divisionibus temporum at one point (69ra) containing glosses in Old Breton (Bisagni 2020 passim).
    Ratio qualiter secundum latinos uel grecos argumenta recto pascalia tramite inuenire debeas. Latinamque a III non. mar….
    Item quod uerius est. Sancta sinodus ubi CCCti X et VIII pontifices qui apud nicenam ciuitatem…
    Item de die mensis et lunae pascalis qualiter celebratur. Statutum…
    Bisagni 2019, p. 110. Cambis 1770, p. 611-613. Cordoliani 1955, p. 471.
    5973r-88rAnon. text of Irish origin conventionally known as De divisionibus temporum. This work on numbers, and computus, is presented as a master-student dialogue, and sometimes entitled Sententiae sancti Augustini et Isidori de laude compoti, or Computatio graecorum sive latinorum edita a sancto Dionisio graeco episcopo et meturio equitano invitato ab Hylario urbis Romae episcopo (rubric) Incipit prologus de ratione temporum uel de compoto annuali. (text) De numero igitur deo adiuuante pauca dicturi sum…
    Bisagni 2019, p. 106. Cambis 1770, p. 614-615. Cordoliani 1955, p. 448.
    Cf. ed. of Prologue by Cordoliani 19432, p. 242-243; Cordoliani 19431, p. 66.
    Comparanda: D fols. 29r-35r (missing the preface).
    6088vTexts explaining the rotae in nos. 65, 76, 66. The diagrams in question are found in this manuscript, but not in the order implied in the texts.
    (1) Explanatory text for no. 65. (text) Illa rota que uolutionem carte prior est designata per X et VIIII cicli decemnouenalis annos per quem aepacte currunt. indicat quota sit luna per singulos annos in kalendis singulorum mensium…
    (2) Explanatory text for no. 76 (text) Subsequens uero rota. ciclus solaris dicitur. que per XXVIII annos concurrentes. et ferias singulorum dieum premonstrat…
    (3) Explanatory text for no. 66 (text) Rotule quippe que in Vta pagina sunt adscripte ad unum quidem ambe spectant finem. Verum hac differunt. quod superior solummodo temporum anni que climatum celi concordiam signat…
    Cambis 1770, p. 615-617.
    Comparanda: L fol. 46r (3); P3 fol. 13v (3).
    6189rFig. 1.1 (top left) Rota showing length of day. Rota divided into 7 segments, labelled “I Feria” to “VII Feria” around rim. Reading inwards, the rings contain for each segment “Horas XXIII”, “Punctos XCVI”, “Minuta CCXL”, “Momenta DCCCC” “XCL”.
    6289r(Top right) Rota of Egyptian months. Rota labelled around hub “Annus Aegyptiorum” and divided into 12 segments, labelled with the names of the Roman months on the rim. Reading inwards, the rings contain the dates of the beginning of the Egyptian months and the indication that each month was 30 days long. Outside the rota at the top, and the junction of August and September, is the word “caput” i.e. the beginning of the Egyptian year.
    6389r(Bottom) Rota of termini of moveable feasts for each year of the 19-year cycle. Inscription in hub: “Hic est ciclus decemnouenalis. Termini.” The 19 segments read inwards: (1) the epact; (2) the terminus for Septuagesima, terminus for Quadragesima, date of beginning of Paschal lunation, terminus of Easter, terminus of Rogations, terminus of Pentecost, the Paschal regular, and indication of whether the year is common or embolismic. Around the rim is the argumentum for finding the year of the 19-year cycle, based on AD.
    6489vFig. 1.2 (top) Personified Luna in a chariot drawn by two horses, carrying two torches, and surrounded by a large halo. Around the rim of the halo is the following inscription: “Splendens sidereas depeluit luna tenebras”.
    6589v(bottom) Rota showing age of the moon on the kalends of each month through the 19-year cycle. Inscription around hub: Hic est circulus lunaris. On ring around hub: the monthly solar regulars, beginning with September. On the 19 segments, reading inwards: (1) the year of the lunar cycle; (2) the numbers 8, 19, 30, 11 etc. i.e. one less than the age of the moon on 1 January of that year; (3) the annual lunar epact; this and the previous ring also contain the litterae punctatae for hollow and full months. (4) the 12 months of the year and the age of the moon on the kalends.
    For the more conventional presentation of this rota see A fol. 35r (Abbo Floriacensis 2019, p. 41); P3 fol. 15r; P4 fol. 166r.
    6690r(top) Two syzygiae elementorum. On the left, a rota with “Annus” in the hub, surrounded (1) paired qualities, e.g. “Humidum. Calidum”; (2) the corresponding season, with the date in which it begins and its length expressed as the number of days; (3) the corresponding cardinal direction. On the right, a similar rota with in the hub: “Caibahir (?) / Mundus / Annus / Homo.” and reading outwards: (1) the four humours, (2) their corresponding seasons and (3) the corresponding paired qualities. Above these two rotae: “Expositionem istarum rotarum require retro”, and beside the right hand rota “Inferior rota”.
    Comparanda: A fol. 38v (Abbo Floriacensis 2019, p. 61); P3 fol. 14r; L fol. 46v.
    6790r(bottom) Horologium i.e. rota of equivalent length of day and night across the 12 solar months. In hub: “Concordia mensuum. Ianuarius cum decembro in horarum mensura concordat. Februarius et Nouember spacium aequalem consumant. Martius et October concordant. Aprilis et September equantur. Maius et Augustus pares sunt. Iunius et Iulio respondit”. “There are 12 segments, one for each month. Reading inwards, the rings contain: (1) the length of day and night, e.g. “Nox habet horas XVI. dies VIII.”; (2-7) the name of the month, and the length in pedes of the sundail shadow in each hour, e.g. “Ianuarius horae I et XI pedes XXVIII / horae II et X pedes XVIIII / Horae III et VIIII pedes XVII / Horae IIII et VIII pedes XV / Horae V et VII pedes XIII / Horae VI pedes XI.”
    Edition: Cf. Borst 2006, p. 1236-1237 where it appears as part of the Aachen Computus of 809 (Liber computi).
    Comparanda: A fol. 38v (Abbo Floriacensis 2019, p. 60) also accompanies the syzygiae but is represented as a semi-circular “sundail” with a “gnomon”. The lengths of the shadows, and the progression across the months (-10, -2, -2, -2, -2, +2, +2, +2, +2, +10) are those found in ps-Bede De mundi celestis terrestrisque constitutione: see Schaldach 2008, p. 9-16.
    6890v-91rFig. 1.3 Pair of rotae showing the length of moonlight and distance relative to the sun of the moon on each day of the lunation.
    90v: Waxing Moon: Rubric in large display caps at top De luna quomodo eius lux unaquaque nocte quattuor punctis crescit: a prima usque in quintam decimam quomodo uero ex ipsis punctis horas facimus et qualiter per XII sign infra XXX dies currit et elongatur a sole. The 15 rings of the rota are read outwards. Each contains the length of moonlight on that day, and the moon’s distance from the sun along the Zodiac, i.e. “Luna I quattuor punctis lucet. quattuor I IIII. Quattuor punctis lucet luna I et distat a sole similiter IIII punctis.” In the hub is a hand holing a ring inscribed with the initial letters of the months of the year and the corresponding sign of the zodiac.
    91r: Waning Moon: (rubric) “De luna quomodo eius lux unaquaque nocte quattuor punctis decrescit a sextadecima usque in XXVIIII et quomodo hoc quo de punctis minuitur in signa transfertus et qualiter per signa discurrens elongatur a phebo”. Below is the corresponding rota for the waning moon. The rings are read in the reverse direction from the rota on fol. 90v, i.e. inwards. The identical hand appears at the hub.
    6991v-92rLitterae punctatae table. This is an unusual version of the litterae punctatae table. It is oriented sidewise to be read across the opening. The table is in 19 columns as usual, but instead of the cells containing the litterae punctatae with the age key in the margin, the cells contain the age of the moon, and the litterae punctatae are in the margin. At the bottom of the table, i.e. the right margin of fol. 92r, are seven interlaced rings containing the sequence of common and embolismic years (identified by C and E, and aligned with the corresponding column of the table) with the embolisms numbered.
