The cladogram above (Figure 1) shows the relative similarity of Old English words across the oldest digitized manuscripts of De temporum ratione, chapter 15. The manuscripts were written between 780-836 CE and are the earliest record of Anglo-Saxon month names and calendar terms (Table 1). Descending from a 725 CE original, they contain many spelling variations, with less than 50% consensus in 13 of 30 phrases (Table 2). Since consensus-based reconstruction can also be biased by error propagation, a phylogeny was computed to determine their most likely initial spelling (Table 3):
Excluding capitalizations, nearly half are spelled differently to the 1943 reconstruction[2] and 1999 translation[3] of De temporum ratione. Also interesting is the consistent spelling of lida and trilidi as lfda and trilfdi in only the oldest manuscript (A). This was either a systematic error or the sole instance of the correct spelling. Both options are possible in one model, but the latter requires all other mentions to descend from copy errors. If lfda was correct, it may be related to the Old English word ælfe[4] for the river Elbe. This is supported by the associated Latin translation of navigable[5] and the different initial appearance of i and f. This is unsupported by the lack of a preceding vowel in lfda.
Input data was derived from base transcriptions in plain-text format excluding whitespaces, punctuation, capitalization, and separable latin words. The 30 phrases were considered individually, and all variants present in at least two manuscripts were scored numerically as 0, 1 or NA (Table 4). A neighbor-joining phylogeny was coded in R, with nodes defined as the collective mean of every descendant, and similarity scores as the negative mean absolute difference of each trait. Collective means were used instead of progressive means to limit the bias of individual manuscripts on the reconstructed nodes in situations of close similarity (example FLJM). Mean absolute differences were used instead of Euclidean distances to limit the influence of missing data or NA.
A leave-one-out cross validation for each manuscript (n=13) and trait (n=41) was done to account for individual biases, and repeated after removing 8 redundant traits (1,9,10,11,13,21,27,35) to allow for systematic changes (example uu for u). Each one resulted in the same overall structure of the 4 color-coded groups shown in the cladogram, which are loosely associated with geography and share unique variants. The red Gallo-Romance group (FLJMBI) used hr in hredmonath and hreda, o in ueodmonath, d in the first drimilci, and replaced e with æ and o with u in the first æustur. The green Franconian group (CGE) added u to uueudmonath and uuintirfyllith, and a distal h to trimilchi. The purple Franconian group (HK) added a proximal h to thrimilci. Both Franconian groups used rh in rhedmonath and rheda, and u in ueudmonath. The brown Irish group (AD) shared an absence of h and a near-absence of i to y substitutions in trimilci, trilidi and uintirfillit, and used rh in rheda.
The first two principal components of the numeric dataset excluding NA-containing traits were then graphed to check if the 4 groups showed continuous or discrete variation (Figure 2). A uniform manifold approximation and projection[6] was used to verify same-color clustering across all dimensions (Figure 3).
A second neighbor-joining phylogeny was also coded in R, following the principle of inclusive uncertainty. Each node began as a matrix consisting of all unique non-NA variants of its constituents, and either maintained or expanded uncertainty in non-matching scenarios or else collapsed into strictly matching variants when forming a secondary node. Similarity scores were defined as the percentage of matching traits. This method allows for anachronistic reconstruction unlike the collective-mean phylogeny, but requires a higher trait to sample ratio to resolve nodes that bifurcate close in time, since it is not clearly defined for simultaneously matching clusters. Although it produced the same four color-coded groups, it then encountered the described error matching the green, purple and brown groups. Leave-one-out cross validation of manuscripts produced inconsistent results, and removing the 8 redundant traits resulted in the red group being split, suggesting the model did not fit the data.
Next, the number of internal inconsistencies and unique variants in each manuscript were counted as measures of reliability (Table 5). Although the first measure can be biased by the inconsistency of the source manuscript and the second by a high copy number, they are both proportional to the mutation rate and transmission number. The most reliable manuscript from each group (FGHA) was then used in an inclusive-uncertainty phylogeny, which produced the same branch order seen in the collective-mean approach.
