Towards a history of Tonoi

ta TB UNIVERSITY OF CALIFORNIA PRESS JOURTALE + DIGITAL OH Ge a 8 a Towards a History of Tonoi Author(s): Jon Solomon Source: The Journal of Musicology, Vol. 3, No. 3 (Summer, 1984), pp. 242-251 Published by: University of California Press Stable URL: http://www.jstor.org/stable/7638 14 Accessed: 27/01/2010 15:03 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher? publisherCode=ucal. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Universityof California Pressis collaborating with JSTOR to digitize, preserve and extend access to The http://www jstor.org

Author(s): Jon Solomon Source: The Journal of Musicology, Vol. 3, No. 3 (Summer, 1984), pp. 242-251 Published by: University of California Press Stable URL: http://www.jstor.org/stable/763814 Accessed: 27/04/2010 07:53 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucal. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. University of California Press is collaborating with JSTOR to digitize, preserve and extend access to The http://www.jstor.org

JON SOLOMON tonos element of ancient Greek music and ancient Greek music theory and the scholarshiptreatingtonos in the modern era-"modern" meaning the era beginning with Boethius-have offered us a variety of difficulties and contradictorysolutions. At the outset, let me assure you that I have no intentionsof doing or contributinganythingto this tonic can of worms other than discussing and relating several of these difficulties, therebyadding a worm or two. I will focus briefly on one particularaspect of the problem-the discussions of tonos and species in Cleonides' Eisagoge harmonike.In doing so, I intendto touch briefly on the tonos theories of Aristoxenusand his predecessors,Eratoclesand the Harmonists,as well as on the shifting thetic system of Ptolemy. Hopefully I can assist any ensuing discussion of these matters by highlighting the diversity of our evidence and proposing a chronologicalframeworkfor its development. I expect that the learned members of this panel can individually or collectively do more with this materialthan I have. At best I have tried to make some chronologicalsense out of a chronicallychaotic situation. At the outset let me attemptto clarify why we do not have and could never have a completely unified, consistent, coherentaccountingof ancient Greek music and music theory. Ancient Greek music included the Ionian (that is, Asian) epic chants of Homer and the rhapsodes,the Aeolic (Greek islander)songs of Sapphoand Alcaeus, the Dorian (SouthernGreek) lyrics of Pindar(the epinician poet), Aeschylus, Sophocles, Euripides(the tragic poets), and Aristophanes(the comic poet), the Hellenistic Delphic (Northern Greek)paeans to Apollo, the funerary,pagan, Seikilos inscriptionfrom the first century, a "Christianhymn" from the fourth,' and the rest of an entire corpus, almost all of it lost, of Greek music composed without, and then with, the aid of notationand technicalschooling throughoutthe period of some 1200 years from Homer to Boethius. Finding a consistent strain of any significant sort in such a collection of regional dialects, ethnic tra'All of the music of Homer, Sappho, Alcaeus, Pindar,Aeschylus, and Sophocles is, so far as we know, lost. I do not admit the reconstructionof Homer's music as proposed by M. L. West, "The Singing of Homer and the Modes of Early Greek Music," The Journal of Hellenic Studies 101 (1981) 113-29, nor does the modem consensus consider Athanasius Kircher's music to Pindar Pythian 1 genuine. It could be that a musically notatedtragic fragmentsuch as P.Berol. 6870, lines 16-23, could be Aeschylean, but this has not yet been proven. The paeans, Seikilos inscription, and "Christian Hymn" (P.Oxy. 1786) as well as the EuripideanOrestes fragmentare to be found in Egert Pohlmann, Denkmaler altgriechischer Musik (Nmrnberg1970) #20, 18, 19, 21, and 34, respectively. For the EuripideanIphigeneia fragment, see most recently Thomas J. Mathiesen, "New Fragmentsof Ancient Greek Music," Acta musicologica LIII (1981), 14-32.