    7092vFig. 1.5 (top) Diagram of the cardinal directions and the dissemination of the Word of God. The diagram is a square, divided orthogonally and diagonally into eight triangles, painted in dark blue, light blue, deep greenish blue, and yellow. In the middle of each side is the bust of a nimbed figure, rising out of a ring centred on the centre of the square. There is a smaller ring at the hub, inscribed: “Sensus spiritualis interius uoluens.” The ring from which the busts emerge is inscribed: “Hystoria legis et prophetarum exterius in littera ab initio mundi usque in finem eius uelut rota uoluitur et propter III mundi partes et quattuor elementa quattuor facies habere dicuntur.” On the frame of the square is inscribed: “Oriens euangelica predicatio. / Meridies apostolorum predicatio. / Occidens lex Moysi. / Septentrion prophete ueteris testamenti.”
    7192v(Bottom) Solstice-equinox diagram with rectangular “mundus”.
    This version of the solstice diagram consists of four concentric circles, of which the inner three represent the path of the Sun at the summer solstice, the equinox, and the winter solstice. The earth (“MVNDVS”) is represented as a square imposed on the three rings on the left side, with three rings labelled “SOL” on the top and bottom sides, representing the sunrise and sunset on the solstices and equinoxes. The dates of the equinoxes are inscribed around the central SOL. Outside MVNDVS are the four cardinal directions, and inside the square are inscribed the names of the 12 winds.
    Comparanda: cf. D fol. 74r; P1 fol. 35r (for an alternative concentric version with a round “earth-viewpoint” in the centre, and east at the top, see P2 fol. 9r)
    7293r(top) Rota of planetary spheres and the sphere of the fixed stars, represented by the zodiac. The rota in divided into 12 segments for the 12 signs of the zodiac, and 7 rings for the planets. At the hub: “Terra”. Moon is in Cancer, Mercury in Virgo and Gemini, Venus in Libra and Taurus, Sun in Leo, Mars in Aries and Scorpio, Jupiter in Pisces and Sagittarius and Saturn in Aquarius and Capricorn. Note that this make a radiating pattern, with Saturn’s two signs adjacent, Jupiter’s separated by 2 signs, Mars’ by 4, the Sun with only one sign, Venus’ signs separated by 4, Mercury’s by 2 and the Moon with only one sign.
    7393r(bottom) Rota and argumentum for identifying the zodiac sign currently rising. (text) Ortum XII signorum qualibet diei uel noctis hora quisque liquido deprehensurus est. si a kl. octobris horas dierum ac noctium usque ad eam quam sibi preposuit colligens per XXIIII metiatur. et quod excreuerit diuidit quemadmodum subiecta instruit formula. The rota is divided into 12 segments, each with the remainder from the above calculation and the resulting sign, e.g. “Si I aut II remanserint. oritur Libra.”
    Edition: cf. Borst 2006, p. 1294-1296, where it appears as part of the Aachen Computus of 809 (Liber computi). See also the text “In quo signo uersetur Mars” edited by Juste 2004, p. 216-217, and Borst 2006, p. 1298-1299.
    Comparanda: L fol. 45v; P1 fol. 53v; P3 fol. 13r.
    7493vFig. 1.5 (top) Rota indicating visibility of zodiac signs. Text: Quibus signis orientibus que occidant uel centrum celi supra uel infra eodem tempore teneant ista formula continetur. Each of the twelve segments has an inscription, e.g.: Aries oriente II horis occidit libra et centrum superioris zodiaci tunc Capricorum inferioris optinet Cancrum.
    Edition: cf. Borst 2006, p. 1294-1296, where it appears as part of the Aachen Computus of 809 (Liber computi).
    Comparanda: L fol. 45v; P3 fol. 13r.
    7593v(bottom) Rota of concurrents through 28-year cycle, with number of years in the future when the same concurrents will obtain. (Text) Haec \scilicet inferioris/ figura ut uidetur mihi potius causa exercicii quam alicuius est reperta commodi…. Que omnia melius uiua uoce quam scripture panduntur. Rota is divided into 28 segments, marked with the concurrents through the solar cycle (leap years indicated above by a “B”) and the number of years in the future when the same concurrents will recur below.
    Comparanda: A fol. 35v (Abbo Floriacensis 2019 p. 47), with different text; L fols. 26v-27r; P3 fols. 51v-53r.
    7694rRota of weekday of kalends of the month through the 28-year cycle. Months inwards read from March through February in Abbonian fashion.
    Comparanda: A fol. 35v (Abbo Floriacensis 2019, p. 44)
    7794vFig. 1.6 Tidal rota through 30 days of the month. In the hub: an OT map. Four wedges off the hub form a cross, between each of which are two winds, e.g. (NNE) Aquilo qui et boreas sinister septentrionis. (ENE) Vulturnus qui et Boetias dexterior subsolani. Four rings attached at the corners of the outermost rim indicate the beginnings of the maline and ledones. The explanatory text straddles fols. 94r-v: (rubric) De concordia maris et lunae. (text) Haec subsequens figura excogitata est ad demonstrandam oceani cum luna concordiam…
    Comparanda: A fol. 35v (Abbo Floriacensis 2019, p. 42); L fol. 48r (same text as Madrid); P3 fol. 16r (same text as in Madrid).
    7895rSemi-circular horologium with two smaller rotae affixed to upper rim, showing (left) length of moonlight for each day of the month and (right) the relationship of the solar months to the zodiac signs.
    Comparanda: A fol. 38v (Abbo Floriacensis 2019, p. 60); L fols. 48v-49r; P3 fol. 17r. The two smaller diagrams alone appear in D fol. 73r.
    7995v
    (1)
    Explanatory texts for no. 78.:
    (1) explanatory text of moonlight rota: Figura ista haec continet. Prior ex illis superioribus rotulis per singulas lunae aetates. ostendet quot horas uel punctos singulis noctibus luceat. habens per circuitum ipsas lunae aetates…
    (2) explanatory text for the months-zodiac signs: Sequens uero rotula per singulos menses demonstrat. quot horas habeant dies. Noti ergo sunt ipsi menses extrinsecus ex minio…
    (3) explanatory text for horologium: Inferior sane rota ques est et maior horologium dicitur….
    Comparanda: L fols. 48v and 49v; P3 fol. 17v
    8096rTract on divisions of solar year. (rubric) De diuisionibus anni solaris. (text) Annus habet IIIIor tempora. Menses XII. ebdomadas LII. dies CCLXV et quadrantem…
    8196r-vTract on movement of sun and moon through zodiac. (rubric) De cursu solis et lunae per duodecim signa. (text) Tante magnitudinis sunt signa singula. ut minus quam duarum horarum spatio uel occidere uel de loco moueri non possint….
    8296vTract 1 on visibility of moon over synodic lunar month. cf. no. 74. No rubric. (text) Dodrante transmisso et semiuncia. luna lucet quando prima est…
    96v-97rTract 2 on visibility of moon over synodic lunar month. (rubric) Luna quot horas luceat. (text) Traditur autem secundum quosdam argumentum qui horam IIIIor punctis determinant…
    8397r-vDidactic dialogue on divisions of time, parts of body, etc. (text) Apud grecos uero ab hornatu appelatur mundus cosmos…
    Conparanda: P3 fols. 31r-32r.
    8497v-98raTract on Old Testament feasts. (rubric) Festi dies in ueteri lege isti sunt. (text) dies azimorum phase XIIIIo die mensis primi …
    Comparanda: This text also follows the preceding one in L fol. 14v and P3 fols. 32r-v.
    8598ra-99vaTreatise on the divisions of time. = Irish De divisionibus temporum “auctus 3”. Bisagni 2019, p. 111. (text) Diuisiones temporum XVI sunt. Idem athomum. momentum. minutum. Punctum. hora. quadras. dies. ebdomada. Mensis. tempus. annus. ciclus. uicissitudo triformis. Seculum aetas. mundus… Ends at De mensibus fol. 99va.