A third neighbor-joining phylogeny using progressive means and absolute differences was also performed. This phylogeny maintained the four color-coded groups, but joined brown to green and purple before red. Leave-one-out cross validation of manuscripts reversed this finding in 5 of 13 cases. Removing redundant traits also reversed the initial finding, and continued to produce the same configuration as the collective-mean phylogeny in 12 of 13 leave-one-out cross validations. The collective mean approach was probably most reliable because some manuscripts may have been copied from the same source, making their precise chronological order less significant than their overall average trait values, and because it considers the rarity of variants rather than treating all possibilites equally.
Three approaches were used to determine the most parsimonious variants of the root node (Table 6), all following the phylogeny produced by collective means. The first used all manuscripts individually (n=13), the second used all variants in each manuscript group (n=4), and the third used only the most reliable manuscript from each group (n=4). Each result shared at least one variant at every trait, however their intersection maintained ambiguity in 6 traits. Two traits (20 & 24) were resolved by comparison to similar traits (6,32 & 14,39), one (30) by considering a previously unclassified unique variant (u after t before r in phrase 6), and the remaining 3 (15,25,40) by considering terminal d a substitute for th in manuscript A (see phrases 11,28). In the third approach where A was the only representative of its group, all consistent unique variants were also possible root variants: lfda (n=5), uintirfyllid (n=3), modronecht (n=1), eostree (n=1).
Overall, the main limitations of these methods are that reconstruction is limited to the most recent common ancestor, which may not be the initial 725 CE draft, and that classification of traits involves some degree of interpretation. Next steps would be to include the 3 undigitized same-period manuscripts when available, as well as expanding the date range to include other 9th century manuscripts.[7] To compensate for the higher sample number, the entirety of chapter 15 should be transcribed and converted into variant format, not just the Old English words. Edit transcriptions could also be used as potentially independent samples, and models expanded to allow for hybridization scenarios. Additionally, transition likelihoods between variants to convert them to n-dimensional space could be applied (example Δ hred-hered < Δ rhed-hered).
Table 1. ^ Manuscripts in phylogeny
Table 2. ^ Old English transcripts
Table 4. ^ Variant assignments
Table 5. ^ Internal inconsistencies (α) and unique variants (β)
Table 6. ^ Root variant reconstructions (R1-3), intersection (R0) and resolution (R)
1. ^ The initial appearance is based on the alphabet used in the earliest surviving fragment of De temporum ratione (725 CE), shelfmark Hs-4262 in the Universitäts- und Landesbibliothek Darmstadt.
2. ^ In Bedae Opera de temporibus (Jones 1943), pages 211-212: mona, monath, giuli, solmonath, hredmonath, eosturmonath, thrimilchi, lida, vveodmonath, halegmonath, vvinterfilleth, blodmonath, modranect, thrilidi, Hreda, Eostre. Digitized copy.
3. ^ In Bede The Reckoning of Time (Wallis 1999), pages 53-54: mona, monath, Giuli, Solmonath, Hrethmonath, Eosturmonath, Thrimilchi, Litha, Weodmonath, Halegmonath, Winterfilleth, Blodmonath, Modranecht, Thrilithi, Hretha, Eostre. Digitized copy.
4. ^ First attested in an Old English adaptation of Historia adversus paganos (early 9th century) on folio 7v, shelfmark Add MS 47967 in the British Library.
5. ^ In De temporum ratione (780-820 CE) on folio 3v, shelfmark Cod. 15298 in the Österreichische Nationalbibliothek.
6. ^ R package umap based on UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (McInnes 2018).
7. ^ De temporum ratione manuscripts reviewed here.
Archived on 2020-07-24.
| Phrase | Association | Index | Appearance[1] |
| mona | moon | B1 |  |
| monath | month | A2 |  |
| giuli | December/January | A3 |  |
| solmonath | February | A4 |  |
| rhedmonath | March | A5 |  |
| eosturmonath | April | C6 |  |
| trimilci | May | A7 |  |
| lida | June/July | B8 |  |
| ueodmonath | August | B10 |  |
| halegmonath | September | B11 |  |
| uintirfyllith | October | B12 |  |
| blotmonath | November | B13 |  |
| modranect | midwinter night | B15 |  |
| trilidi | intercalary year | D17 |  |
| rheda | March goddess | A22 |  |
| eostre | April goddess | D24 |  |
Excluding capitalizations, nearly half are spelled differently to the 1943 reconstruction[2] and 1999 translation[3] of De temporum ratione. Also interesting is the consistent spelling of lida and trilidi as lfda and trilfdi in only the oldest manuscript (A). This was either a systematic error or the sole instance of the correct spelling. Both options are possible in one model, but the latter requires all other mentions to descend from copy errors. If lfda was correct, it may be related to the Old English word ælfe[4] for the river Elbe. This is supported by the associated Latin translation of navigable[5] and the different initial appearance of i and f. This is unsupported by the lack of a preceding vowel in lfda.
