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Notes
Any manuscript in the tradition is either (a) lost and without extant progeny, (b) a lost manuscript of which one direct copy survives or leaves extant progeny, (c) a lost manuscript of which two or more direct copies survive or leave extant progeny, or (d) extant. Any line of the stemma joins two manuscripts of types (c-d), and conceals any number of manuscripts of type (b), whose errors are indistinguishable from errors of the manuscript at the bottom of the line. Among the manuscripts along and at the bottom of the line, one identifiable error arising in any of them, is all that (v) and (vi) require.
The 'ancestors' and 'descendants' of a manuscript are here defined to include the manuscript itself.
The above procedure is due to J. Froger, La critique des textes et son automatisation (Paris 1968), p. 74, though Froger does not normally apply it to error sets. Equivalently, Greg (pp. 45 ff) would nest the error sets, in the form [(A)(B)] [C(D)], and draw a stemma showing an exclusive common ancestor for every bracketed group and no other.
This rendering of Froger's term "enchaînement" (p. 44) appears in D. Najock's article cited in n. 50.
A case noted by Greg is the "ambiguity of three texts" (p. 21). A general explanation (not supplied by Froger) of the ambiguity of every pattern, however complex, of agreement and disagreement is as follows. When a relevant manuscript errs, the line above (or containing) it is severed, so that the stemma divides in two; a three-way split results from simultaneous errors that sever two lines; and so on. Now if the orientation is changed, the new stemma will generate the same splits, in the event of error(s) in the manuscript(s) at the lower end(s) of the same line(s).
Storia della tradizione e critica del testo (Florence, 19522), p. 126. With n manuscripts the total number of possible error sets is (2n-2) if the tradition is uncontaminated but (2n-2) if it is totally open.
"La tradition manuscrite du Lai de l'Ombre", Romania, LIV (1928), 161-196, 321-356: 340. These are just two (nos. 1 and 5) of eleven pedigrees which, Bédier claimed, were all admitted by the textual evidence. The other nine, however, presuppose a multiple original or different verdicts on truth and error, against assumptions (i) and (vi) above.
M.P. Weitzman, "Computer Simulation of the Development of Manuscript Traditions", ALLC (= Association for Literary and Linguistic Computing) Bulletin, X (1982), 55-59.
For example, the errors of ABCG may be due not to the inferred ancestor w (fig. 3a) but to the different genealogy of fig. 3b.
If Froger's method of construction was used, we may have to re-phrase: "part of the superior group has been known elsewhere to preserve the truth against the inferior group among others". In fig. 2d, for example, an error in A may not have been identified, but, given a split A:BCD, we may prefer BCD on the grounds that (i) CD alone are sometimes correct against A and B, and (ii) no determinate passage suggests that BCD err against A.
One can readily check that Bédier's alternative pedigrees make no difference to the evaluative policy. In fig. 3b, for example, one would still hesitate before ABCG:DE, prefer ABDE to CG, and so on.
M. Bévenot, The Tradition of Manuscripts: A Study in the Transmission of St. Cyprian's Treatises (1961), pp. 96-123.
One could occasionally invoke coincidence, or suppose that ABCD derived from a faulty archetype which either AB or CD corrected by conjecture, but generally agreement must go back to a common source on which the remaining manuscripts do not wholly depend.
This distinction is due to S. Timpanaro, La genesi del metodo del Lachmann (Padua, 19812), pp. 143 ff.
For example, in a model tradition of twenty-two manuscripts invented by Quentin (Mémoire, pp. 213 ff), EK agree 17 times against L, EL 13 times against K and LK twice against E. Yet E, which shows a quasi-zero, is in no way intermediary between KL. For the genealogy see fig. 28 below.
"The Families of Vulgate Manuscripts in the Pentateuch", Revue Bénédictine, XXXVII (1925), 5-46, 365-403: 5n,6.
E. C. Colwell, Studies in Methodology in Textual Criticism of the New Testament (Leyden, 1969), p. 77 (citing Dr W. N. Lyons's investigation).
"Premiers essais de solution algorithmique des problèmes de contamination dans la Chanson de Roland", in Actes du Sixième Congrès International de la Société Rencesuals (Aix-en-Provence 1974), pp. 109-146. Zarri admits that the reduction resembles a "coup de pouce" (p. 126). The thirteen variants are listed on pp. 135 f.
"Une étude quentinienne sur la tradition manuscrite de la Copa", Revue: LASLA (= Laboratoire d'Analyse Statistique des Langues Anciennes, in conjunction with the International Organization for Ancient Languages Analysis by Computer), 1974, no. 1, pp. 1-16.
If the lowest manuscript never erred, an additional zero would stand in BD against C in the first case, and in AC against D in the second.
"The recovery of trees from measures of dissimilarity", in F. R. Hodson et al. (ed.), Mathematics in the Archaeological and Historical Sciences (Edinburgh, 1971), pp. 387-395.