    Comparanda: P3 fols. 33r-36r (also ends at De mensibus).
    8699vaArgumentum for finding lunar epacts. (rubric) Quomodo inueniantur decessores lune. (text) Si uis cognoscee decessores lunae. quibus aetas lunae per totum annum conprobatur…
    8799va-bArgumentum for finding lunar epacts. (rubric) Item de eadem re. (text) Si uero adhuc leuius hoc approbare uoluerit. tene aepactam anni presentis et VIII regulares adice…
    8899vbArgumentum for finding Paschal terminus. (rubric) De fundamento pasche. (text) Si per hunc numerum fundamentum pasche hoc est luna XIIII inuenire cupis…
    8999vb-100raCriteria for Easter. (rubric) De die sancto Pasche. (text) Si uero diem sanctum paschae desideras. peractae ebdomada in qua tibi XIIII occurrit. prima feria inciente alterius ebdomade sanctum paschae diem cum omni ueneratione celebrabis…
    90100raArgumentum for Paschal terminus. (rubric) Ad inueniendam lunam XIIII primi mensis id est terminum paschalem. (text) Sume numerum epactarum in leua manu. Verbi gratia…
    91100ra-bPaschal terminum. (rubric) Ad terminum paschalem. (text) Quando autem XV epacte nichil addes numeri. sed tantum XIo kl. aprilis facit terminum.
    92100rbArgumentum for finding lunar epacts. (rubric) Secundum alium ordinem. (text) Si autem uolueris alio ordine aepactarum computare. de quibus superius dictum est…
    93100rb-vaConcerning argumentum for annus mundi. (rubric) De eadem re. (text) Si uis scire quare VII regulares addes in argumento de initio mundi hoc memorato quia in VII dies fecit deus caelum et terram…
    94100va-bLeap year. (rubric) Quid sit bissextus uel senarius numerus. (text) Hoc certissime debet calculator scire. uel diligentissime reuolui. qui sit bissextus uel senarius numerus…
    95100vbArgumentum for finding age of the moon on kalends of month. Ianuar. I. adde epacta qualis fuerit ipso anno. iunge simul. talis erit luna in kl. ianuarii…
    96100vbExplanation of monthly lunar epacts. (rubric) Ad regularum unum probandum. (text) Si uis scire unde procedit regularis unus. unde dicitur unum id est sume dies communis anni…
    97100vb-101raTermini of moveable feasts. (rubric) Argumentum ad inueniendum terminum Paschalem. et Quadragesimalem. et LXX. et Rogationalem. et Pentecosten. (text) Hunc ergo terminum paschae diligentius haben inquisitum siue feriam in qua euenerit…
    98101raArgumentum for Paschal terminus. (rubric) illeg. (text) Marcius habet regulares XXXVI. aprilis XXXV. Ergo si uis scire terminum pasche in martio aut in aprili…
    99101ratract 1 on saltus lunae. (rubric) Naturalis saltus lunaris. et eiudem salus dies. quare uel quando absumatur. (text) Vt autem haec tarditas quadriennio unum colligit adiciendum diem ita lunaris celeritas…
    100101ra-btract 2 on saltus lunae. (rubric) Item. Super hac re non incongrua disposicio. (text) Plures in mense nouembri hunc lunae saltum computant…
    101101rbExcerpt for Helperic on the epacts. (rubric) Item Hylpericus. (text) Quia secundum aegiptios inquit aepactas a septembrio inchoamus secundum illos in luna iulii mensis…
    102101rSuite of notes and argumenta on Paschal reckoning, beginning with the relation of age of moon on Easter to age of moon on Quadragesima. (rubric) Quomodo paschalis inueniatur luna. (text) Omnis paschalis luna cuiuscumque aetatis est si detrahas ab ea XII fiet tibi etas lunae. qua fit in initio quadragesime…
    101rbCalendar limits of Easter Sunday. (rubric) Quomodo dies inuenatur Paschalis. (text) Sciendum est quod pasche dies ab XI kl aprilis…
    101rb-vaRefutation of false teaching on Calendar limits of Easter. (text) Ratio contra eos qui dicunt VIII kl. maii Pascha fieri non possunt. (text) Anno XIIIIo ante natiuitatem domini fuit terminus paschalis die dominica XIII kl. maii….
    101va-bArgumentum for finding weekday of termini of moveable feasts. (rubric) Ratio ad Pascha inueniendum. (test) Si uis scire subito quota feria terminus paschalis seu quadragesimalis uel rogationalis euenerit…
    101vbTract on why Christians may not celebrate “with the Jews” on the 14th day of the Paschal lunar month. (rubric) De ratione Pasche. (text) Iuxta decretum partum non licet chatolicis cum hebreis celebrare pascha…
    101vb-102rbArgumenta for finding the termini of the moveable feasts. (rubric) Argumentum de Septuagesimum inueniendum. (text) Si uolueris scire septuagesimum in quantos dies…
    102vaTract on the pre-Lenten moveable feasts. (text) Solet queri a nonnullis cur septuagesima. sexagesima et quinquagesima siue quadragesima in sacris codicibus certis temporibus…
    103102vbSeven wonders of the Ancient World. (text) Primum miraculum mundi capitolium rome…
    104103raEight signs of Last Judgement. (text) Primum indicium. stella prefulgente gladio similis…
    105103raNote on beginning of the year amongst various peoples. (text) Principium anni incipit secundum hebreos…
    106103rb(rubric) Titulus orologii. (text) Spera caeli quarter senis horis de reuoluitur omnes stelle fixe caelo que cum ea ambiunt… Added by the main text hand, but in a different colour of ink.
    Edition: Ascribed to Pacificus of Verona (cf. no. 54 above). Ed. in Migne 1850, p. 953-954, Strecker 1923, p. 692 and by Meersseman and Adda, p. 169.
    107103vBlank, with a partially erased early modern inscription, now illegible.
    108104r-112rClaudius of Turin, Chronicon. (rubric) Domini piissimo et in Christo michi diligendo Claudius peccator. (text) Periculo summe opus. (explicit) Explicit prima aedicio Claudii de sex aetatibus. The first part (Allen’s “display section”) runs from fols. 104r-112r, and the second “reckoning section” from fols. 113r-116r, separated by no. 109 (below).
    Cambis 1770, p. 617.
    Bibliography: Allen 2000, p. 288-319 at 294; Ferrari 1973, p. 304-305; Dümmler 1895, pt. 1, p. 442, n. 7. Cf. Edition of letter-preface by Ferrari 1973, p. 307-308. Madrid Mss/9605 is her Ms A.
    109111vTract on the calendar date of Christ’s passion. (text) Victorinus homo equitanus inuitatus a sancto hilario urbis romae episcopo conposuit paschalem recursum…
    Cambis 1770, p. 623-626.
    110113r-116raClaudius of Turin, Chronicon pt. 2 (Allen’s “reckoning section”). (rubric) Claudius iterum Adoni presbytero sermonum dirigit in Christo. (text) Quia igitur factore deo…
    Cambis 1770, p. 626-631.
    111116ra-vSummary of Six Ages of the World. (rubric) Item supputatio annorum edita a beato Iuliano Toletane sedis episcopo. (text) Prima etas. Premissis quinque diebus…
    Cf. edition in Migne 1880, p. 581-584.
    112116v-117Summary Chronology. (rubric) Excerptum ex cronica sancti Ysidori. A tabular arrangement of Etymologiae 5.29.1-25, with the Sixth Age replaced by the following:
    Octauianus LVI. Huius anno XLoIo Christus dominus nascitur.
    Si enim hos annos id est quadraginta et unum necnon et cainan annos CXXX quos alii scriptores computant. superioribus annis addere uolueris colliguntur ab inicio mundi usque ad Christum secundum hanc supputationem anni V CCC XXV.
    A natiuitate uero domini nostri Ihesu Christi secundum carnem usque ad annum quadragesimum regni gloriosissimi karoli filii piissimum imperatoris Hludouuici supputantur anni DCCCL. Ad quibus annis usque ad presentem annum in quo nostra deuenit aetas uidelicet quo felix adalax comitissa dormiuit in pace. colliguntur anni CLXXII. Qui in summa collecti a natiuitate Christi Millesimum uicesimum sextum. presentem annum efficiunt. in quo iste libellus conscriptus est a quodam fragili monacho Arnulfo nomine. Residuum sextae aetatis tempus Deo soli cognitum est.
    Quoted in part by Jean Mabillon, Annales ordinis Sancti Benedicti… T. 4, (Lucca: L. Venturini, 1739) book 55, ch. 96, p. 298 and by Cambis 1770, p. 631-632; Ewald 1880, p. 303; Ferrari 1973, p. 304-305.