Input data was derived from base transcriptions in plain-text format excluding whitespaces, punctuation, capitalization, and separable latin words. The 30 phrases were considered individually, and all variants present in at least two manuscripts were scored numerically as 0, 1 or NA (Table 4). A neighbor-joining phylogeny was coded in R, with nodes defined as the collective mean of every descendant, and similarity scores as the negative mean absolute difference of each trait. Collective means were used instead of progressive means to limit the bias of individual manuscripts on the reconstructed nodes in situations of close similarity (example FLJM). Mean absolute differences were used instead of Euclidean distances to limit the influence of missing data or NA.
A leave-one-out cross validation for each manuscript (n=13) and trait (n=41) was done to account for individual biases, and repeated after removing 8 redundant traits (1,9,10,11,13,21,27,35) to allow for systematic changes (example uu for u). Each one resulted in the same overall structure of the 4 color-coded groups shown in the cladogram, which are loosely associated with geography and share unique variants. The red Gallo-Romance group (FLJMBI) used hr in hredmonath and hreda, o in ueodmonath, d in the first drimilci, and replaced e with æ and o with u in the first æustur. The green Franconian group (CGE) added u to uueudmonath and uuintirfyllith, and a distal h to trimilchi. The purple Franconian group (HK) added a proximal h to thrimilci. Both Franconian groups used rh in rhedmonath and rheda, and u in ueudmonath. The brown Irish group (AD) shared an absence of h and a near-absence of i to y substitutions in trimilci, trilidi and uintirfillit, and used rh in rheda.
The first two principal components of the numeric dataset excluding NA-containing traits were then graphed to check if the 4 groups showed continuous or discrete variation (Figure 2). A uniform manifold approximation and projection[6] was used to verify same-color clustering across all dimensions (Figure 3).
 |  |
A second neighbor-joining phylogeny was also coded in R, following the principle of inclusive uncertainty. Each node began as a matrix consisting of all unique non-NA variants of its constituents, and either maintained or expanded uncertainty in non-matching scenarios or else collapsed into strictly matching variants when forming a secondary node. Similarity scores were defined as the percentage of matching traits. This method allows for anachronistic reconstruction unlike the collective-mean phylogeny, but requires a higher trait to sample ratio to resolve nodes that bifurcate close in time, since it is not clearly defined for simultaneously matching clusters. Although it produced the same four color-coded groups, it then encountered the described error matching the green, purple and brown groups. Leave-one-out cross validation of manuscripts produced inconsistent results, and removing the 8 redundant traits resulted in the red group being split, suggesting the model did not fit the data.
Next, the number of internal inconsistencies and unique variants in each manuscript were counted as measures of reliability (Table 5). Although the first measure can be biased by the inconsistency of the source manuscript and the second by a high copy number, they are both proportional to the mutation rate and transmission number. The most reliable manuscript from each group (FGHA) was then used in an inclusive-uncertainty phylogeny, which produced the same branch order seen in the collective-mean approach.
A third neighbor-joining phylogeny using progressive means and absolute differences was also performed. This phylogeny maintained the four color-coded groups, but joined brown to green and purple before red. Leave-one-out cross validation of manuscripts reversed this finding in 5 of 13 cases. Removing redundant traits also reversed the initial finding, and continued to produce the same configuration as the collective-mean phylogeny in 12 of 13 leave-one-out cross validations. The collective mean approach was probably most reliable because some manuscripts may have been copied from the same source, making their precise chronological order less significant than their overall average trait values, and because it considers the rarity of variants rather than treating all possibilites equally.
