Music 526, History of Theory  (Ancient, Medieval, Early Renaissance)

Winter 2005

John Rahn (jrahn@u, 543-2291, office Music room 217)


Jan 4, 2005


I will be updating this syllabus as the class goes on, keeping an updated copy on the web at I am starting us off with the syllabus and class notes from this course a few years ago so you can see how it might go, but we will follow our own threads and so will probably diverge from this map increasingly.


Rather than trying to cover all the theory written during the 5th century B.C. through 1500 – that is a temporal velocity of 100 years per hour! – we will focus on selected periods and treatises in some depth, leaving other periods to other avatars of this seminar. (We will ignore theory before 500 B.C. However, see this bibliography. )This year, we will begin with ancient Greek music theory and will spend at least half the term on this, trying to cover it pretty well. The remainder of the seminar will be spent on a very few selected Latin treatises, notably Franco of Cologne (13th-c), with some attention to attendant issues of developing polyphonic notation in an age of innovation, and intellectual context. A reading knowledge of any of Greek, Latin, and Italian, (and German and French) would be useful but is not required for this class.

Throughout the term, we will ask members of the seminar to report on special topics, and will rely increasingly on such reports as the term goes on. In particular, we expect reports on subjects such as Boethius (tr. Bower), Chant theory, Tinctoris, and on later theorists such as Vicentino, Zarlino and Gafurius, who to some extent follow up the thread of scalar constructions initially developed in the Greek period.

Grades will be based on class participation, including seminar reports, and on a final term paper.


Members of the seminar: [list]. 


Week 1: introductory discussion.


Textbooks: Andrew Barker, Greek Musical Writings Vol. II: Harmonic and Acoustic Theory, on reserve. This is the primary textbook for the course. The first edition is out of print but a second edition is due out in January 2005 and has been ordered for the class at the Ustore. We expect it to arrive by February, but in the meantime we will have to rely on a copy on reserve. (This is checked out but should be back on reserve within a week.)

A secondary textbook is M. L. West, Ancient Greek Music, at the bookstore. This is a general survey and discussion by a scholar, covering areas not represented well in the treatises (such as instruments) and including transcriptions of surviving musical fragments.

I will also put on Music reserve the following:

“CHRONOLOGICAL BIRD’S-EYE VIEW OF THE WHOLE PERIOD” This is a handout from a class on medieval philosophy taught by a Jesuit, a time-line for all Greek and Latin (and some Arabic) philosophical and theological writers in 100 AD-1631 AD!

Select Bibliography from my 1990 Music 526, concentrating on Latin music theory.

Two time-line bibliographies of music theory from 1470-1600.

Other books as time goes on.


Sources: Greek texts will be read in translation in Barker. Greek and, later, Latin original texts are available in the Music Library. In general I will not put these on reserve as they are often library use only and are in any case not in high demand. See Barker for the editions he uses; most of the Greek authors – Aristoxenus, Euclid, Nicomachus, Alypius, Gaudentii, Philosophi, Bachii Seniores -- were collected in 1652 in Meibom, Marcus (Greek with Latin translation and commentary), Antiquae musicae auctores septem : Graece et latine;  ML167 .M45 1652a, and  880.878 M475a  – this is library use only so it is not on reserve. Ptolemy in Greek with Latin translation by Wallis (1682) is in ML 168 P97 1682a. See also Karl von Jan 888.9 J26m (1895), and Fortlage, Karl, 1806-1881, Das musikalische System der Griechen in seiner Urgestalt : aus den Tonleitern des Alypius / zum ersten male entwickelt von C. Fortlage1964 (reprint of 1847 edition), 780.938 F776m (Alypius is our only source concerning Greek musical notation; text is in Meibom). See also the Strunk/Treitler series, ML160 .S89 1998 v. 1 and 2. Editions of original sources are not always easy to find in the catalog system; sometimes you just have to browse. Ripe patches include MT5.5xxx, ML 113-114xxx, ML160-72xxx, 780.9 C817 v.1-xxx (the AIM series of texts) and its surrounds, 888.9xxx. All the Latin music theory sources seem to be available on line through the Thesaurus Musicarum Latinarum site,, and some general (but not most musical) Greek sources are available at Thesaurus Linguae Graecae, .



Week 1:

Sources. Summary of the current and past situation with regard to sources and translations.

The Big Picture. We mapped  a grid of issues and topics in music theory vs. chronology from 6th-c BC Greeks to current times (21st-c), noting the patterns of activity, how topics wax and wane, and what new topics and areas have arisen in music theory (such as music history and musicology, since the advent of music history!).