    Illustrations


    Fig.
    1.1 Madrid, BNE, Mss/9605, fol. 89 : « (top left) Rota showing the length of the day for the seven days of the week (Appendix, no. 61); (top right) Rota of Egyptian months (Appendix, no. 62) (bottom) Rota of termini of moveable feasts for each year of 19-year cycle (Appendix, no. 61) », c. 1026.

    Image

    © BNE.

    Fig. 1.2 Madrid, BNE, Mss/9605, fol. 89v : « (top) Personified figure of Luna in her chariot (Appendix, no. 64); (bottom) Rota showing age of the moon on the kalends of each month through the 19-year cycle (Appendix, no. 65) », c. 1026.

    Image

    © BNE.

    Fig. 1.3 Madrid, BNE, Mss/9605, fol. 90 : « (top) two syzygiae elementorum (Appendix, no. 66); (bottom) horologium (Appendix, no. 67) », c. 1026.

    Image

    © BNE.

    Fig. 1.4 Madrid, BNE, Mss/9605, fols. 90v-91 : « Pair of rotae showing duration of moonlight and relative distance of moon from sun on each day of lunar month (waxing moon on fol. 90v; waning moon on fol. 91). (Appendix, no. 68) », c. 1026.

    Image

    © BNE.

    Fig. 1.5 Madrid, BNE, Mss/9605, fol. 92v : « (top) Diagram showing the cardinal directions and the dissemination of the word of God through the Law, Prophets, evangelists and apostles (Appendix, no. 70); (bottom) Diagram of solstices and equinoxes (Appendix no. 71) », c. 1026.

    Image

    © BNE.

    Fig. 1.6 Madrid, BNE, Mss/9605, fol. 93 : « (top) Rota of planetary spheres and zodiac (Appendix, no. 72); (bottom) Rota and argumentum for identifying the zodiac sign currently rising (Appendix, no. 73) », c. 1026.

    Image

    © BNE.

    Fig. 1.7 Madrid, BNE, Mss/9605, fols. 93v-94 : « (fol. 93v, top) Rota indicating visibility of zodiac signs (Appendix, no. 74). (fol. 93v, bottom) Rota of concurrent through 28-year cycle, with number of years in the future when the same concurrent will obtain (Appendix, no. 75); (fol. 94) Rota of weekday of kalends of the month through the 28-year cycle (Appendix, no. 76) », c. 1026.

    Image

    © BNE.

    Fig. 1.8 Madrid, BNE, Mss/9605, fols. 94v-95 : « fol. 94v: Tidal rota (Appendix, no. 77), fol. 95: Horologium with two smaller rotae affixed to upper rim, showing (left) length of moonlight for each day of the month and (right) the relationship of the solar months to the zodiac signs (Appendix, no. 78) », c. 1026.

    Image

    © BNE.

    Bibliographie

    Des DOI sont automatiquement ajoutés aux références bibliographiques par Bilbo, l’outil d’annotation bibliographique d’OpenEdition. Ces références bibliographiques peuvent être téléchargées dans les formats APA, Chicago et MLA.