Three approaches were used to determine the most parsimonious variants of the root node (Table 6), all following the phylogeny produced by collective means. The first used all manuscripts individually (n=13), the second used all variants in each manuscript group (n=4), and the third used only the most reliable manuscript from each group (n=4). Each result shared at least one variant at every trait, however their intersection maintained ambiguity in 6 traits. Two traits (20 & 24) were resolved by comparison to similar traits (6,32 & 14,39), one (30) by considering a previously unclassified unique variant (u after t before r in phrase 6), and the remaining 3 (15,25,40) by considering terminal d a substitute for th in manuscript A (see phrases 11,28). In the third approach where A was the only representative of its group, all consistent unique variants were also possible root variants: lfda (n=5), uintirfyllid (n=3), modronecht (n=1), eostree (n=1).
Overall, the main limitations of these methods are that reconstruction is limited to the most recent common ancestor, which may not be the initial 725 CE draft, and that classification of traits involves some degree of interpretation. Next steps would be to include the 3 undigitized same-period manuscripts when available, as well as expanding the date range to include other 9th century manuscripts.[7] To compensate for the higher sample number, the entirety of chapter 15 should be transcribed and converted into variant format, not just the Old English words. Edit transcriptions could also be used as potentially independent samples, and models expanded to allow for hybridization scenarios. Additionally, transition likelihoods between variants to convert them to n-dimensional space could be applied (example Δ hred-hered < Δ rhed-hered).
Materials
Table 1. ^ Manuscripts in phylogeny
| Ms | Library | Shelfmark | Folios | Date (bold link) | Reference | BODT |
| A | ÖNB Wien | Cod. 15298 | 3v | 780-820 CE | CLA 1551 | - |
| B | UB Würzburg | M.p.th.f.46 | 48r-48v | 792-807 CE | CLA 1413 | 103 |
| C | EDDB Köln | Cod. 103 | 80r-81r | 801-810 CE | - | 2 |
| D | EDDB Köln | Cod. 83-II | 104r-104v | 805 CE | SCHH 6 | 32 |
| E | BA Vaticana | Pal. lat. 1448 | 49r | 810 CE | DQH 1448 | 90 |
| F | SB St. Gallen | Cod. Sang. 251 | 69-70 | 810-820 CE | BStK 210 | 10 |
| G | BA Vaticana | Pal. lat. 1449 | 52v-53v | 812 CE | DQH 1449 | 91 |
| H | BSB München | Clm 14725 | 63v-65r | 1st quarter 9th century | VKHBS 245 | 7 |
| I | UB Leiden | SCA 28 | 58v-59r | ~816 CE | - | 42 |
| J | BNF Paris | Latin 13013 | 71r-71v | 1st third 9th century | - | 70 |
| K | UB Kassel | 2° Ms. astron. 2 | 24r-24v | 1st third & mid 9th century | BStK 325 | 3 |
| L | B Genève | Ms. lat. 50 | 60v-61r | ~825 C | - | 12 |
| M | VBA Milano | D 30 inf. | 47v-48r | ~836 CE | - | 14 |
Table 2. ^ Old English transcripts
| Phrase | A | B | C | D | E | F | G | H | I | J | K | L | M |
| 1 | _a | mona | mona | maon | mona | mona | mona | mona | mona | moena | mona | mona | mona |
| 2 | monath | monath | monath | monath | monath | monath | monath | monatis | monath | monath | monath | monath | monath |
| 3 | giuli | giuli | giuli | giuli | guli | giuli | giuli | giuli | giul_ | giuli | giuli | giuli | giuli |
| 4 | solmonath | solmonath | solmonath | solmanath | solmonath | solmonath | solmonath | solmonath | solmonath | solmonath | solmonath | solmonath | solmonath |
| 5 | rhed_nath | hredmonath | rehdmonath | remmonath | redmonath | hredmonath | rethmonath | rhedmonath | hredmonath | heredmonath | rhedmonath | hredmonath | redmonath |
