^{page 133 note 1} B.S.A. xxi. 125–147.

^{page 133 note 2} Riemann, H., die byz. Notenschrift, pp. 12–15Google Scholar, assumes a fundamental scale in conformity with the above. Gastoué, , Introduction à la Paléographié Musicale Byzantine (Paris, 1907), p. 31Google Scholar; Fleischer, Neumenstudien, T. 3, Chapter V.; Rebours, , Traité de Psaltique, App. III., pp. 276 ff.Google Scholar, are all in substantial agreement. Gaisser, as will be seen, inverts the order of the modes; but this does not change their essential character.

The table above given will be found in Neale, and Hatherley, , Hymns of the Eastern Church with Music, p. xxxi.Google Scholar The arguments are well summed up by Fleischer, pp. 42 ff.

^{page 134 note 1} One of these examples I published with the Byzantine notation in Mus. Antiquary, 1911; a very similar piece is given by Fleischer, op. cit. Facs. p. 2.

^{page 136 note 1} Op. cit. Facs. p. 7 he begins Mode I. from a, Mode II. from e, etc., just as we would recommend to suit the compass of the voice.

^{page 136 note 2} Op. cit. § 1. In Byz. Zeitschr. xx. pp. 433 ff. I have referred to some of the errors in Riemann's assumption. I would again strongly protest against his idea that the plagal modes started one note below the corresponding authentic: such a view is against all evidence of manu script usage.

^{page 136 note 3} Op. cit. p. 27. The fact that Gastoué does not transcribe all the facsimiles that he gives and fails to supply the originals of most of his versions prevents us from testing his theory in detail.

^{page 136 note 4} Op. cit. p. 47.

^{page 137 note 1} Paranikas, M. in Ἑλλ. Φιλ. Συλλ. κά 167Google Scholar publishes the example here used, but gives no transcription.

^{page 137 note 2} In each case we begin in the mode first mentioned and reach the Finalis described as ‘mediant.’

^{page 138 note 1} Vocative of ἄναξ.

^{page 138 note 2} This question has been discussed by Fleischer, loc. cit., at full length. Rebours, op. cit. pp. 279 ff., also gives many data for the mediaeval practice with regard to this matter. For the relations between the Byzantine and ancient Greek formulae, see Riemann, , Zeitschr. d. internat. Musikgesellsch. 1913, p. 273.Google Scholar Too much stress ought not perhaps to be laid on the survival of formulae so easily corrupted. But the result of Riemann's acute observations strengthens the case for the view here adopted.

Some mediaeval exercises on these formulae are given both by Rebours, loc. cit., and also by Fleischer, App. C, p. 3 seqq. Cf. also Gastoué, op. cit. p. 29.

The fact that the Gregorian modes were also enumerated by the Greek ordinal numbers, protus, deuterus, etc., is another proof of their similarity to the Byzantine modes.

^{page 138 note 3} See his works La Musiqne ecclés. gr. d'après la Tradition; and Les Heirmoi de Pâques.

^{page 138 note 4} See Rassegna Gregoriana, Fase. 9–10, 1905, p, 5. The Graeco-Albanian hymns are in many cases of great beauty and well worth preserving.

^{page 138 note 5} Slavonic versions of the Easter Canon are given in Gaisser's Heirmoi de Pâques, pp. 18 etc.

^{page 139 note 1} Riemann, , d. byz. Notenschr., p. 46Google Scholar, protests against Gaisser's theory, but does not refute it in detail.

^{page 139 note 2} The discrepancies between mediaeval accounts of the modes are well displayed in the table given by W. Christ and Paranikas, , Anthol. p. cxx.Google Scholar This should convince anyone of the futility of basing any argument on such names. Riemann, op. cit. p. 2, also discusses the matter. His view of the Martyriae on p. 5 is mistaken, as I have tried to prove in Byz. Zeitschr. xx. p. 433.

^{page 139 note 3} Apparently ΤΩ would have meant g, not e, a further argument against the traditional explanation.

^{page 140 note 1} B.S.A. xix. 101.