ditions, polytheistic and monotheistic religions, and various artistic purposes and technicaltrainingswould be even harderthanfinding a consistent strain of any significant technical/theoreticalsort in the last 1200 years of "modem" Westernmusic, the prospectsof which, one must agree, are not encouraging.2 The same will need to be said for the theoretical studies which have survived from antiquity. We cannot realistically expect theoreticians trained in two diametricallyopposed philosophical schools-the Pythagoreanand Aristoxenian-who could not agree whetherthe study of music was a mathematicalscience or an aural experience, and who wrote over the course of seven centuries-to concur on every major theorem, methodology, or even terminology,no matterhow conservativetheir trainings were. "Ancient Greek music" encompasses over 1200 years or more of differentmusics and 700 years or more of differentmusical theories.3 Complicatingthe matterfurtheris what has been traditionallyunderstood to be a lack of interchangebetween those who made ancient music and those who wrote about it. In the past, late-nineteenth-and twentiethcenturyscholarshipfound little connectionbetweenthe fragmentsof ancient Greek music and the extant treatises of the music theorists, but contemporaryscholarshipis in the process of remedyingthis blanket misconception.4 I have elsewhere bored people to the point of tears by inspecting ad nauseam the elements of one of the surviving pieces of Greek music, the Seikilos inscription, through an Aristoxenianmusic theoretical analysis;5 and ProfessorMathiesenelsewhere and here shows that ancient theories of ethos and musicalrhythmandmeteras foundin AristidesQuintilianusapply very neatly to several extant pieces of Greek music, including the new EuripidesIA fragment.6Even so, the correspondencebetweenancientGreek music and ancient Greek theory seems to be far from total, and this must be attributedfor the most part to the first two factors described above, namely, that we are dealing with theoreticiansand musicians who geo2Modem scholarshiprecognizes these difficulties in the metrical, linguistic, contextual, and organological aspects of the poetry and iconography. See, for instance, W. Sidney Allen, Vox Graeca2 (Cambridge, 1974) and M. L. West, Greek Metre (Oxford, 1982) passim. There is as yet no current work on the organological differences between musical genres, but a large volume on chordophones and their usages by ProfessorJane Snyder of the Ohio State University is in the final stages of preparation. 3The 1200 years encompass the period from Homer (c. 700 B.C.) to Boethius (d. 524 A.D.), but it is known that Homer had Mycenaeanand Minoan musical predecessorsantedatinghim by as much as a millenium. The ancienttheoristsbegin with Aristoxenus(c. 300 B.C.), but one could easily include Damon of the fifth century B.C. The terminologyvaries between authors;tonos, harmonia,tropos, and modus are terms used often indistinguishablyto describe the same phenomenon. It can vary even within one treatise;Cleonides, for instance, uses skema and eidos ("figure," "species") interchangeably. 4The traditionalconsensus is still found in Annemarie Neubecker, Altgriechische Musik; eine Einfuhrung(Darmstadt,1977) 93, "Ob die musikalischePraxis gegen Ende dieser langen Zeitspanne der dargestelltenTheorie noch entsprach,ist mehr als zweifelhaft." 5This was a paper, "The Seikilos Inscription:An AristoxenianAnalysis," delivered for a panel on ancientGreekmusic and music theoryat the annualmeetingof the AmericanPhilologicalAssociation in San Francisco in 1981. A written version of that paper, "The Seikilos Inscription:A Theoretical Analysis," has been submittedfor publication. 6See Thomas J. Mathiesen, "New Fragments"(supra, n. 1), his AristidesQuintilianusOn Music (New Haven and London, 1983), 94-113, and his paper in the presentvolume, pp. 264-86.