| 6 | eustormonath | aesturmunath | eosturmonath | eosturmanath | eosturmonath | aeusturmonath | eosturmonath | eosturmonath | esturmunath | aeusturmonath | eosturmonath | eusturmonath | aeusturmonath |
| 7 | trimilci | drymilci | trimilchi | trimilci | trimilchi | drimylci | trimilchi | thrimilci | drimilci | drimylci | thrimilci | drimylci | drymylci |
| 8 | lfda | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida |
| 9 | lfda | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida |
| 10 | ueodmonad | ueodmonath | uueudmonath | ueutmonath | uueudmonath | ueodmonath | uueudmonath | ueudmonath | ueodmonath | ueodmonath | ueudmonath | ueodmonath | uuaeodmonath |
| 11 | halegmonath | halegmonath | alegmonath | alegmonath | halegmonath | alegmonath | halegmonath | halegmonath | halegmonath | halegmonath | haleggemonath | alegmonath | halegmonath |
| 12 | _ntirfyllid | uintirfyllith | uuintirfillith | uintirfilit | uuintyrfyllith | uintirfyllith | uuintirfillith | uintirfyllith | uintirfillit | uintirfyllith | uintirfyllith | uintirfyllit | uintirfyllit |
| 13 | blothmonad | blotmonath | blatmonath | blotmonath | blodmonath | blodmonath | blotmonath | blotmonath | blotmanoth | blotmonath | blotmonath | lotmonath | blothmonath |
| 14 | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giuli | giliu |
| 15 | modronecht | modranect | modranect | modranect | moderanea | modranect | modranect | modranect | modranect | modranect | modraneht | modranect | modranect |
| 16 | _fda | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida |
| 17 | trilf_ | thrilidi | thrilidi | trilidi | thrilidi | thrilidi | thrilidi | thrilidi | trhilidi | thrilidi | thrilidi | trilidi | thrylidi |
| 18 | _rfillid | uinthyrfyllth | uuintirfillith | uintirfillit | uuintyrfyllit | uintirfyllith | uuintyrfyllith | uintirfyllith | uinthyrfyllit | uintirfullith | uintirfyllith | uintirfillith | uinturfyllith |
| 19 | gi_li | giuli | giuli | giuli | singuili | giuli | giuli | giuli | giuli | giuli | giuli | gili | giuli |
| 20 | s_nath | solmanoth | solmonath | solmonath | solmonath | solmonath | solmonath | solmanoth | solmonath | solmonath | solmanoth | solmonath | solmonath |
| 21 | rhedmonad | hredmonath | rethmonath | redmonath | redmonath | hredmonath | rhedmonath | rhedmonath | hredmonath | hredmonath | ruedmonath | hredmonath | hredmonath |
| 22 | rheda | hreda | rheda | rheda | rheda | hreda | rehda | rheda | hreda | hreda | rheda | hreda | hreda |
| 23 | eustormo_ath | eosturmonath | eosturmonath | eostormonath | eosturmonath | eosturmonath | eosturmonath | eostrmonath | eosturmunat | eusturmonath | eosturmonath | eosturmonath | eosturmonath |
| 24 | eostree | eostrae | eostrae | eostre | eostrae | eostre | eostrae | eostrae | eostre | euster | eostrae | eostrae | eostre |
| 25 | trimilci | trimylci | trimilchi | trimilci | trimilchi | thrimylci | trimilchr | thrimilci | trimilci | trimilchi | theimilci | thrimilci | thrymilci |
| 26 | lfda | lidaru | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida | lida |
| 27 | ueodmonad | ueothmonath | uueudmonath | neutmonath | ueuudmonath | ueodmonath | uueudmonath | ueudmonath | veodmonath | ueodmonath | ueudmonath | ueodmonath | ueodmanath |
| 28 | halegmonad | halegmonath | halegmonath | halegmonath | halegmonath | halegmonath | halegmonath | halegmonath | halegmo_ath | halegmonath | aligmonath | halegmonath | halegmonath |
| 29 | uintirf_llid | uintirfyllith | uuintyrsyllith | uintirfillit | uuintyrfyllit | uintirfyllith | uuintyrfyllith | uintirfyllith | uinthyrfyllith | uintirfillit | uintirfyllith | uintirfillith | uintirfyllith |
| 30 | blothmonad | blothmonath | blotmonath | blothmonath | blodmonath | blotmonath | blotmonath | blotmonath | blothmonath | blothmonath | blotmonath | blotmonath | hlothmonath |
