"Psellus" Treatise on Music' in Mizler's 'Bibliothek'

‘PSELLUS’ TREATISE ON MUSIC’ ER, LL. AX! Quadrivium.* All of Mizler’s numerous activities were subordinated to his rationalistic ‘main intention...to give to music the full stature of a science, to study its history, and set it IO in order.’ This undertaking did not, however, remain unchallenged. The sensuous approach of the most influential contem- Dr. Lukas Richter porary music theorist, Johann Mattheson, for instance, diverged BERLIN, GERMANY . , . on Psellus’ Treatise on Music’ in Mizler’s ‘Bibliothek’ UNDER the influence of the ideas of the Enlightenment th wasa complete change in the trad itional understandin “of music as a scie nce, a conception on which its educ ational al . had rested since the days of Ancien t Greece.1 From the begin. ning oftates amen century the view prevailed that music is er than an expressi loan The „Musica theoretica had me in the curricula of th of the study of natural science. Now musical practice disappeared also already been neglect ir iversiti i en Toba an from the gym nasia a and Lorenz Christoph Mizler (1711-78 ), whose views w strongly shaped by the rationalisti c philosophy of Chri tian Wolff (1679-1 754), tried, as in his diss ertation ‘Quod musi ca ars sit pars eruditionis philosophiae’ (173 6), to demonstrat th i music was the mathematical elemen t of Philosoph the hi h. est science of all. In other words, Mizler advocated a to. date renewal of music’s former stat us as a component of the |1 L. 1961) Richt pee er,ak Zür Wissen senscha aftslehre von der Musik i beibei Platon und Aristoteles Cf. H. i Hüschen, > article ‘Musik’ i (Berlin, n Musik i in à Geschichte und Gegenwart, 9 (1961), : precially cols, o88ff. and the bibli ography cited there. : oe) ai de geschichte der Universität, ’ Archiv Jür Musikwissenschaft | Im) ee » p. 8ff.; G. Schiine mann, Geschichte } der deutschen Schulmusik J (Leipzig,; is article represents a translation i i published in Beiträge zur Musikwissenscha ft Vern 69), pr enn Wen study are due assist ancetoinProfe ssor prepa ringHeinr an ich Hockk<of the Uni cn Hoe a. nivers ity Pe tions of Illino isVan for hishaak kinds 112 113 greatly from Mizler’s view of music as a ‘sounding mathematics.’ Thus Mattheson’s encyclopedic Der vollkommene Cappellmeister (1739) directed some polemical blows at Mizler, and in the title of the pamphlet Aristoxenis junioris Phtongologia systematica (1748), Mattheson unfurled ‘the name of Aristoxenos as a banner’ against the Pythagoreanism of Mizler (and Leonhard Euler as well).? Mizler expressed his views on the theory of music in the journal, which became the organ of the society he had founded, Neueröffnete Musikalische Bibliothek oder gründliche Nachricht nebst unpartheyischem Urteil von musicalischen Schriften und Büchern, which he published himself from 1736 until 1754. At first it appeared twice yearly, but later, when his difficulties in making a livelihood forced him to move to Poland, at ever longer intervals.® Obsessed with missionary zeal and increasingly isolated, Mizler, as the propagator of a musical view ‘more geometrico’, was not much interested in reporting on actual musical life or in reviewing new publications. He rather concentrated on the presentation of his own theories, but in independent articles, in general reviews of the literature, and even in notes on individual publications. At first he gave preferential treatment to German 4 F. Wöhlke, L. Chr. Mizler, Ein Beitrag zur musikalischen Gelehrtengeschichte des 18. Jahrhunderts [Diss.] (Berlin, 1940), pp. 8ff. and pp. 38ff.; for bibliography cf. H. G. Hoke, ‘Mizler,’ MGG, g (1961), cols. 388f. 5 They included, among others: teaching at the University of Leipzig, theoretical publications (mostly in his own periodicals), and finally the organization of the first genuine musicological society in Germany—the ‘correspondierende Societat der musicalischen Wissenschaften’ (which counted as its members Handel and Bach). Cf. Wöhlke, op. cit., pp. 96f.; also A. Schering, 7. S. Bach und das Musikleben Leipzigs, iii (1941), pp. 193ff.; W. C. de Jong, “Händel, Bach en de Mizlerse Societeit in Leipzig,’ Mens en Melodie, vii (1952), 2. 6 Cited from his autobiography published in Joh. Mattheson’s Grundlage einer Ehrenpforte (Hamburg, 1740, new ed. by M. Schneider, Berlin, 1910), p. 230. ? J. Handschin, Der Toncharakter, eine Einführung in die Tonpsychologie (Zürich, 1948), 177; cf. W. Braun, 7. Mattheson und die Aufklärung [Diss.} (Halle, 1951), pp. 8f.; R. Schäfke, Geschichte der Musikästhetik (Berlin, 1937), pp. 300ff. 8 Wöhlke, op. cit, pp. 18ff. and 86ff. (with citations of contemporary views).