Pre-intro. Then we went over the elements of the The Lesser Perfect System and Greater Perfect System, and the Harmoniae (pre-400BC version) as ancient Greek World Music and its eventual homogenization, with some references to later tonoi and so on, in preparation for reading Barker’s Introduction.

Corollary reading: how the modal infrastructures are now evolving in Bali, from Wayne Vitale, “Balinese Kebyar Music Breaks the Five-Tone Barrier,” Perspectives of New Music 40/1.


Week 2: Read and discuss Barker II, 1-118 (Introduction, Early Pythagoreanism, Plato, Aristotle, the Aristotelian Problemata, The Peripatetic De Audibilibus, and Theophrastus). Read West Ch 1 (pp. 13-39). We will be discussing West 1, 5, and 9 in class as the weeks go on, but you can browse through the rest of West, too.


Discussion of Barker’s Intro’s remarks on the inferential harmoniai and the tonoi. In both cases question arise as to what Barker’s evidence is for his assertions, and his support for one alternative among many in various cases. Original sources are lacking. Some of this debate we deferred until we shall have all read the rest of his texts, e.g. Aristides Quintilianus and Ptolemy. One interesting issue that came up: what exactly does it mean to change harmonia or tonos? Does a change really necessitate retuning as Barker says, or might it mean a simple repositioning within the system, perhaps including tunes “wrapping around” (when interval series are rotated) bringing the intervals pushed off the top of the system back in at the bottom, as in some gamelan music? We would need a Greek theory of melody to answer this. We’ll see what Aristoxenos brings.

We discussed Plato’s “music of the spheres” passage. What is the significance of the widths of the rims of the spindles (which must not be equated to the diameters of the rims, but probably mean width as in thickness)? Plato’s parallel construction of the soul as a three-dimensional Turing machine presented no insuperable difficulties. 

Student report on this?


Week 3: Aristoxenus on rhythm. Rhythm and Greek verse and language. Read  Barker II 119-208 (Aristoxenus Elementa Harmonica and The Euclidean Sectio Canonis).  Read West Ch 5 (Rhythm, pp. 129-160).


A’s Harmonica or the Sectio Canonis may be deferred to next week as time requires.

We  discussed tonoi and harmonia (octave species), clarifying how the “modal” and “transpositional” interpretations interact, and that we would need to know whether there were melodic reference tones with respect to which a tonos or mode was structured, in order to determine how all this works. According to M. L. West, there is in all the surviving music from ancient Greece in fact no consistent relation between octave species, tonos notated, and tonos indicated by reference pitches, leaving much still up in the air.

Then we read Aristoxenus on rhythm, and John presented lengthily on Greek language and verse and its relation to the rhythm of Greek music (anticipating a student presentation next week on pitch notation). Ancient Greek had a number of independent musical elements built into the language, which formed a multiple counterpoint: 1. pitch accent (high, lower, circumflex), 2. stress accent (antepenultimate in general), 3. quantity (longs and shorts with long = 2 shorts; musical rhythm follows text quantity except in through-composed forms, but in any case follows the same principles as verse. In addition, for verse, we have 4. feet (iambs, dactyls etc) and their boundaries, 5. arsis and thesis, variably placed within different kinds of feet, and having unknown (if any) effects on musical treatment, 6. verse forms such as the iambic (or trochaic) metron, hexameters etc, paeonic, dochmiac, Ionic, Aeolic, elegiac couplets, Sapphic and Alceaic stanzas, and so on. Each verse from has its own internal structures; the quantities and structures can be reflected in musical rhythm.

M. L. West, an authority on Greek verse, has what John thought was sometimes a peculiar and unsustainable way of interpreting the verse duration-patterns in modern musical notation’s meters. For example, according to West, the last (4th, short) line of the first, Sapphic stanza of Sappho’s poem number 1 (poikilothron’ athanat’ Aphrodite), which is “potnia, thumon”, contains a iamb, trochee, spondee L S / S L / L, which perversely contradicts the ineluctably clear grouping due to pitch accent, word ending, phrasing, and so on; this one of many such examples. (The more usual interpretation is dactylic: L S S/ L L.) West argues that his interpretation preserves the principle that all shorts are of equal length (though elsewhere his transcriptions transgress this principle); but we can also preserve that principle in this dactylic interpretation without a ruffle.