Table 4. ^ Variant assignments
| Trait | Phrase | Code 1 | Code 0 | A | B | C | D | E | F | G | H | I | J | K | L | M |
| 1 | 5 | h before r | h after r before m | 0 | 1 | 0 | NA | NA | 1 | 0 | 0 | 1 | 1 | 0 | 1 | NA |
| 2 | 6 | a before e | no a before e | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 |
| 3 | 6 | o before r | no o before r | 1 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 |
| 4 | 6 | u after m | no u after m | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 5 | 7 | starts with d | starts with t | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 6 | 7 | h before r | no h before r | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
| 7 | 7 | y before m | no y before m | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 8 | 7 | y after m | no y after m | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 | 1 |
| 9 | 7 | h after c | no h after c | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 10 | 10 | starts with uu | does not start with uu | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 |
| 11 | 10 | o before m | no o before m | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 12 | 11 | starts with h | starts with a | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 13 | 12 | starts with uu | does not start with uu | NA | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 14 | 12 | y after f | no y after f | 1 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 1 | 1 |
| 15 | 12 | ends with h | does not end with h | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 0 | 0 |
| 16 | 13 | d before m | no d before m | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 17 | 13 | h before m | no h before m | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 |
| 18 | 15 | c after e | no c after e | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 |
| 19 | 15 | h before t | no h before t | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
| 20 | 17 | h before l | no h before l | 0 | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 |
| 21 | 18 | starts with uu | does not start with uu | NA | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 22 | 18 | h before r | no h before r | NA | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
| 23 | 18 | y before r | no y before r | NA | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 24 | 18 | y after f | no y after f | 0 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
| 25 | 18 | ends with h | does not end with h | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 0 | 1 | 1 | 1 | 1 |
| 26 | 20 | a before n | no a before n | NA | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 |
| 27 | 21 | h before r | h after r before m | 0 | 1 | 0 | NA | NA | 1 | 0 | 0 | 1 | 1 | NA | 1 | 1 |
| 28 | 22 | h before r | h after r | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 29 | 23 | o before s | no o before s | 0 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 30 | 23 | o after t before r | no o after t before r | 1 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 31 | 24 | a after r | no a after r | 0 | 1 | 1 | 0 | 1 | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 0 |
| 32 | 25 | h before m | no h before m | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 1 |
| 33 | 25 | y after m | no y after m | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
| 34 | 25 | h after c | no h after c | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 0 |
| 35 | 27 | uu before m | no uu before m | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 36 | 27 | o before m | no o before m | 1 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 1 |