writers on music from the period 1650-1750 and, as Johann Adolf Scheibe said in a review, the personal ‘views [of Mizler the publisher] too strongly penetrate the [original] text’ 9 Later Mizler increasingly reproduced the original Classical sources, with annotations. Already in his preface he had stated his aim ‘to examine the works of the Greek writers on music . . [but] it would be even more useful to translate them verbatim and henceforth to give to our readers one such writer with our annotations as an appendix to each volume.’10 Mizler had recourse to the ancient Greek writers in order to strengthen his own position. For, according to him, they ‘were much more concerned with the origins, relationships, and concordances of notes than our present-day Musici, who cannot really be blamed for not understanding anything about Ancient Greek music, since for such an understanding knowledge of both the Greek language and the mathematical sciences is needed ...1 Mizler realized that for an understanding of Greek music theory a combination of both mathematical and philological knowledge is necessary, the latter being normally inaccessible to a professional musician of his time. Nevertheless Mizler undoubtedly overestimated his own powers when he considered himself equipped for this task. Mizler apparently intended to append complete German translations to the existing editions of Greek writers on music instead of the customary Latin translations. Thus, Mizler hoped, he could exercise some influence on the larger audience of professional musicians and interested laymen.12 He had already furnished a summary translation of the treatises in the collections of Marcus Meibom (Antiguae musicae auctores, Amsterdam, 1652) and of John Wallis (Opera mathematica, III, Oxford 1699),!® together with notes on Aristoxenos (partly from Mei9 J. A. Scheibe, in Hamburgische Berichte von gelehrten Sachen of Pp. 394); see also Wöhlke, op. cit., pp. 20 and 88ff. June 14, 1737 (No. 42 10 L, Chr. Mizler, Musikalische Bibliothek, I, Preface. 1 Jbid., 1/1, p. 2. 12 Jbid,, III /2, p. 200, n. 24. 18 For references to the editorial activities of Meibom and Wallis (beside those contained in the new editions of the nineteenth century), cf. above all R. Schafke Aristides Quintilianus (Berlin, 1937), p. 25f.; I. Düring, ‘Die Harmonielehre des Klaudios Ptolemaios,” Géteborgs Högskolas Arsskrift, XXXVI (1930), fasc. 1 p. xciii. See also G. Fellerer, ‘Zur Erforschung der antiken Musik im 16.—18 Jh ” Jahrbuch Peters, 42 (1936), pp. Bafl. nn 115 ‘PSELLUS’ TREATISE ON MUSIC’ bom’s preface and partly from Suida’s lexicon). According to ly his plan each volume of his journal was to end with a scholar supplement containing an annotated translation of an ancient treatise. The only publication which he completed, however, was that of a Byzantine treatise. Michael Psellus (1018-78), a Platonist philosopher and productive writer of excellent mastery of form and abundant encyclopedic knowledge, enjoyed a reputation which spread from Byzantium into Western Europe.!5 It is, therefore, no accident that sixteenth-century editions of his writings may include a compendium of the four mathematical disciplines (Zévrayua edotvortov eis tag Teoodgas naßnuarızas Eruornuas) which is not correctly attributed to him.16 The first publisher of the treatise, Arsenius, in his Praefatio of 1532 only tentatively ascribed the Syntagma to Psellus. The attribution to Psellus was however adopted in the Paris edition by Bogardus (1545). From that time on Psellus’s name is found in all editions, among which that by Wilhelm Xylander (Basel, ı 556) stands out on account of its valuable critical and exegetical notes to the Latin translation. “Psellus’ treatise on music’ was also published separately in Paris (ed. Vinet, 1557) and in Wittenberg (1560). It started gaining importance from a musicological point of view after its appearance in the appendix to Lampertus Alardus’ work De veterum musica (Schleusingen, 1636, pp. 177-203), in spite of the fact that he used a corrupt text derived from the Paris edition of 1545.17 chen Musik’ 14 ‘Meiboms Vorrede über die Scribenten von der alten Griechis alten Musik der hung Vergleic .. ‘Wallisi. sf; pp. 1/1, , Musikalische Bibliothek i Harmonik mit der zu seiner Zeit,’ Ibid., 1/2, pp. ıfl.; ‘Nachricht von Aristoxen und dessen Leben,’ Ibid., I/3, pp. 1ff. (München, 15 See especially K. Krumbacher, Geschichte der byzantinischen Literatur? pub1897), pp. 439ff.; the monographs by Chr. Zervos and E. Renaud (both passages lished in 1920) and by B. Tatakis (publ. in 1949); also the pertinent ky, in G. Moravesik, Byzantinoturcica, 1 (1958), pp. 437ff.; G. Ostrogors G. Beck, Geschichte des byzantinischen Staates? (München, 1952), pp. 261ff.; H. pp. 538ff. Kirche und theologische Literatur im byzantinischen Reich (München, 1959), m, Quadriviu et Logica Anonymi Heiberg, L. 1 J. by edited edition new A critical . Hist.-filol Selskab. kabernes Videns Danske Kgl. [Det cum scholiis antiquis r in Meddelelser, XV/1] (Copenhagen, 1929). Cf. review by K. Praechte Byzantinische Zeitschrift, 31 (1939 ),PP- 82-90. ‘Antike 17 For a demonstration that Psellus is not the author, see L. Richter, Überlieferungen in der byzantinischen Musiktheorie,’ Deutsches Jahrbuch Musikwissenschaft für 1961,6. Jg. (Leipzig, 1962), pp. 95 and 112 (bibliography,