graphicallyspan the entire Mediterraneanbasin from Ptolemy's Alexandria to Aristoxenus' Italy to Nicomachus' Gerasa and who temporallyspan a period from the time of Homer's predecessorsto the time of Boethiusmore than one millenium. It would thereforeseem to be almostdangerousto proposeany unifying theoryseparatefrom a carefullyanalyzedchronologicaldevelopmenthrough this millenium. Unfortunately,the space allotted here forbids such a carefully analyzed chronological development;a full chronologicalhistory of tonos alone would burst the seams of one volume. So what I presenthere is rathersketchy and newborn. I will try out these ideas here in the hope that they may be nurturedor mercifullyput out of their misery before they grow into a scholarly nuisance. Covered by all these disclaimers and caveats, I can now move on to Cleonides' seemingly isolated discussions of tonos and species. I say "seemingly isolated" since these discussions in particular,representative of Aristoxeniantheory, seem not to concernthemselves with musical practice but with only neatly packaged and progressivelybuilt theoreticaldefinitions. This is only partly true, as I hope to demonstrate.7 Cleonides (202.6ff) tells us that the word"tonos" refers to a variety of things. Most importantfor our purposes is his third definition of the term.8 Actually, it is not a definition at all; he says merely, and I translate literally, V 'o e (bS T6Tros (pOV]s, 'oTrtvXe^Y'y6pLOVeovb Yq'pprytLov'T,XvLOv1 'T TWV EOL oE KaXT ApLcrT6oEVovLy T6VOL. 'ri. TLv XXXWV [Tonos is described] as the locus of the voice whenever we speak of the Dorian, Phrygian, Lydian, or one of the other [tonoi]. There are, according to Aristoxenus, thirteen. Cleonides then lists the tonoi. He lists thirteenwhich is, incidentally, not the numbergiven by Aristoxenuswho does not actually list them at all in the extant works. Cleonides lists the tonoi in descending order and by geographicalappellationfrom the Hypermixolydian(Hyperphrygian)to the Hypodorian.9In a brief, concluding paragraphbatteredin the manuscript tradition, he tells us that each tonos stands one halftone apart from its 7Cleonides is absolutely unknown to us except for Aristoxenus as a terminuspost quem. The second-centuryA.D. date found in the handbooksandencyclopediashas no basis. The text of Cleonides has been reeditedand will appearin a forthcomingvolume of the Musici scriptoresgraeci I am preparing for B. G. TeubnerVerlag (Leipzig). For a translation,see Jon Solomon, CleonidesEisagoge harmonike; a critical edition, translation, and commentary(Ph.d. diss., Chapel Hill, 1980) 145-61, or Oliver Strunk, "Harmonic Introduction," in Source Readings in Music History (New York, 1950), 34-46. The textual referencesused in this paperare to Carl von Jan, Musici scriptoresgraeci (Leipzig, 1895). 'Cleonides (202.6 - 202.8) defines tonos as 1) a note, 2) an interval (= one wholetone), 3) a region of the voice, and 4) a tuning. The thirddefinition is the one in question. 9Cleonides (203.7 - 204.8): "Hypermixolydian,also called Hyperphrygian;two Mixolydians, a higher and a lower, of which the higher is also called 'Hyperionian,'and the lower 'Hyperdorian';two Lydians, a higher and a lower, of which the lower is also called 'Aeolian'; two Phrygians, a higher and a lower, of which the lower is also called 'Ionian'; one Dorian;two Hypolydians, a higher and a lower, of which the lower is also called 'Hypoaeolian';two Hypophrygians,of which the lower is also called 'Hypoionian';Hypodorian."