| 37 | 29 | starts with uu | does not start with uu | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 0 |
| 38 | 29 | y before r | no y before r | 0 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 0 |
| 39 | 29 | y after f | no y after f | NA | 1 | 1 | 0 | 1 | 1 | 1 | 1 | 1 | 0 | 1 | 0 | 1 |
| 40 | 29 | ends with h | does not end with h | 0 | 1 | 1 | 0 | 0 | 1 | 1 | 1 | 1 | 0 | 1 | 1 | 1 |
| 41 | 30 | h before m | no h before m | 1 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 1 | 1 | 0 | 0 | 1 |
Table 5. ^ Internal inconsistencies (α) and unique variants (β)
| Ms | α | β | mona | (mona)_th | giuli | sol | rhed | eost | (eost)_ur | tri | milci | lid | (lid)_a | ueod | haleg | uintirfyllith | blot | modranect | (trilid)_i | (rhed)_a | (eost)_rae |
| A | 3 | 5 | mona | d th | giuli | sol | rhed | eust eost | or | tri | milci | lfd | a | ueod | haleg | uintirfyllid uintirfillid | bloth | modronecht | NA | a | ree |
| B | 10 | 4 | mona muna mano | th | giuli | sol | hred | aest eost | ur | dry thri tri | milci mylci | lid | a aru | ueod ueoth | haleg | uintirfyllith uinthyrfyllth | blot bloth | modranect | i | a | rae |
| C | 6 | 2 | mona | th | giuli | sol | rehd reth rhed | eost | ur | tri thri | milchi | lid | a | uueud | aleg haleg | uuintirfillith uuintyrsyllith | blat blot | modranect | i | a | rae |
| D | 9 | 5 | maon mona mana | th | giuli | sol | rem red rhed | eost | ur or | tri | milci | lid | a | ueut neut | aleg haleg | uintirfilit uintirfillit | blot bloth | modranect | i | a | re |
| E | 6 | 5 | mona | th | guli giuli singuili | sol | red rhed | eost | ur | tri thri | milchi | lid | a | uueud ueuud | haleg | uuintyrfyllith uuintyrfyllit | blod | moderanea | i | a | rae |
| F | 4 | 1 | mona | th | giuli | sol | hred | aeust eost | ur | dri thri | mylci | lid | a | ueod | aleg haleg | uintirfyllith | blod blot | modranect | i | a | re |
| G | 5 | 1 | mona | th | giuli | sol | reth rhed rehd | eost | ur | tri thri | milchi milchr | lid | a | uueud | haleg | uuintirfillith uuintyrfyllith | blot | modranect | i | a | rae |
| H | 3 | 2 | mona mano | tis th | giuli | sol | rhed | eost | ur r | thri | milci | lid | a | ueud | haleg | uintirfyllith | blot | modranect | i | a | rae |
| I | 10 | 5 | mona muna mano | th t | giuli | sol | hred | est eost | ur | dri trhi tri | milci | lid | a | ueod veod | haleg | uintirfillit uinthyrfyllit uinthyrfyllith | blot bloth | modranect | i | a | re |
| J | 9 | 3 | moena mona | th | giuli | sol | hered hred | aeust eust | ur | dri thri tri | mylci milchi | lid | a | ueod | haleg | uintirfyllith uintirfullith uintirfillit | blot bloth | modranect | i | a | er |
| K | 5 | 4 | mona mano | th | giuli | sol | rhed rued | eost | ur | thri thei | milci | lid | a | ueud | halegge alig | uintirfyllith | blot | modraneht | i | a | rae |
| L | 8 | 3 | mona | th | giuli gili | sol | hred | eust eost | ur | dri tri thri | mylci milci | lid | a | ueod | aleg haleg | uintirfyllit uintirfillith | lot blot | modranect | i | a | rae |
| M | 10 | 6 | mona mana | th | giuli giliu | sol | red hred | aeust eost | ur | dry thry | mylci milci | lid | a | uuaeod ueod | haleg | uintirfyllit uinturfyllith uintirfyllith | bloth hloth | modranect | i | a | re |
Table 6. ^ Root variant reconstructions (R1-3), intersection (R0) and resolution (R)
| Trait | Phrase | Code 1 | Code 0 | R1 | R2 | R3 | R0 | R |
| 1 | 5 | h before r | h after r before m | 0 | 0 | 0 | 0 | 0 |
| 2 | 6 | a before e | no a before e | 0 | 0 | 0 | 0 | 0 |
| 3 | 6 | o before r | no o before r | 1 | 1 | 1 | 1 | 1 |
| 4 | 6 | u after m | no u after m | 0 | 0 | 0 | 0 | 0 |