The treatise on harmony, written in the beginning of the eleventh century and in some manuscripts attributed to a monk named Gregorios Solitarios, deserves attention as the earliest known musical treatise from Byzantium, though eclectic in content.18 It would be too much to expect the rationalist Mizler to comprehend all the special problems involving this treatise, when he included in the third volume of his Musikalische Bibliothek a study entitled “Des Psellus vollständiger kurzer Inbegriff der Musik.’19 The personality of the alleged author was no doubt thought likely to exert a greater attraction on the potential reader than the little-known names of the authors of the truly ancient treatises. The description of the eventful life of Psellus,20 appeared to Mizler an additional inducement for the interested reader to study the didactic treatise that followed. The compendium-like, didactic design of that treatise probably appeared to serve Mizler’s intention of popularizing his views, while its largely arithmetical aspect must have seemed to him an authoritative support for his own philosophical and mathematical tendencies. In a procedure which for his time undoubtedly was very modern, Mizler provided a German translation which was generally fluent and clear and which was printed parallel to the Greek text, and commentary in the form of footnotes. Shunning the corrupt text and often absurd translation of Alardus, Mizler used Xylander’s version (although it too was not a definitive edition by any means), and completed Xylander’s annotations by his own notes. especially C. v. Jan, Musici Scriptores Graeci (Leipzig, 1895), pp. xxxiv ff, Ix ff, Ixx ff). 38 Richter, op. cit., pp. 95ff. (survey of concordances). 19 The title of this treatise, which is listed after the table of contents, is the following: ‘Psellus kurzer Inbegriff der Musik, aus dem Griechischen ins Deutsche übersetzt, mit Xylanders u. L. Mizlers Anmerkungen,’ in Musikalische Bibliothek, IIL/2 (1746), pp. 171-200. 20 ‘Michael Psellus lived at the time of Romanus Diogenes, Emperor of Constantinople, and was well known in the year 1070 A.p. He was a Greek theologian and historian, and beside many other writings, he also compiled this short treatise on music. Psellus was born in Constantinople, of noble parents. He was a teacher of Emperor Michael VII Ducas, as is reported in the chronicle of the monk John Zonaras. But when this emperor was deposed and sent into a monastery, Psellus, his favourite, also had to resign his high positions and become a monk, and as such he lived for about another thirty years...’ Musikalische Bibliothek, IIIa, p. 171, n. 1. (Even the rumour formerly current about an ‘older’ Psellus is found in this note.) ‘PSELLUS’ TREATISE ON MUSIC’ 117 The very first mention of the alleged author, Psellus, is connected with an argumentum e consensu gentium for Mizler’s basic thesis that music is a mathematical discipline. This contention is accompanied by an attack on Mattheson.?! Itis also significant how Mizler, while interpreting music in a strictly rationalistic sense, retraces the argument raised in the prooimion of the treatise, namely that the harmony of the world manifests itself in music.22 Though Mizler is far from providing a critical examination of sources or a historical interpretation of the text, he nevertheless clearly understands that, contrary to modern usage, ‘harmony’ in this context is to be interpreted as a horizontal sequence of notes.23 Yet elsewhere in the text he interprets the intervals in a harmonic (in the modern sense) fashion. 24 While pursuing his secondary aim of advertising his own ideas by using an ancient writer as an authority for those views, he by no means forgets his basic aim of providing easily understandable information about ancient music theory. Besides the interpretation of technical terms which is implied by the choice of words in the translation, he achieves this aim by discussing specific topics. In the case of some matters of importance, such as the catalogue of names of notes (p. 176f.), the composition of intervals (p. 184f.), the sections on modes and tetrachords (p. 197), and on scales (p. 198), Mizler does not give any deeper explanations but refers to earlier systematic descriptions, above all to the article based on John Wallis s ‘Comparison of the Ancient Music and that of the present day (Musikalische Bibliothek, 1/2). Mizler undoubtedly considered Xylander’s mathematical account of the divisibility of the whole tone (p. 178ff.) to be sufficiently exhaustive not to warrant any additional comments. But he personally concerns himself with 21 ‘In his days no one thought of denying that music is a mathematical science or, what amounts to the same, is a part of mathematics, In these our own days, however, Herr Mattheson desires to reverse the matter by stating that mathematics in a way is a part of music. Such a view, however, so far has not found any acceptance by any of our contemporary scholars.’ Ibid. P- 173, n. 1. 22 ‘Now, since music depicts in miniature the very best order which the human mind can envisage, the Ancients were correct in saying that music represents the harmony of the whole structure of the world.’ Jbid., p. 174, n. 2. 28 ‘Psellus here uses the word “harmony” in a meaning different from that in which we understand it today. In his text, the word means “a combination of different tones in accordance with a certain order”, i.e., a ‘‘mode”’, a musical scale, a system.’ Ibid., p. 194, n. 18. 24 See below, p. 125f.