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    Obrist, B. (1997). Wind Diagrams and Medieval Cosmology. University of Chicago Press. https://doi.org/10.2307/2865863
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    Wilmart 1945 : Wilmart (André), Codices reginenses latini. I.II. Codd. 251-500, Vatican City: BAV, 1945.

    Worm 2010 : “Diagrammatic Chronicles”, in The Encyclopedia of the Medieval Chronicle, R. Graeme Dunphy (ed.), Leiden: Brill, 2010, p. 522-532.

    Worm 2013 : “Visualizing the Order of History: High of St Victor’s Chronicon and Peter of Poitiers’ Compendium Historiae”, in Romanesque and the Past: Retrospection in the Art and Architecture of Romanesque Europe, Richard Plant and John McNeill (eds.), Leeds: Maney, 2013, p. 243-263.

    Worm 2014 : Worm (Andrea), “‘Arbor human genus significant’: Trees of Consanguinity and Genealogical Trees of Salvation History in the Romanesque Bible Manuscripts of Parc, Floreffe and Foigny”, in The Tree: Symbol, Allegory and Mnemonic Device in Medieval Art and Thought, Andrea Worm and Pippa Salonius (eds.), Turnhout: Brepols, 2014, p. 35-67.

    Zaluska 1991 : Zaluska (Yolanta), Manuscrits enluminés de Dijon, Paris: CNRS, 1991.

    Notes de bas de page

    1 Obrist 20041, p. 144.

    2 Wallis 2017, p. 195-224.

    3 Cf. Appendix at the end of this paper, also described in the BNE’s digital catalogue: <http://bdh.bne.es/bnesearch/detalle/bdh0000054177>. Digitized in full at <http://bdh-rd.bne.es/viewer.vm?id=0000054177&page=1>. See also Gras 2021, cat. 2, p. 44-48.

    4 It was under this older shelfmark that the manuscript was briefly noted by Knust 1843, p. 781 and Ewald 1881, p. 302-303.

    5 E.g. Cordoliani 1955, p. 435-481. In his item-by-item survey of the manuscript, Cordoliani cites the correct folio number up to fol. 37 (p. 454); thereafter, his folio numbers are one less than the present foliation. This discrepancy is also found in Allen 2000, p. 288-319 at 294-295.

    6 Cordoliani 1955, p. 486, n. 3.

    7 Cambis 1770, p. 570-636. The manuscript was number 173 in his library.

    8 Cambis 1770, p. 578-580.

    9 Cambis 1770, p. 633.

    10 Granget 1862, t. II, p. 350-351.

    11 Bouland 1895, p. 161-164.

    12 Chossat 1896, p. 495.

    13 Cambis 1770, p. 584.

    14 Mabillon 1707, lib. LV, cap. XCV, p. 321-322.

    15 Cambis 1770, p. 574 and 651-652.

    16 Bede 1977, c. 66, p. 468 ll. 161-175; trans. Wallis 2004, p. 163. Cf. Epistola ad Pleguinum 1980, c. 6, p. 619-620 ll. 98-110; trans. Wallis 2004, p. 408.

    17 Note that Cambis’s account (Cambis 1770, p. 585) is not accurate.

    18 Cambis 1770, p. 607-609.

    19 Barcelona, Valencia, Cordoba but also southern France (Lyon, Arles, Anger, Tours, Chalons-sur-Saône): Cordoliani 1955, p. 453 and n. 65.

    20 “1. Un traité sur le comput des Grecs et des Latins, par rapport au jour de Pâques, conformément à la définition du Concile de Nicée” [cf. Mss/9605 fol. 19r].
    2. Le comput du Moine Helperic, écolâtre de Grandfel. [cf. Mss/9605 fol. 1r-10v].
    3. Plusieurs écrits sur le nombre d’or, les indictions, l’embolisme, sur la manière de trouver le jour de Pâques en se servant de la période Julienne, enfin sur le comput annuel, ou supputation des temps pour tout le cours de l’année.
    4. Un traité sur les présages des temps. [cf. Mss/9605 fol. 11vb].
    5. La Chronique de saint Isidore de Séville. [cf. Mss/9605 fols. 116v-117v].
    6. Un traité de comput attribué à Julien, évêque de Tolède. [cf. Mss/9605 fols. 53v-54r].
    7. Les livres du vénérable Bède sur les douze mois, les jours de la semaine et les règles pour trouver les Calendes. [cf. Mss/9605 fols. 17ra-b(?)].
    8. La Chronique de Claude, évêque de Turin, adressée au Prêtre Adon, depuis archevêque de Vienne. [cf. Mss/9605 fols. 104r-116v]; Cambis 1770, p. 576.

    21 Cambis 1770, p. 581.

    22 Cambis 1770, p. 652.

    23 Borst 2006.

    24 Cordoliani 1955, p. 447.

    25 Borst 2006, t. I, p. 249-250. See also my review of Borst in Wallis 2008, p. 668-670.

    26 For perceptive analysis of this manuscript as a “album” see Germann 2006, ch. 2; see also Barbara Obrist’s introduction to Abbo Floriacensis 2019, p. VIII-IX.

    27 Obrist 20042, p.141-186.

    28 Nothaft 2012, ch. 4, esp. p. 103-105; Verbist 2004, p. 61-93.

    29 Omont 1889, p. 106-109; Jeudy and Riou 1989, p. 483-500; Borst 2006, p. 224-225; Zaluska 1991, p. 30-33.

    30 British Library catalogue description at: <http://www.bl.uk/manuscripts/FullDisplay.aspx?Source=BrowseScribes&letter=A&ref=Sloane_MS_263> ; Borst 2006, p. 246-247.

    31 Borst 2006, p. 272-273.

    32 Borst 2006, p. 274-275.

    33 Delisle 1868, p. 37; Borst 2006, p. 277-278.

    34 Samaran and Marichal 1974, t. III, part. I, p. 275.

    35 Wilmart 1945, p. 160-174; Borst 2006, p. 303-304.

    36 Fohlen, Jeudy and Riou, 1982, p. 423-426; Borst 2006, p. 308.

    37 Borst 2006, no. 17, p. 1054-1334 (Liber computi).

    38 Divination played a not insignificant role in Abbo’s science albums: Juste 2004, p. 95-127. Despite Abbo’s influence on the contents of Madrid Mss/9605, there is no prognostica or divination in this manuscript, apart from the rubric of no. 4.

    39 Clavis scriptorum 2010, p. 421-430. Earlier manuscript surveys are: Traube 1909-1920, t. III, p. 128-153, a revised version of an article which originally appeared in Neues Archiv, 18 (1893), p. 73-105; and McGurk 1974, p. 1-5.

    40 The connection to Auxerre, coupled with the fact that the author’s name appears as “Heiricus” or “Heriricus” in some Loire valley codices, prompted Ludwig Traube to suggest that “Helperic” was actually the Carolingian scholasticus Heiric of Auxerre, a theory he later withdrew in favour of the traditional ascription: Traube 1909-1920, p. 146 and 128, note. Van de Vyver 1935, p. 149 suggested that Heiriricus, abbot of St-Mesmin de Micy (a dependency of Fleury) in the reign of Louis the Pious, may have lent his name to the Loire valley exemplars.