Apart from the interpretation of verse rhythm itself, it is problematic to represent verse rhythm, and therefore Greek musical rhythms, in modern music notation. Modern notation introduces performatives about “strong beats” and groupings which represent nothing in Greek verse, and often contradict it. Modern notational representation also leaves out many important features present in Greek verse. For example, the familiar epic dactylic hexameter has an important break after the fifth long, grouping in 5L, 7L

(--uu –uu --/ --  --uu –uu -- --); see the first line of the Iliad, or, not by accident, the Aeneid. Elegiacs, Sapphics, and so on all have such structural features, which do not naturally map over into modern music-metrical notation.


Week 4: Discuss Aristoxenus Elementa Harmonica and The Euclidean Sectio Canonis (Barker II 119-208). Read Barker II 245-391 (Nicomachus Enchiridion and Ptolemy Harmonics). Read West Ch 9, Notation (254-77). Student report on Greek pitch notation.


Week 5: Read and discuss Ptolemy.

 This is a lot of material, and we may go through it rather fast. We may continue this next week, bumping the rest of the weeks forward.

We admired Ptolemy’s empirical bent. We defer decisions on tonoi until we have read Aristedes. N.B. Barker’s tables of tonoi fig 11have the wrong table in 11.3; the correct one can be supplied by rotation. Base 60 does not seem very apt for the ratios. Why the varying base numbers (e.g. 60, 60 21/21, 60 1/3 …56 136/729)? Ptolemy confuses pitch-line distances (from Aristoxenus) with string distances (for ratios). The table on p 359 of tonoi actually in use is quite interesting.


Week 6: Read and discuss Barker II 392-535 (Aristides Quintilianus De Musica).

The discussion of rhythmic theory (music vs verse) in Book 1 is of interest. AQ’s ancient harmoniai (pp. 419-423) are of real interest, as are his entirely different wing diagram tonoi. The AQ harmoniai are somewhat consistent with tunings deducible from auloi tone-hole distances (but they do not support Barker’s rotational interpretation).

About tonoi: we have Aristoxenus’s discussion which is lost; we have Ptolemy’s two versions – those actually in use, and Pt’s grand system; we have AQ’s quirky harmoniai which are not consistent with either of Ptolemy’s tonoi systems; we have AQ’s grand system which is inconsistent with everything else. Bear in mind that this period stretches from ca 500 bc to ca 200 ad. A lot can happen in 700 years, and the documents are sketchy. Also, different instruments had different styles and tunings…


Week 7: Read and discuss Franco of Cologne.  (Best Latin text source: Franco de Colonia Ars cantus mensurabilis / Franconis de Colonia ; ediderunt [sic] Gilbert Reaney et André Gilles, American Institute of Musicology, 1974, 780.9 C817 v.18, on reserve. (Also at English translation in Strunk’s Source Readings revised edition, vol 2, pp. 116-134 (ML160S891198v.2, on reserve).  See ML160 .S89 1998 v. 2.

See also for notation,  Apel, The Notation of Polyphonic Music, ML431.A6 N6 1961 on reserve.

Read Jeremy Yudkin, “The Influence of Aristotle on French University Music Texts,” in Music Theory and Its Sources ed. Barbera (on reserve), pp 173-189. Read Chapter 1 of Dorit Tanay, Tanay, Dorit Esther, Noting music, marking culture : the intellectual context of rhythmic notation, 1250-1400, ML431 .T35 1999, on reserve.

Presentations: on Boethius, on Guido et al.

Class notes: Two excellent presentations on Boethius and Guido may take a lot of time here. If needed we will defer Franco.

We will note the radical change that occurred in the 500 years or so separating Boethius from Guido: B’s modes were essentially Ptolemy’s grand system (sort of), but G’s were rotational rather than transpositional, with a different kernel tetrachord (TST rather than STT reading up) – a huge change which we can only attribute to the intervening diverse musical practice tempered by mostly inexplicit sub rosa pressures for uniformity – the natural urge to make sense of a repertory by generalizing – and of course, to fiat (Gregory).


Week 8: Discuss Tanay, Yudkin; Franco, notation; as time permits, selections from Jacobus Leodiensis Speculum de Musica Book 7: Jacques, de Liège, ca. 1260-ca. 1330 Speculum musicae. Edidit Roger Bragard, 780.9 C817 v.3, on reserve  (also at Selections are translated in Strunk’s Source Readings revised edition, vol 2. See also Philippe de Vitry, Ars Nova (ed Reaney et al, 780.9C817v8, Latin with French translation, on reserve.)

Presentations: on de Vitry and Ars Nova, on the Berkeley MS.


Week 9 Presentations by members of the seminar: on Tinctoris, on Glarean, on Vicentino, on Zarlino


Week 10: blank for having been bumped, or more presentations.