^{page 141 note 1} The ingenious pleadings of Riemann on this point, (die byz. Notenschr., pp. 11 ff.), seem to me entirely wide of the mark. In the passages cited by him from Fleischer's, Neumenstudien (Riemann, p. 14)Google Scholar a confusion between the modulants of Modes I. and III. invalidates the argument.

^{page 141 note 2} Op. cit. 28, etc.

^{page 141 note 3} This is denied by one Greek theorist, Margantes, Θεωρητικὴ καὶ Πρακτικὴ ᾿Εκκλ. Μουσική Constantinople, 1851, who holds that the Greek scales use only European intervals. But the view of Chrysanthus (founder of the modern system) was generally accepted in the Levant, until more recent western influence came in.

^{page 142 note 1} I have generally followed Chrysanthus, the author of the modem notation. See his Θεωρητικὸν μέγα τῆς μουσικῆς (Trieste, 1S32: reprint, Athens, 1911.)

^{page 145 note 1} I.e. hymns in quick time without florid passages.

^{page 146 note 1} ῾ Ιερὰ ῾Ψμνῳδία p. 208.

^{page 146 note 2} Traité de Psaltique, pp. 115–119.

^{page 147 note 1} Δοκίμιον ἐκκλης. μελῶν Athens, 1856.

^{page 147 note a} Op. cit. p. 84.

^{page 147 note 8} I.M.G. Sammelbände (Quarterly Mag. of Internat. Mus. Soc.), year XV. Pt. 1, p. 1.

^{page 147 note 4} Kiesewetter, R. G., d. Musik d. Araber.

^{page 147 note 6} Chilesotti, O., I.M.G. Sammelbände, year III. p. 595.Google Scholar

^{page 147 note 3} Thibaut, J., Revue Musicale, S.I.M., 15th Feb. 1910 (French section of Internat. Mus. Soc.

^{page 148 note 1} For this musician (who died in 1777, after a brilliant musical career at Constantinople and elsewhere) see Papadopoulos, G., Συμβολαὶ είς τὴν ‘Ιστορίαν τῆς καθ' ήμᾶς έκκλ. Μουσικῆς, 318 ff.Google Scholar The various stories told of him all point to the intimate connexion between Byzantine and Oriental music at that epoch.

^{page 149 note 1} Sitzungsberichte d. k. bayerischen Akademie d. Wissenschaften, phil.-hist. Klasse, 1870, vol. ii. pp. 241–270. (A lucid and valuable study.) In the Appendices W. Christ published the Papadiké, from a Vienna MS., but-failed to discover in it the key to the Round System of notation.

^{page 149 note 2} Παχτικός, Γ. Α. 260 Δημῴδη Ἑλληνικά Ἄισματα (Athens, 1905).

^{page 149 note 3} Folksongs from Scyros. Δημῴδη Ἄισματα Σκύρου.

^{page 149 note 4} Thus Burgault-Ducoudray (a man of unimpeachable judgment, himself a composer) has edited Greek folksongs (Trente Mélodies Populaires de Grèce, etc.) and states that there are no irrational intervals in them. Pernot, Île de Chio, gives a phonographic series of folksongs from Chios: here too the scales are normal. A few examples noted by Heilig, O., Samtnelbände d. I.M.G. 4th year, 1902–1903, pp. 293 ff.Google Scholar, are similar in character; while a more elaborate collection by L. Bürchner (friend and collaborator of Pachtikos) shews nothing irrational in the tonality. We are not of course doubting the accuracy of so able a musician as M. Psachos, whose examples, from the remote island of Scyros, may well have had peculiarities of their own. (See Bürchner, L., Sammelbände, I.M.G. 3rd year (April–June, 1902), p. 403.Google Scholar)

^{page 150 note 1} Those who heard the lecture-recital of Serbian Folksongs given by Miss V. Edwards at Cambridge at the close of the summer school for Russian studies (Aug. 1916) may have noted the likeness of these songs to those of Greece.

^{page 150 note 2} Another version with different words, v. Pachtikos, p. 54.

^{page 154 note 1} For this MS. see B.S.A. xxi. 134.