the interpretation of textual passages which were especially attractive to him as a music theorist, namely those dealing with consonant intervals and the numerical ratios contained therein (p. 188ff.). The fact that Mizler also possessed some philological and antiquarian knowledge is demonstrated in the last note (referring to Exodius), which happens to be the only note in which he corrected and supplemented Xylander and the only note which is not essentially theoretical in character. In Mizler’s treatment of the central questions of the theory of consonant parallel passages elsewhere and had considered it necessary to intervals, only th: conclusiveness of given doctrines is open to debate, while their development is not. In spite of the fact that Mizler is aware of the essential difference between the ancient and the contemporary musical systems, his deductive and theoretical disposition prevents him from grasping the importance of any questions about the historical conditioning which may have limited certain parts of the theory, let alone about the existence of different layers of tradition in the transmission of the text. While the line of investigation of harmony pursued in Pseudo-Psellus basically follows that of the Aristoxenian School,2% the actual core of the text, the theory of intervals, progresses from an Aristoxenian determination, in terms of additive distances in space, to the Pythagorean-Platonic interpretation of the consonances as numerical ratios, mostly in the version expounded by Theon of Smyrna.?6 The classification of intervals according to their degree of consonance presented by Pseudo-Psellus (p. 187ff. Mizler =p. 68. ıgff Heiberg) creates certain problems because of its odd terminology. These problems vexed Mizler, just as they had bothered Xylander, but neither of them attempted to undertake an analytical investigation of the original sources.?? Meibom, however, alread had cited 26 Cf. G. Seydel, Symbolae ad doctrinam Graecorum harmoniae historiam [Diss.] (Leipzig, 1907), pp. 5-7, 56ff.; see also C, v. Jan, Scriptores. … pp. 167; Gymnasium Program (Landsberg, 1870); Gymnasium Program (Strassburg, 1890 and 1891); R. Schäfke, Aristides ..., pp. off. 38 The basic work is C. Stumpf, Geschichte des Consonanzbegriffes, 1, publ. in Abhandlungen d. Münchner Akad., Philos.-Philol. u. Hist. KL, 21 (1901); see also especially J. Handschin, Der Toncharakter, Pp. 133ff. and 2osff. #7 The passage which is especially in need of interpretation, in Pseudo-Psellus (p. 187, 1-8 Mizler = p. 68, 19-21 Heiberg), together with Mizler’s translation (which partly paraphrases it and partly corrects it) is the following: Zuupawei 62 À uév dia veaodowv Sidatacic xai ú Ota névre zard naodpuwor, 119 make a conjectural emendation (at p. 187, 3 M =p. 68, 21 H). In connection with Gaudentius’ classification of the melodic tones (c. 9, p. 338, 37 Jan)?# he attempted to give further instances of the rare technical term paraphonia (which here designates the intermediate value between the sym-phonous and dia-phonous intervals), as it occurs in Thrasyllos, an author quoted by Theon, together with the more usual term antiphonia (i.e. opposition of voices, or repetition of a melos on a different pitch).2® The expression antiphonia, which was probably first used by Plato (Laws 812 D) as a technical term referring to musical phenomena,?% serves in the pseudo-Aristotelian Problemata above all to characterize similarities of the octave-species (esp. Probl. XIX 7, 13, 17, 39b). Since the first century A.D. it was considered a special case of the symphonia (ie. ‘simultaneous sounding’, or tonal relationship, or consonance).®! In Thrasyllos’ article in Theon of Smyrna’s work (p. 48, 17ff. Hiller) we find for the first time consonances divided into the two categories of antiphony and paraphony, i.e. in terms of two degrees of relationship which are manifested by their greater or lesser fusion. Consonances in the sense of antiphony (odjugwra zur’ dvripwvov) were the intervals of octave and the double octave, consonances in the sense of paraphony (oóupwva xara naodpwvov are the intervals of the fourth and fifth. Thereafter consonances 7} 68 dıd zac» xai 7 dis dua tecodguw xai 7 dis dud névre xai 7 dis did zacdrv* xarà âvripwvorv. = ‘But the intervals of the fourth and the fifth agree according to the genus which the Greeks call ‘‘paraphonum’’, whereas the octave, the superimposed fourth and fifth, and the double octave agree according to the genus of consonances which the Greeks call “antiphonum”.’ 28 M. Meibom, Antiquae musicae auctores, Nota ad Gaudentium, p. 35; cf. C. v. Jan, Scriptores..., p. 338. Meibom conjectures that before the last two words of the text (indicated by an asterisk *) the following words are to be added: xai jj dia tecodguwy xai 7 dud naody xai dia névre. 29 On the term ‘paraphonia’ see J. Handschin, ‘Musikalische Miszellen,’ Philologus, 86 (1930), pp. 52ff., especially p. 54 listing the derivation of the term from a passage in Ps. Longinus’ J/egi dpovs (‘On the sublime’), 21.1. 30 On this much discussed passage see especially C. Stumpf, Geschichte des Consonanzbegriffes, pp. 13ff. and in Sammelbände für vergleichende Musikwissenschaft, I (1922), 167; also Handschin, Der Toncharakter, p. 23 and Musikgeschichte, p. 61; C. Sachs, The Rise of Music in the Ancient World (New York, 1943), 257f. 31 C. Stumpf, ‘Die Pseudo-Aristotelischen Probleme, über Musik,’ Abhandlungeu d. Berliner Akad., Phil. Hist. Klasse, 3 (1896), pp. 25ff., especially 32; cf. Handschin, Toncharakter, pp. 227 and 353.