    41 D f. 94r-107v (annus praesens 930); L f. 1r-13v (903); P2 f. 9v-38v (annus praesens is 975, but author is identified as “Helpericus”); and P3 f. 20r-31r (section of text with annus praesens missing but author named as “Helpericus”). On Helperic as a major source for Abbo, see Obrist 2019, p. xxiii-xxiv; Van de Vyver 1935, p. 146-149.

    42 These two are examined in detail by Eastwood 1988, p. 265-280, with illustrations of fols. 12r-v on p. 277-278. See also Eastwood 1987, p. 141-172, esp. p. 155; Eastwood 2007, ch. 3 and p. 357-358; and Eastwood and Grasshoff 2004, p. 30-40. Abbo’s version in A fol. 38r (Abbo Floriacensis 2019, p. 59) is distinguished by the omission of vertical lines: see Obrist 2019, p. XLV-XLVI, and Eastwood 1997, p. 251.

    43 These two formats are discussed and illustrated in Wallis 2015, p. 18-23.

    44 Cordoliani 1955, p. 440, calls them “quelques lignes de piété”.

    45 Cordoliani 1955, p. 439-440; cf. PL 90.735-736.

    46 Cordoliani 1955, p. 441.

    47 Bede 1977, p. 333. Ausonius’ Ecloga 16 1978, p. 108-109. On the genre of computus poetry see Strecker 2003, p. 178-179.

    48 Jones 1943, p. 198-210.

    49 Cordoliani 1955, p. 433. Ed. PL 94.605 and PL 129.1369; Strecker 1923, p. 682. For a list of manuscripts, see Di Pasquale 2003, p. 178-179.

    50 Cordoliani 19431, p. 59.

    51 Cordoliani 1955, p. 448-450, who also notes the unique character of this collection.

    52 See above, notes 16-17.

    53 It is thus not, as Cordoliani claims, “absolument semblable” to the Madrid Ms (Cordoliani 1955, p. 452-453).

    54 L fols. 34r-38r has a very skeletal martyrology, but the tables are visually striking, with their cell walls thickened and decorated to produce the effect of a maze or an interlaced “carpet”.

    55 Lapidge and Baker 2019, p. 35-36.

    56 Wallis 2015, p. 23-29.

    57 Hillgarth 1958, p. 7-26. See also no. 111.

    58 Wallis 2017, p. 203-216, and Wallis 1995, p. 122-127.

    59 The phrase in Obrist 2019, p. XLII. For her analysis of Abbo’s portfolio in A, see Obrist 20042, p. 143-173.

    60 Obrist 2019, p. XLIII. Obrist sees these schemata as didactic props for the classroom, rather than meditations on the relationship of time and the universe: Obrist 20042, p. 183. I do not regard these two purposes as mutually exclusive.

    61 Wallis 2017, p. 203-217.

    62 Wallis 2015, p. 29. The evident difficulty of consulting a circular table did not discourage its precocious use as a format for computus data. The oldest circular computus table is the 95-year Paschal table inscribed on a marble tablet now in the cathedral of Ravenna, dating from the 6th century, and called “Ciclus Paschalis”: Obrist 20042, p. 152.

    63 Wallis 2015, p. 3; Obrist 20041, p. 20-24 et p. 300-304; Obrist 1996, p. 95-164; Vossen 1950, p. 33-46.

    64 Isidore de Séville 2002, p. 202 bis (illustrating ch. 7) and p. 216 bis illustrating ch. 11, where Isidore quotes Ambrose on the interweaving of the qualities “concordi societate” (p. 215, line 29).

    65 Cf. A fol. 38v (Abbo Floriacensis 2019, p. 61); P3 fol. 14r; L fol. 46v. The Abbonian version of the first syzygia, unlike Isidore’s, also contains the dates for the beginnings of each season and the length of the season expressed in days.

    66 Cf. A fol. 38v (Abbo Floriacensis 2019, p. 60).

    67 Obrist 2019, p. XL-XLVI.

    68 Jones 1943, p. 209-210.

    69 Obrist 1997, p. 66-75, esp. fig. 27, showing the wind-diagram in Isidore of Seville’s De natura rerum in Laon, Bibliothèque municipale, Ms 422, fol. 6v (s. IX in.). It is worth noting that the Laon figures are divided vertically and coloured differently on each side, to suggest the shared elemental qualities of the four cardinal directions. The halos of the personifications in the Madrid manuscript are likewise divided down the middle and coloured like the adjacent triangles.

    70 This is a prominent feature of the maps in manuscripts of Beatus of Liebana (9th c.), Commentary on the Apocalypse, e.g. Cathedral of Burgos de Osma, Archives, Ms Cod. 1 (1086), or the Saint-Sever manuscript, Paris, BNF, Latin 8878, fols. 45bisv-45ter (11th c.). Von den Brincken 2006, p. 355-379, esp. p. 361, fig. 4.

    71 See Obrist 1997, p. 57-66, esp. figs. 16 and 17 (the latter from D fol. 74v), and Obrist 2000, p. 72-73 and figs. 1-3.

    72 Eastwood and Grasshoff 2004, p. 49-55; Eastwood 2007, p. 86-88.

    73 Juste 2007.

    74 Bede 1977, p. 442, lines 19-28; trans. Wallis 2004, p. 136.

    75 Bede 1977, p. 443 line 6, p. 444, line 18; trans. Wallis 2004, p. 137-138.

    76 On the Ephemerida see above, note 52. On riddles and games in science albums, see Wallis 2012, forthcoming.

    77 Obrist 20042, p. 168-172. This rota also appears L fol. 48r and P3 fol. 16r with the same text as is found in Madrid.

    78 Obrist 20042, p. 181 and fig. 48. D fol. 73r contains the two smaller rotae only.

    79 Allen 2000, p. 291. The letter-preface is edited by Ferrari 1973, p. 307-308. Madrid Mss/9605 is her Ms A.

    80 Allen 2000, p. 295.

    81 Allen 2000, p. 295-296. See catalogue description in https://manus.iccu.sbn.it//opac_SchedaScheda.php?ID=50386.

    82 Allen 2000, p. 313.

    83 Allen mistakenly thinks that Bede endorsed the position that the Passion occurred on 25 March (Allen 2000, p. 314, n. 130). In fact, he refutes this with heavy irony in De temporum ratione, ch. 47.

    84 Nothaft 2012 and Verbist 2004.

    85 The blank page on fol. 103v (no. 107) for instance, is intentional: Allen 2000, p. 295, Ferrari 1973, p. 304 and n. 2, and Cordoliani 1955, p. 436 agree that the page was left blank on purpose, so that the Chronicon could be laid out across a double-page opening, with the preface on the initial verso.