| 5 | 7 | starts with d | starts with t | 0 | 0 | 0 | 0 | 0 |
| 6 | 7 | h before r | no h before r | 0 | 0 | 0 | 0 | 0 |
| 7 | 7 | y before m | no y before m | 0 | 0 | 0 | 0 | 0 |
| 8 | 7 | y after m | no y after m | 0 | 0 | 0 | 0 | 0 |
| 9 | 7 | h after c | no h after c | 0 | 0 | 0 | 0 | 0 |
| 10 | 10 | starts with uu | does not start with uu | 0 | 0 | 0 | 0 | 0 |
| 11 | 10 | o before m | no o before m | 01 | 01 | 1 | 1 | 1 |
| 12 | 11 | starts with h | starts with a | 1 | 1 | 1 | 1 | 1 |
| 13 | 12 | starts with uu | does not start with uu | 0 | 0 | 0 | 0 | 0 |
| 14 | 12 | y after f | no y after f | 1 | 1 | 1 | 1 | 1 |
| 15 | 12 | ends with h | does not end with h | 01 | 01 | 01 | 01 | 1 |
| 16 | 13 | d before m | no d before m | 0 | 0 | 0 | 0 | 0 |
| 17 | 13 | h before m | no h before m | 0 | 0 | 01 | 0 | 0 |
| 18 | 15 | c after e | no c after e | 1 | 1 | 1 | 1 | 1 |
| 19 | 15 | h before t | no h before t | 0 | 0 | 01 | 0 | 0 |
| 20 | 17 | h before l | no h before l | 01 | 01 | 01 | 01 | 0 |
| 21 | 18 | starts with uu | does not start with uu | 0 | 0 | 0 | 0 | 0 |
| 22 | 18 | h before r | no h before r | 0 | 0 | 0 | 0 | 0 |
| 23 | 18 | y before r | no y before r | 0 | 0 | 0 | 0 | 0 |
| 24 | 18 | y after f | no y after f | 01 | 01 | 01 | 01 | 1 |
| 25 | 18 | ends with h | does not end with h | 01 | 01 | 01 | 01 | 1 |
| 26 | 20 | a before n | no a before n | 0 | 0 | 0 | 0 | 0 |
| 27 | 21 | h before r | h after r before m | 0 | 0 | 0 | 0 | 0 |
| 28 | 22 | h before r | h after r | 0 | 0 | 0 | 0 | 0 |
| 29 | 23 | o before s | no o before s | 1 | 1 | 01 | 1 | 1 |
| 30 | 23 | o after t before r | no o after t before r | 01 | 01 | 01 | 01 | 0 |
| 31 | 24 | a after r | no a after r | 0 | 01 | 0 | 0 | 0 |
| 32 | 25 | h before m | no h before m | 0 | 0 | 01 | 0 | 0 |
| 33 | 25 | y after m | no y after m | 0 | 0 | 0 | 0 | 0 |
| 34 | 25 | h after c | no h after c | 0 | 0 | 0 | 0 | 0 |
| 35 | 27 | uu before m | no uu before m | 0 | 0 | 0 | 0 | 0 |
| 36 | 27 | o before m | no o before m | 01 | 01 | 1 | 1 | 1 |
| 37 | 29 | starts with uu | does not start with uu | 0 | 0 | 0 | 0 | 0 |
| 38 | 29 | y before r | no y before r | 0 | 0 | 0 | 0 | 0 |
| 39 | 29 | y after f | no y after f | 01 | 01 | 1 | 1 | 1 |
| 40 | 29 | ends with h | does not end with h | 01 | 01 | 01 | 01 | 1 |
| 41 | 30 | h before m | no h before m | 1 | 01 | 01 | 1 | 1 |
Notes
1. ^ The initial appearance is based on the alphabet used in the earliest surviving fragment of De temporum ratione (725 CE), shelfmark Hs-4262 in the Universitäts- und Landesbibliothek Darmstadt.
2. ^ In Bedae Opera de temporibus (Jones 1943), pages 211-212: mona, monath, giuli, solmonath, hredmonath, eosturmonath, thrimilchi, lida, vveodmonath, halegmonath, vvinterfilleth, blodmonath, modranect, thrilidi, Hreda, Eostre. Digitized copy.
3. ^ In Bede The Reckoning of Time (Wallis 1999), pages 53-54: mona, monath, Giuli, Solmonath, Hrethmonath, Eosturmonath, Thrimilchi, Litha, Weodmonath, Halegmonath, Winterfilleth, Blodmonath, Modranecht, Thrilithi, Hretha, Eostre. Digitized copy.
4. ^ First attested in an Old English adaptation of Historia adversus paganos (early 9th century) on folio 7v, shelfmark Add MS 47967 in the British Library.
be ƿestan eald seaxum is ælfe muþa
to the west of old saxony is the elbe's mouth
5. ^ In De temporum ratione (780-820 CE) on folio 3v, shelfmark Cod. 15298 in the Österreichische Nationalbibliothek.
lfda dr̄ blandus sū nauigabilis
lfda is called bland or navigable
6. ^ R package umap based on UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction (McInnes 2018).
7. ^ De temporum ratione manuscripts reviewed here.
Archived on 2020-07-24.