‘according to relation’ (xard ovveyeıav) are listed, such as the whole tone and the quarter tone (diesis). These latter then arc melodically useful intermediate steps which are only indirec tly: related to the immediately related basic tones of the tonal system (cf. Aristoxenos, p. 27 M 35, off. Da Rios). Accor ding to this treatise, the intervals of antiphony are ‘sym-phono us’ insofar as the low-pitched tones ‘symphonize’ with the juxtaposed high-pitched tones (cf. Theon, 51, 4ff ). The interv als of paraphony are ‘sym-phonous’ insofar as one tone in relati on to the other tone sounds neither ‘mono-tonous’ nor ‘dia-p honous’, but sounds similar, though it is at a clear distance (rapa Tu voor dudatnua Öuowv). Those small intervals which previously, in terms of melodic sequence, were called symph onous, are now considered dia-phonous (‘sounding apart from each other’). For though they represent a ‘principle of symphonia, yet they are not the symphonia itself.’32 _——_ antiphona: Octave, Double Octave sym-phonous “~~ paraphona: Fifth, Fourth symphonous ‘according to relation’ = diaphonous (principle of symphonia): Whole tone, Diesis From this particular section derive syncretistic paraphrase s in the writings of the Byzantine music theoreticians. They transf er into Thrasyllos’ system, with its distinction of differ ent degrees of consonance, the added-octave intervals which had been classified as consonances by Claudios Ptolemaios. Ptole maios disagreed with the Pythagoreans who excluded from the consonances the interval of ‘octave plus fourth’, or the eleve nth (3-8, as one not belonging either to the numerical ratios obtained by a clear division, such as n: 1, or by a division with a rest, such as (n +1): 1. He equated the ‘upper fourth’ (i.e. the eleventh) with the simple fourth as a corollary of the (assu med) identity of the octave (Harm 1.5.6). As far as the intervals of uneven tensions (anisotones) are concerned, Ptolemaios group ed them in terms of the degree of approximation toward identi ty and established the following ranking: (a) homophonic intervals, such as the octave and octave with the ratios 2: 1 and 4: 1; 32 C. Stumpf, Geschichte. . -» 48ff.; Handschin, double Zbid., 229; see also C. Dahlhaus’ article ‘Konsonanz-Dissonanz’ in MGG, 7 (1958), cols. 1504-5, 121 (b) symphonous intervals, such as the fifth and the fourth, both being the first ratios of a division with rests, 3:2 and 4:3. To these he added those intervals consisting of these two and the homophonic octave-expansion, i.e. the twelfth (2:1 x 3:2=3:1) and the eleventh (2:1 :4=8:8). (c) emmelic as (melodically usable ones), such as the whole tone (8:9) and the series of the micro-intervals, i.e. those ratios which exceed the ratio 4 : 3 (Harm. 1.7). Thus the same degree of fusion was ascribed to the expansion of an interval by means of an octave as was ascribed to the simple intervals within the range of the octave; in other words, the intervals of the type N-plus-octave were considered equivalent to the primary consonances (N).3? x homophonous: Octave, Double Octave Anisotones— symphonous: emmelic: Fifth, Fourth, Twelfth, Eleventh Whole tone and micro-intervals The Ptolemaic teachings on harmony strongly influenced the archaizing tendencies in Byzantine writings on music theory. Since no intermediate stages can be found between Ptolemy and Pseudo-Psellus, let us first, in order to reconstruct the historical development, quote parallels to this passage from the far better investigated treatises of late Byzantine music theory. Georgios Pachymeres (1242-1310) refers (c.10) specifically to the argument by which Ptolemy counts the eleventh as a consonance (at the same time adding the arithmological argument of the tetraktys). But his analysis of the main consonances (c. 13, 14) which is an addition to Ptolemy’s refutation of the Aristoxenians (I.10, 11) does not go beyond the realm of the octave. Manuel Bryennios (early fourteenth century) who systematized the Byzantine musical writings sanctioned by Ptolemy, grafts the Ptolemaic ‘octave-expansion (1.5) into the hierarchy of consonances found in Theon’s writings in such a way that Theon’s trichotomy was expanded into a four-fold 7 “ ee : i id. . 88, 115, 151-2, 208-9, 222-37 nen Waerden, Die Harmoneichre der Pythagoreer, Hermes 78 (1943), pp. 166ff.; also I. Düring, ‘Ptolemaios und Porphyrios über die, Musik,’ Göteborgs Högskolas Arsskrift, xl (1934), pp. 173ff. 84 L. Richter, ‘Antike Überlieferungen ...’, pp. 84ff. and g3ff. 35 Ibid., pp. 98ff. and ror ff.