"Principles and Modifications of Local Genealogical Algorithms in Textual History", Computers and the Humanities, XIV (1980), 171-179.
Bévenot (see n. 15), pp. 96-97. The majority reading is cited. No. 3 concerns the suffix; the first letter is the subject of another variant (c/g).
"Textual Analysis: A Consideration of some Questions raised by M.P. Weitzman", in ibid., XXIX (1979), 355-359.
"Clustering Variants in the Lai de l'Ombre Manuscripts: Techniques and Principles", ALLC Journal, III (1982), 1-8. The index between two groups of m and n manuscripts respectively may be defined as either the greatest, the average or the least, of the mn indices for all the pairs that are divided between them.
Galloway, p. 7; F. G. Berghaus, "Remarques sur la validité de différentes méthodes de groupement automatique . . ." in J. Glénisson et al. (ed.), La pratique des ordinateurs dans la critique des textes (CNRS, Paris, 1979), pp. 97-111. P. Tombeur, "La génération automatique d'un stemma codicum" (ibid., pp. 163-183) considers his own trees historically significant if not perfectly accurate (pp. 169 f), but an appendix by J.-C. Boulanger emphasises that the tree "ne constitue pas un stemma en tant que tel" (p. 177).
"Fundamentals of a Formal Theory of Manuscript Classification and Genealogy", in La pratique (see n. 36), pp. 193-205.
A better index would have been v, which gives stemmata that in simple uncontaminated traditions are accurate but elsewhere founder on the objections of §2.3.
"Stemmatisierungsversuche zur Überlieferung des Sentenzenkommentars des Gregor von Rimini", ALLC Bulletin, X (1983), 95 f.
P. Canivet and P. Malvaux, "La tradition manuscrite du IIερigragr Τeecirgrς θεiacugrας asmogrγáπης", Byzantion, XXXIV (1964), 385-413: 390-404.
For consistency the distinctive readings of sub-groups (eleven for CHP, eleven for ET, etc.) should also have been excluded.
Pp. 407 (1501 B 11f etc.), 410 (1509 D 13), 411 (1504 C 5—with reserve). Furthermore, in a split F:CHP:ETN:QGWAZYBR Canivet followed F (p. 405).
One reason that Malvaux found GQW closer to CFHP than to AYZBRENT is that the distinctive readings of CFHP had been removed, while those of AYZBRENT remained.
The only divergence from Canivet is at 1505 D 8f (p. 411), where the longer text of FCHP AZY now has priority. It agrees with 2 Cor. 5:14 and Theodoret's commentary thereon (Migne, Patrologia Graeca, LXXXII, 409 B 10-11, misquoted by Canivet); its briefer rivals can be attributed to eye-skip.
"Les états du texte d'un Herbier médiéval: Essai de classement automatique", Revue: LASLA (1980), no. 2, pp. 15-58; see especially pp. 24f, 33ff.
"A Taxonomic Study of the Manuscript Tradition of Juvenal", Museum Helveticum, XXV (1968), 101-138; "Numerical Taxonomy and some Primary Manuscripts of the Gospels", Journal of Theological Studies, XX (1969), 389-406. The arrangement for Juvenal was obtained by trial and error (p. 123), and that for the Gospels by a method devised by Mr. J. R. McKenzie (p. 400).
Abbaye Saint-Pierre de Solesmes, Le Graduel Romain: Edition Critique, IV/1 (1960), opposite pp. 152, 213 etc. See also Froger (n. 4 above), pp. 129-136.
See the combined geographical and textual map at the end of vol. IV/1, and, on evaluation, vol. IV/2 (1962), pp. 38 ff.
"Automatic Classification of Texts by Methods of Multivariate Statistics", Revue: LASLA (1973), no. 2, pp. 31-54.
"Classification des états d'un texte, mathématiques et informatique", Revue d'Histoire des Textes, V (1975), 249-309: 284 ff.
"Le classement des manuscrits par l'analyse factorielle", in ibid., pp. 311-330: fig. 5 and p. 322. Elsewhere (fig. 9) he adds a third dimension, in which H stands apart from the rest; its biblical citations are conformed to some Old Latin version (pp. 320 ff).
"Non-stemmatic Classification of Manuscripts by Computer Methods", in La pratique (see n. 36), pp. 73-86. On Griffith's maps, each distance, if all dimensions were retained, would equal not the number of textual divergences, as he states on p. 78, but the square root of twice that number.
This criticism applies equally to the present writer's intuitive interpretations of textual maps in "The Tradition of Manuscripts: A New Approach", Heythrop Journal, XIX (1978), 28-45.
"The Preparation of a Critical Edition Illustrated by the Manuscripts of St. Cyprian", in Studia Patristica, X = Texte und Untersuchungen zur Geschichte der altchristlichen Literatur, CVII (Berlin, 1970), 3-8:7. No two team members shared more than twelve errors (The Tradition, p. 126).