    86 I signal here the important work by Worm 2010, p. 522-532; Worm 2013, p. 243-263; Worm 2014, p. 35-67.

    87 On the contours of this form of early medieval erudition, see Wallis 2010, p. 113-126; Wallis 2007, p. 80-111; and Wallis 2006, p. 61-94.

    Auteur

    • Faith Wallis

      McGill University

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    1 Obrist 20041, p. 144.

    2 Wallis 2017, p. 195-224.

    3 Cf. Appendix at the end of this paper, also described in the BNE’s digital catalogue: <http://bdh.bne.es/bnesearch/detalle/bdh0000054177>. Digitized in full at <http://bdh-rd.bne.es/viewer.vm?id=0000054177&page=1>. See also Gras 2021, cat. 2, p. 44-48.

    4 It was under this older shelfmark that the manuscript was briefly noted by Knust 1843, p. 781 and Ewald 1881, p. 302-303.

    5 E.g. Cordoliani 1955, p. 435-481. In his item-by-item survey of the manuscript, Cordoliani cites the correct folio number up to fol. 37 (p. 454); thereafter, his folio numbers are one less than the present foliation. This discrepancy is also found in Allen 2000, p. 288-319 at 294-295.

    6 Cordoliani 1955, p. 486, n. 3.

    7 Cambis 1770, p. 570-636. The manuscript was number 173 in his library.

    8 Cambis 1770, p. 578-580.

    9 Cambis 1770, p. 633.

    10 Granget 1862, t. II, p. 350-351.

    11 Bouland 1895, p. 161-164.

    12 Chossat 1896, p. 495.

    13 Cambis 1770, p. 584.

    14 Mabillon 1707, lib. LV, cap. XCV, p. 321-322.

    15 Cambis 1770, p. 574 and 651-652.

    16 Bede 1977, c. 66, p. 468 ll. 161-175; trans. Wallis 2004, p. 163. Cf. Epistola ad Pleguinum 1980, c. 6, p. 619-620 ll. 98-110; trans. Wallis 2004, p. 408.

    17 Note that Cambis’s account (Cambis 1770, p. 585) is not accurate.

    18 Cambis 1770, p. 607-609.

    19 Barcelona, Valencia, Cordoba but also southern France (Lyon, Arles, Anger, Tours, Chalons-sur-Saône): Cordoliani 1955, p. 453 and n. 65.

    20 “1. Un traité sur le comput des Grecs et des Latins, par rapport au jour de Pâques, conformément à la définition du Concile de Nicée” [cf. Mss/9605 fol. 19r].
    2. Le comput du Moine Helperic, écolâtre de Grandfel. [cf. Mss/9605 fol. 1r-10v].
    3. Plusieurs écrits sur le nombre d’or, les indictions, l’embolisme, sur la manière de trouver le jour de Pâques en se servant de la période Julienne, enfin sur le comput annuel, ou supputation des temps pour tout le cours de l’année.
    4. Un traité sur les présages des temps. [cf. Mss/9605 fol. 11vb].
    5. La Chronique de saint Isidore de Séville. [cf. Mss/9605 fols. 116v-117v].
    6. Un traité de comput attribué à Julien, évêque de Tolède. [cf. Mss/9605 fols. 53v-54r].
    7. Les livres du vénérable Bède sur les douze mois, les jours de la semaine et les règles pour trouver les Calendes. [cf. Mss/9605 fols. 17ra-b(?)].
    8. La Chronique de Claude, évêque de Turin, adressée au Prêtre Adon, depuis archevêque de Vienne. [cf. Mss/9605 fols. 104r-116v]; Cambis 1770, p. 576.

    21 Cambis 1770, p. 581.

    22 Cambis 1770, p. 652.

    23 Borst 2006.

    24 Cordoliani 1955, p. 447.

    25 Borst 2006, t. I, p. 249-250. See also my review of Borst in Wallis 2008, p. 668-670.

    26 For perceptive analysis of this manuscript as a “album” see Germann 2006, ch. 2; see also Barbara Obrist’s introduction to Abbo Floriacensis 2019, p. VIII-IX.

    27 Obrist 20042, p.141-186.

    28 Nothaft 2012, ch. 4, esp. p. 103-105; Verbist 2004, p. 61-93.

    29 Omont 1889, p. 106-109; Jeudy and Riou 1989, p. 483-500; Borst 2006, p. 224-225; Zaluska 1991, p. 30-33.

    30 British Library catalogue description at: <http://www.bl.uk/manuscripts/FullDisplay.aspx?Source=BrowseScribes&letter=A&ref=Sloane_MS_263> ; Borst 2006, p. 246-247.

    31 Borst 2006, p. 272-273.

    32 Borst 2006, p. 274-275.

    33 Delisle 1868, p. 37; Borst 2006, p. 277-278.

    34 Samaran and Marichal 1974, t. III, part. I, p. 275.

    35 Wilmart 1945, p. 160-174; Borst 2006, p. 303-304.

    36 Fohlen, Jeudy and Riou, 1982, p. 423-426; Borst 2006, p. 308.

    37 Borst 2006, no. 17, p. 1054-1334 (Liber computi).

    38 Divination played a not insignificant role in Abbo’s science albums: Juste 2004, p. 95-127. Despite Abbo’s influence on the contents of Madrid Mss/9605, there is no prognostica or divination in this manuscript, apart from the rubric of no. 4.

    39 Clavis scriptorum 2010, p. 421-430. Earlier manuscript surveys are: Traube 1909-1920, t. III, p. 128-153, a revised version of an article which originally appeared in Neues Archiv, 18 (1893), p. 73-105; and McGurk 1974, p. 1-5.

    40 The connection to Auxerre, coupled with the fact that the author’s name appears as “Heiricus” or “Heriricus” in some Loire valley codices, prompted Ludwig Traube to suggest that “Helperic” was actually the Carolingian scholasticus Heiric of Auxerre, a theory he later withdrew in favour of the traditional ascription: Traube 1909-1920, p. 146 and 128, note. Van de Vyver 1935, p. 149 suggested that Heiriricus, abbot of St-Mesmin de Micy (a dependency of Fleury) in the reign of Louis the Pious, may have lent his name to the Loire valley exemplars.

    41 D f. 94r-107v (annus praesens 930); L f. 1r-13v (903); P2 f. 9v-38v (annus praesens is 975, but author is identified as “Helpericus”); and P3 f. 20r-31r (section of text with annus praesens missing but author named as “Helpericus”). On Helperic as a major source for Abbo, see Obrist 2019, p. xxiii-xxiv; Van de Vyver 1935, p. 146-149.

    42 These two are examined in detail by Eastwood 1988, p. 265-280, with illustrations of fols. 12r-v on p. 277-278. See also Eastwood 1987, p. 141-172, esp. p. 155; Eastwood 2007, ch. 3 and p. 357-358; and Eastwood and Grasshoff 2004, p. 30-40. Abbo’s version in A fol. 38r (Abbo Floriacensis 2019, p. 59) is distinguished by the omission of vertical lines: see Obrist 2019, p. XLV-XLVI, and Eastwood 1997, p. 251.