hierarchy (but cf. IL.2). Bryennios divided the symphonous symphonia is concerned, it is said to represent a coincidence and octave, paraphonous intervals, which include only the fifth anc the twelfth, while he uses the general term symphonia for the the sense perception of a total fusion, so that it is no longer possible to perceive the individuality of each of the two components one of the two sounded notes is said to dominate (for textual concordances cf. Cleon, p. 187, 19ff. with some added manuscripts; Gaudentius, p. 337, 8ff.; Aelian in Porph. in Ptol. 33, 13ff.).38 These disquisitions are embedded as the second section in a comprehensive chapter on the intervals, which are characterized in terms of the following five criteria: range, degree of intervals into antiphonous intervals, such as octave and doubl. interval of the fourth and the eleventh, that is, he considers the which are smaller than the fourth, such as the diesis and its latter intervals to be unqualified consonances. Following the Aristoxenian model, he interprets as diaphonous those intervals combinations up to the di-tonus, as well as the intermediarı intervals betwen the symphonies, which comprise three, four and five tones (cf. Aristoxenus, p. 20 M 25, 11 Da Rios, and esp. Cleonides, c.5, p. 187, 15ff., as the direct model) .36 antiphonous: Octave, Double Octave Symphonous <— paraphonous: Fifth, Twelfth N generally symphonous: Fourth, Eleventh Diaphonous: Diesis, Half-tone, Whole tone, Tone-anda-half, Ditonus Acoustical properties serve as an argumentum a posteriori for the differentiation of the individual groups of intervals. Some notes about intervals as relationships of rhythmical impulses (frcquencies) lead on to a paraphrase of the theory of consonances as mixtures of tone, the psychological consequence of physical relationships. It is stated that paraphonous intervals symphonize, but not simultaneously, by virtue of the fact that the sounds follow each other in a well-regulated and rhythmically wellordered fashion. In antiphonous intervals the higher pitch is said to symphonize with the lower one simultaneously and in an identical manner, as for instance the octave with the prime (i.e. unison), the ninth with the second (cf. the more detailed presentation by Heracleides in Porphyrios in Ptol., p- 32. Düring; Euclid, Sectio canonis, p. 148f. Jan, Ps. Aristotelische Problemata, XIX 39b; Adrast. in Theon 50, 4ff.).37 As far as the % For the diesis, as the smallest unit of measurement in Aristoxeno s, cf. L. Lalo: Aristoxène du Tarente (Paris, 1904), pp. 113ff., 185ff. and passim, See als: R. P. Winnington-Ingram’s study in Classical d Handschin, ob cit, PD 146 and 140. artery, 26 (1992), p. 195 an 37 Cf. Jan, Scriptores..., pp. 134ff.; E. Graf, ‘Die Theorie der Akustik in: griechischen Altertum’ Gymnasium Program (Gumbinnen, 1894), p. 6; L. Schonberger, ‘Studien zum 1. Buch der Harmonie des Cl. Ptolemäus,’ Gymnasiur: eenAugsburg, 1914), pp. 26ff.; and especially, van der Waerden, op. cu. p. 192ff. 123 blending of two tones which differ in weight and pitch, with consonance, composition, tonal gender, and rationality. The disposition of these criteria is based on the Aristoxenian tradition, as it was first mapped out in Aristoxenos’ own writings (Aristox. Harm. p. 16 M. 21, 17ff.) and developed further and more elaborately by Cleon. c. 5, p. 187, 3ff. (cf. Aristides I.2, Anon. Bellermann, § 58). The first three of these distinctive characteristics recur in the synopsis of the Pseudo-Psellus, although only in a rudimentary form. Various agreements between that treatise and Bryennius seem to indicate a relationship of dependency. Certain abbreviations, deviations, and obvious misunderstandings in the Pseudo-Psellus, however, would rather suggest the use of a common source. In the treatment of distances between tones, for instance, Pseudo-Psellus arranges them in the Aristoxenian way, starting with the quarter-tone as the smallest unit,3® and hence proceeding all the way to the octave which is said to have been named diapason (‘through-all’), since all others find their completion in the octa-chord, and if one were to go beyond the octave, such intervals then become ‘doubled’: the intervals which follow the octave are said to be the ‘double fourth’ (disdiatessaron) and the ‘double fifth’ (disdiapente), etc. (cf. p. 185f. M =68, 14-18 H; for the terminology of the consonances, cf. Theon, p. 51, 4ff.). The over-schematic interpretation of the concept of duplication as covering all intervals in the octave leads Pseudo-Psellus astray. He not only speaks about the double octave, but also erroneously about a dis d:atecodowr and a dic duanérte instead of the correct dıd naoëy xai teoodour and did nacwy xai dianérte 38 Jan, pp. 322ff.; Stumpf, pp. 41f. and 47f.; Düring, pp. 158, Handschin, p. 144f. 3® See note 36, above.