Ibid., p. 43. "Ancient" means "true, and not found by conjecture, or else attested by an ancient source unavailable to the scribes".
The statistics of common error sometimes yield a "serviceable" stemma for a few of the manuscripts, as West shows (pp. 39f), but not in traditions as complicated as Cyprian's.
Pasquali (see n. 9), pp. 211 ff; R. D. Dawe, The Collation and Investigation of Manuscripts of Aeschylus (1964), Ch. 5.
The modification is for the sake of the theory here developed; the original definition remains ideal for its own purpose, viz the selection of manuscripts for the apparatus criticus.
In fact coincidence and conjecture (classed under scribal behaviour) can have the same result (§1.1) as contamination (here termed genealogical) and increase team size. Ideally, cases of coincidence and conjecture are eliminated.
West, "Tragica I", Bulletin of the Institute of Classical Studies, XXIV (1977), 89-103, argues for eleven; Dawe (see n. 59) and D. Page, "Notes on Manuscripts of Aeschylus" in J. L. Heller (ed.), Serta Turyniana (1974), pp. 227-238, together reach about twenty.
Similarly Froger (see n. 4), pp. 117ff. A two-way split between separate errors, such as would result if ω and D erred separately (whence separate errors in ABC, which are no genealogical family, and in D), similarly deserves exclusion.
These examples come from Greg (see n. 3), pp. 34-39, though Greg's approach is more elaborate and yields different results.
It is worth checking the few errors ascribed to the preferred group. If these prove doubtful, the chance element disappears.
A less than overwhelming difference would not decide the issue. H. Fränkel, Einleitung zur kritischen Ausgabe der Argonautika des Apollonios (Göttingen, 1964), pp. 132 f, considers two manuscripts (GL) which, over the determinate passages where they diverge, err respectively 62% and 38% of the time. L is the more reliable but, Fränkel observes, the policy of following L in all indeterminate passages would exaggerate the difference in the error frequencies. The greater the imbalance, however, the less serious the exaggeration.
More generally, consider any set of at least three manuscripts. Suppose that every possible group which can be formed from that set and whose size is an even number shows one exclusive error. Then the statistics remain unchanged if "even" is replaced by "odd".
Where all the manuscripts are divided between separate errors, the 'best' reading could be any of them indifferently.
The procedure here used, called 'Minissa', was developed by E. E. Roskam and J. C. Lingoes, A Mathematical and Empirical Analysis of Two Dimensional Scaling Algorithms = Psychometrika, XXXVIII (1973), monograph supplement. A computer programme is included in Edinburgh University's MDS(X) series.
In contrast, MDS generates the 'best-fitting' map in however many dimensions we care to specify in advance (in this case, two).
Monat, using factor analysis, had to add lacunose witnesses to the map separately (see n. 52; p. 316). Again, Griffith was forced, when one of the manuscripts in his study of Juvenal broke off, to compile separate maps for the sections before and after (see n. 53; p. 80).
Unique errors in (say) A affect neither side; their contributions to 'no. of errors in A' and 'no. of divergences between AB' cancel.
Theoretically the result could be negative (and interpreted as zero). With one determinate passage where AB are correct against other witnesses, and one indeterminate passage where AB disagree, the formula gives 1/2(0+0-50) = -25. Note that three percentage distances not based on the same field of variants need not obey the triangular inequality (that none can exceed the sum of the other two); hence the possibility that d(A,ω) + d(B,ω) - d (A,B)<o.
Unless all four points coincide, or unless we invoke complex numbers in three dimensions, e.g. ω = (o,o,o), A = (100/3,o,o), B = 100/3 (-1,i,1), C = 100/3 (-1,i,-1).
The scale, less important than the shape of the map, is chosen to equate the totals of the textual and map distances.
In the terms of §5.1, the best text recoverable from ABC (occupying the central point of the map) is also a mixture of AC alone; hence B cannot prevail over the agreement of AC.
This site for α, the supposed ancestor, ensures that the paths ωαA, ωαB and AαB all embrace obtuse angles, as would be expected if such an ancestor actually existed. The paths ωαA and ωαB would ideally be straight, as both A and B descend from α; but as straight lines (or rather a single line) would falsely suggest that A descended from B or vice versa, the two paths would bend away from each other (cf fig. 23b) and each include an obtuse angle. Again, as α's text could be made up from A and B, it should ideally lie along the line joining them, but in practice the angle AαB too would be obtuse.
Similarly Najock (see n. 50), pp. 51ff, found factor analysis inapplicable when four or more manuscripts derived independently from the original.
Called 'stress' and 'coefficient of alienation'; see Lingoes and Roskam (n. 69 above), pp. 11, 21.
Drawn freely from two alternative versions in Migne, Patrologia Latina, XCIV, 1141 f. See Quentin (op. cit. in n. 18), pp. 213-218.
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