    43 These two formats are discussed and illustrated in Wallis 2015, p. 18-23.

    44 Cordoliani 1955, p. 440, calls them “quelques lignes de piété”.

    45 Cordoliani 1955, p. 439-440; cf. PL 90.735-736.

    46 Cordoliani 1955, p. 441.

    47 Bede 1977, p. 333. Ausonius’ Ecloga 16 1978, p. 108-109. On the genre of computus poetry see Strecker 2003, p. 178-179.

    48 Jones 1943, p. 198-210.

    49 Cordoliani 1955, p. 433. Ed. PL 94.605 and PL 129.1369; Strecker 1923, p. 682. For a list of manuscripts, see Di Pasquale 2003, p. 178-179.

    50 Cordoliani 19431, p. 59.

    51 Cordoliani 1955, p. 448-450, who also notes the unique character of this collection.

    52 See above, notes 16-17.

    53 It is thus not, as Cordoliani claims, “absolument semblable” to the Madrid Ms (Cordoliani 1955, p. 452-453).

    54 L fols. 34r-38r has a very skeletal martyrology, but the tables are visually striking, with their cell walls thickened and decorated to produce the effect of a maze or an interlaced “carpet”.

    55 Lapidge and Baker 2019, p. 35-36.

    56 Wallis 2015, p. 23-29.

    57 Hillgarth 1958, p. 7-26. See also no. 111.

    58 Wallis 2017, p. 203-216, and Wallis 1995, p. 122-127.

    59 The phrase in Obrist 2019, p. XLII. For her analysis of Abbo’s portfolio in A, see Obrist 20042, p. 143-173.

    60 Obrist 2019, p. XLIII. Obrist sees these schemata as didactic props for the classroom, rather than meditations on the relationship of time and the universe: Obrist 20042, p. 183. I do not regard these two purposes as mutually exclusive.

    61 Wallis 2017, p. 203-217.

    62 Wallis 2015, p. 29. The evident difficulty of consulting a circular table did not discourage its precocious use as a format for computus data. The oldest circular computus table is the 95-year Paschal table inscribed on a marble tablet now in the cathedral of Ravenna, dating from the 6th century, and called “Ciclus Paschalis”: Obrist 20042, p. 152.

    63 Wallis 2015, p. 3; Obrist 20041, p. 20-24 et p. 300-304; Obrist 1996, p. 95-164; Vossen 1950, p. 33-46.

    64 Isidore de Séville 2002, p. 202 bis (illustrating ch. 7) and p. 216 bis illustrating ch. 11, where Isidore quotes Ambrose on the interweaving of the qualities “concordi societate” (p. 215, line 29).

    65 Cf. A fol. 38v (Abbo Floriacensis 2019, p. 61); P3 fol. 14r; L fol. 46v. The Abbonian version of the first syzygia, unlike Isidore’s, also contains the dates for the beginnings of each season and the length of the season expressed in days.

    66 Cf. A fol. 38v (Abbo Floriacensis 2019, p. 60).

    67 Obrist 2019, p. XL-XLVI.

    68 Jones 1943, p. 209-210.

    69 Obrist 1997, p. 66-75, esp. fig. 27, showing the wind-diagram in Isidore of Seville’s De natura rerum in Laon, Bibliothèque municipale, Ms 422, fol. 6v (s. IX in.). It is worth noting that the Laon figures are divided vertically and coloured differently on each side, to suggest the shared elemental qualities of the four cardinal directions. The halos of the personifications in the Madrid manuscript are likewise divided down the middle and coloured like the adjacent triangles.

    70 This is a prominent feature of the maps in manuscripts of Beatus of Liebana (9th c.), Commentary on the Apocalypse, e.g. Cathedral of Burgos de Osma, Archives, Ms Cod. 1 (1086), or the Saint-Sever manuscript, Paris, BNF, Latin 8878, fols. 45bisv-45ter (11th c.). Von den Brincken 2006, p. 355-379, esp. p. 361, fig. 4.

    71 See Obrist 1997, p. 57-66, esp. figs. 16 and 17 (the latter from D fol. 74v), and Obrist 2000, p. 72-73 and figs. 1-3.

    72 Eastwood and Grasshoff 2004, p. 49-55; Eastwood 2007, p. 86-88.

    73 Juste 2007.

    74 Bede 1977, p. 442, lines 19-28; trans. Wallis 2004, p. 136.

    75 Bede 1977, p. 443 line 6, p. 444, line 18; trans. Wallis 2004, p. 137-138.

    76 On the Ephemerida see above, note 52. On riddles and games in science albums, see Wallis 2012, forthcoming.

    77 Obrist 20042, p. 168-172. This rota also appears L fol. 48r and P3 fol. 16r with the same text as is found in Madrid.

    78 Obrist 20042, p. 181 and fig. 48. D fol. 73r contains the two smaller rotae only.

    79 Allen 2000, p. 291. The letter-preface is edited by Ferrari 1973, p. 307-308. Madrid Mss/9605 is her Ms A.

    80 Allen 2000, p. 295.

    81 Allen 2000, p. 295-296. See catalogue description in https://manus.iccu.sbn.it//opac_SchedaScheda.php?ID=50386.

    82 Allen 2000, p. 313.

    83 Allen mistakenly thinks that Bede endorsed the position that the Passion occurred on 25 March (Allen 2000, p. 314, n. 130). In fact, he refutes this with heavy irony in De temporum ratione, ch. 47.

    84 Nothaft 2012 and Verbist 2004.

    85 The blank page on fol. 103v (no. 107) for instance, is intentional: Allen 2000, p. 295, Ferrari 1973, p. 304 and n. 2, and Cordoliani 1955, p. 436 agree that the page was left blank on purpose, so that the Chronicon could be laid out across a double-page opening, with the preface on the initial verso.

    86 I signal here the important work by Worm 2010, p. 522-532; Worm 2013, p. 243-263; Worm 2014, p. 35-67.

    87 On the contours of this form of early medieval erudition, see Wallis 2010, p. 113-126; Wallis 2007, p. 80-111; and Wallis 2006, p. 61-94.

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    Wallis, Faith. « Mss/9605:/An/Eleventh-Century/“Science/Album” ». In Lumières Du Nord, édité par Samuel Gras et Anne-Marie Legaré. Villeneuve d’Ascq: Presses universitaires du Septentrion, 2021. doi:10.4000/books.septentrion.137072.
    Wallis, Faith. « Mss/9605:/An/Eleventh-Century/“Science/Album” ». Lumières Du Nord, édité par Samuel Gras et Anne-Marie Legaré, Presses universitaires du Septentrion, 2021, https://doi.org/10.4000/books.septentrion.137072.

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    Gras, Samuel, et Anne-Marie Legaré, éd. Lumières du Nord. Villeneuve d’Ascq: Presses universitaires du Septentrion, 2021. doi:10.4000/books.septentrion.137012.
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