respectively. That this formulation is not used as an abbrev: . . 125 script tradition of air tion for the correct version (excepting, of course, attestations i: certain Greek theoretical writings where, to be sure, the terms disdiatessaron and disdiapente are used, but merely in their on), acceptable meaning, namely in reference to the dissona . [dia-phonous] intervals of the seventh and the ninth [as for instance, in the pseudo-Aristotelian Problemata]),4° is shown in Pseudo-Psellus where immediately alter the passage in question the multiplicative prefix ‘dis- is substituted for the noun diapason’. Later on, dis not only superfluously, but indeed absurdly, precedes the compounds beginning in diapason. The preceding considerations now permit us to submit an interpretation of our starting point. In distinguishing the intervals by their degree of consonance (p. 187f. M — 68, 1off H), Pseudo-Psellus treats the intervals of the fourth and A as symphonizing paraphonically, but the intervals ofthe octave the double fourth’, and the ‘double fifth’ as symphonizing antiphonically. Ptolemaios’ view of the equivalence of the octave extensions is injected into Theon’s structural scheme but with a mistaken use of terminology. The subsequent acoustic derivation of this difference in quality of intervals corresponds to what is later on transmitted by Bryennius. mistake which recurs throughout the manu d in his model this text. The Byzantine author apparently foun octave plus a an of val inter the correct designation for the he want to did r longe no yet fourth, or of an octave plus a fifth, that an reads one Thus x. part with the intrusive spurious prefi , and tones half a and octave plus a ‘double’ fourth equals eight . tones half a and the octave plus a ‘double’ fifth equals nine were to believe the The error now becomes manifest, for if we first octave-expanauthor, there would be eleven tones in the le octave comprises sion, thirteen in the second, while the doub anation of the only twelve! The same applies for the expl s of composite fractional-number ratios of the intervals by mean numbers. of the consoMeibom, in his conjecture about the division H),42 proposes to nances in Pseudo-Psellus (p. 187.3 M =68, 21 the traditional set add the upper fourth and the upper fifth to In so doing he fifth. and h of paraphonies, namely to the fourt rubric, but nd seco s emy’ undoubtedly based himself on Ptol that these fact the given this is not the meaning of the text. For + fifth) h and octave octave-expansions (i.€., the octave + fourt antiphonous have already been mentioned, the following were ) would, if one intervals (‘double fourth’ and ‘double fifth’ though without the latter’s discussion of the phenomenon of a literal sense as to believe Meibom, have to be interpreted in fusion, while the definition of diaphony agrees with the final sentence in Thrasyllos.4 Both Pseudo-Psellus and Bryennius accept the paired concepts of antiphony and paraphony, a pair of consonances. they were derived) and outside the realm corruption at Mizler, following Xylander, noticed the textual and of concepts which emerged in Late Antiquity. The earlier of meetwo Byzantine theorists, however, does not yet go beyond symphonizing _ _ paraphonically: Fourth, Fifth “<< antiphonically: Octave, ‘Double Fourth,’ ‘Double Fifth’ Principles of symphonia: Whole tone, Half tone, Diesis. In the subsequent description of the consonances according their composition (p. 188f. M = 69, off. H) we find the same asic mistake in the nomenclature of the octave-expansions, a 4 . . . D hej a point see especially Stumpf’s ‘Die pseudoaristotelischen Probleme.’ 41 See p. 119. doublings without any reference to the octave (from which the very first appearance of the terms ‘double’ fourth reading should ‘double’ fifth. He pointed out that the correct (=eleventh be ‘superimposed fourth’ and ‘superimposed fifth’ the spurious and twelfth) (annotation 9). Similarly he criticized agwv and dıa zacúv use of the terms à zacóv xal dis did Teso r’s annotations mai die dà névte (at p. 189 M =69, off H; Mizle the fourth and 11 and 12). At the mention of the intervals of consonant their that out ing eleventh, he could not resist point harmonic the upon t nden character is only relative and depe age conr’s Mizle of s view function of that interval.43 Thus the 42 See note 28, above. of the fourth is never a consonance by 43 «But in the same way as the interval also the composite fourth or nature, but only under certain circumstances, thus d among the consonances, counte be ions condit n certai under only can eleventh hek, TI1/2, p. 186, n. 9. Bibliot lische Musika ed.’ exclud from which elsewhere

this interval. In the basically mon i ic of cerning a harmonically regulated counterpoint were, i entirely pohistoric manner, brought to bear upon the interpre. on of Antiquity, it was the framework of the Tetracherd and “28 su h represented a structural consonance . Only with the high developed polyphony of the High Middle Ages, was it subj etes to the degraded to a ‘dissonantia per accidens”.44 Heres As far as the ordering of consonances in Pseudo-Psellus ; concerned, Mizler is inclined to understand the opposin ter N paraphony and antiphony, not as different degrees of relation. ship, but rather as mutually exclusive aspects of tonal relation. ship. Thus he considered the former of these terms to indic te ‘consonance in melody’ and the latter to designate ‘consona ' € in harmony’ (p. 188, annotation 10),45 since the only exam es given for this term are octaves.46 As a rationalistic theori tL Mizler apparently imagined the octave consonance of Anti nity to have been a real ‘di-chord’ (Zweiklang), used for the un ose or singing in parallel motion, partly in lieu of the consonanees 0 the third and sixth (which at that time had not yet been egitimized), partly because of an aversion to motion in parallel fourths or fifths (which would have run counter to the rules of euphony). The probable reason for this view was a belief in historical progress: Antiquity, to be sure, was far removed fr the ideal state (of the eighteenth century) where the third was recognized as a consonance; on the other hand, it had not yet reached the transitional stage of early medieval organum ith its motion in parallel fifths and fourths.47 Is aa . B Dement Geschichte der Musiktheorie” (Berlin, 1920), pp. 11off. and ı86ff.; : in , 7, col, 1506. See also the distincti h Ch as a dissonance nee (th the lower (with the lower te tone in the € B Bass part) and a perfect pn head consonance . Paras (Wien yas) try | oneof this interval) in J. J. Fux, Gradus ad on e same misinterpretation 1 of paraphony as a ‘conso nant progre i i melody is found later on in the relatively thorough representationof the concept adfone in de G among the Ancient Greeks in Fr. W. Marpurg’s Kritische Ein . Dre. ie Geschichte Lehrsät rsdtze der alten und neuen Musik 7 (Leipzig, ipzi 1759). not con“ siine third to be a consonance, and even less so the sixth: and their “Butane jon that he cited only examples of octaves is that the Ancients did g prevented them from moving upward dow i « [parallel] fourths and fifths.’ Musikalische Bibliothek, 1 1/2 p 188 nto.win er discussion as well as a list of more s ecialized li rature concept of consonance in the Middle Ages, see Dahlhaus. loc. ciTature on the ‘pSELLUS’ TREATISE ON MUSIC’ of musicological knowledge and expertise 127 century the which is avail- It would be unfair to expect of the eighteenth t intervals. as such were contrasted with less consonan store might have able today. Nevertheless, the misinterpretations and by proper been avoided by a closer investigation of the text dy been assemreference to parallel passages which had alrea only a quasibled by Meibom. Where Pseudo-Psellus offers cessors would abbreviated and hardly explicit text, his prede octave, but have permitted Mizler to realize that not only the consonances also the fourth and the fifth were considered true It s, Thras lic’ by Ptolemy, while, following Aristoxeno and, (the octave, as would have become evident that those intervals vals, between well as the fourth and fifth) were ‘framework’ inter l for melodic which lay the micro-intervals which were usefu antly called movement. These micro-intervals had been pregn yldiesis serves as the brick, as it were, of which the intervals ‘emme ous depending los (as quoted by Theon) called them ‘symphon of the criteron the context’ or considered them defined in terms ‘principle of ‘on of observable distance, with the addition ion which in symphonia, but not the symphonia itself’, an addit context.48 Yet the Pseudo-Psellus survived alone and out of the ByzanMizler in no way discusses the surprising fact that this Aristoxtine author of the treatise suddenly departs from to which the enian additive view of the intervals (according are complete works, as he had originally done in the foreword to the Pythagorean built) and (p. 189 M =6g, 16 H) moves on to the ding to their computational principle of defining intervals accor numerical ratios. vings about Mizler does not seem to have harboured any misgi as the source the legitimacy of using such an incomplete account or as a vehicle of information about ancient music in general, of his comfor demonstrating his own theories. Yet, at the end t the fact mentary, there is a certain feeling of sadness abou nsive body of that his ambitious plans to translate a comprehe yielded such Greek writings on musical theory had so far lation of diminutive results. He no longer announces the trans detailed aries of Musikalische Bibliothek, but only excerpts or brief summ collections of the ancient writings on music contained in the 48 See note 32, above. Meibom and Wallis, to which he refers for a more

comprehensive orientation. In the meantime, the Byzantine Mizler is thus the first to have translated into German a treatise is offered as a ‘foretaste’ of things to come. For those who are truly interested in the subject-matter, the text is given in its original language, while a German version is provided for the amateur.4® cause. Nor could he as an editor achieve what eluded even the Byzantine treatise on music and to have commented upon it. In this way he contributed to the popularization of Greek teachings on music. The merits of this pioneering work cannot be denied, in spite of its great deficiencies in interpretation. Although Mizler did his best to act as an interpreter of methodology he could not bring himself to cease advocating his own most learned philologists of his time, namely a solid and diplomatically well-founded edition of the text. It was only in the nineteenth century that critical editions were provided, above to those all for the texts of Ancient Greek musical theorists. And even today, the editorial and exegetical study of Byzantine sources has hardly progressed beyond the first tentative steps. 49 ‘Moreover, one can well see that these pages will offer no satisfaction become necessary to present a foretaste of things to come to those who are who wish to obtain detailed information about the music of Antiquity (although be they may perhaps contribute a little to their knowledge). He who wishes to fully informed must consult the writings of the Ancient Greek writers of music and try to understand them. In due time, I shall endeavour to go over those writings and present their most useful aspects in writing. Meanwhile it has Pp. 200, n. 24. interested in this matter; and in order to please them I have appended Psellus’ treatise in the original language, while for the benefit of Germans who know something about music, I have furnished a translation.’ Musikalische Bibliothek, 8) in RicntER L., Psellus’ treatise on music in Mizler's Bibliothek : Stud. e musical | first translated into German and commented upon the Byzantin eastern chant II (ef. ci-dessus) 112-128. | Lorenz Christoph Mizler (1711-177 treatise follows that of the Aristoxenian school, but the theory rean of intervals treatise attributed to Michael Psellus. The investigation of harmony in the proceeds from an Aristoxenian determination to the Platonic-Pythago interpretation of consonances as numerical ratios.