neighboring tonoi.0l Never does he tell us the intervals or the internal structureused in each tonos. Never does he tell us how they derived their geographicalappellations;never does he tell us how they comparewith the octave species (let alone with the harmoniai, which he never even mentions). When he discusses the octave species (197.4ff), on the otherhand, he does describe the intervallic structurewithin each species, which suggests that he recognized some difference between the octave species and the tonoi. However, at the end of each description he associates the octave species with some of the same geographicalappellationshe had used for the tonoi (this time, of course, in ascending order). To describe the intervallic structurehe uses the position of the disjunctive wholetone; each enharmonicand chromaticdia pason, accordingto the AristoxenianCleonides, includes only the one disjunctive wholetone and two pairs each of ditoneplus two quartertonedieses or trihemitoneplus two halftones. Cleonides traces the extraneous, disjunctivewholetone as it progressesin a descending directionwhile its surroundingintervalscorrespondinglyprogress upwards. Cleonides describes this opposite ascending movement by the names of the notes, not by the location of the intervals. So while the bottommostnotes ascend from hypate hypatonto mese and the uppermost fromparamese to nete hyperbolaion,the wholetone intervaldescends from the uppermostlocus to the bottommost. Interestingly,Cleonides describes the descending locus of the wholetone as moving from highest, to second highest, thirdhighest, fourthhighest, fifth highest, sixth highest, and lowest. The movementis describedthroughoutin relationto the highest locus. This contrastsslightly with his analysis of the diatonicdia pason species, for there he describes the position of the two halftones. Again he describes the intervals as descending and the notes as ascending, but the positionings of the halftone intervalshe describes in a more complex manner: In the first species of the the diatonicdia pason, the halftonesare first from the bottom and fourthfrom the top; in the second species, thirdfrom the bottom and first from the top; in the third, second from the bottom and top; in the fourth, first from the bottom and thirdfrom the top; in the fifth, fourthagain from the bottom and first from the top; in the sixth, thirdfrom the bottom and second from the top; and in the seventh, second from the bottom and third from the top. 1 It is only at the very end thatCleonidesadds thatthese diatonicspecies "are called by the same names" as the species of the enharmonicand chromatic. This suggests that the enharmonicand chromaticgenera were of primaryimportanceto him. At least he approachesthe species of the dia tessaron and dia pente in the same order, enharmonicand chromaticfirst, diatoniclast, and this in turnsuggests that the concept of the octave species goes back chronologically at the latest to the pre-Aristoxeniantheorists, '0Thetext here as reportedin Jan (supra, n. 7) 204.9 - 204.12, is corruptin describingthe intervals between each tonos, but it seems clear that no additionalinformationabout the structureof a tonos has been lost. IISee the diagramsin Jan (supra, n. 7) 195 (dia tessaron), 196 (dia pente), and 197 (dia pason).

most likely to Eratocles, in the fifth or fourth century B.C. Such a dating accords with our meager knowledge of the so-called Platonic (fourth-century) scales reported by Aristides Quintilianus, which are not basically diatonic in nature but enharmonic.12 It may be, then, that the octave species as an entity of music theory dates back to the pre-Aristoxenian period, the late-fifth or early-fourth century B.C. Textual evidence for this can be found where Aristoxenus criticizes the Harmonists for omitting any analysis of the octave species.13 They did omit it, but Eratocles alone, Aristoxenus tells us, did "attempt without proof to enumerate the figures [i.e. species] of the dia pason in one genus; he demonstrated it via the 7weptiop& of the intervals." This IrrEpLcopa ("carrying around") of the intervals no doubt refers to the seemingly revolving ascending and descending scales one sees in diagramming the movement of the species'4-where the halftone or wholetone moves in the octave species in order from highest to lowest, in the dia tessaron and dia pente species from first to third and around again cyclically. The actual analysis of the dia pason species is not found in the extant works of Aristoxenus, but it seems clear from this passage that the concept of the dia pason species predates Aristoxenus and was perhaps invented by Eratocles (in the enharmonic species alone). Aristoxenus in the same passage is critical of Eratocles and the Harmonists for not analyzing the species of the dia tessaron and dia pente, but in the extant works of Aristoxenus there is no such analysis to be found. Cleonides, for whose date we have only the aforementioned terminus post quem of Aristoxenus (and the Byzantine Bryennius as a terminus ante quem), is perhaps our earliest source for an analysis of the species of the dia tessaron and dia pente, and he again begins with an analysis of the enharmonic and chromatic. He, or perhaps his source Aristoxenus, described the enharmonic and chromatic dia tessaron and dia pente species first because Eratocles had described the enharmonic dia pason species first. In fact, Cleonides describes the three figures of the enharmonic and chromatic dia tessaron not by the names of the notes or the numerical relationships of the intervals but as being bounded by the barypykna, mesopykna, and oxypykna, respectively. Without precisely defining the word "pyknon," I will remind the reader here that the pyknon is found only in the enharmonic and chromatic genera (which is why these might be labeled the "pyknic genera").15 Since the diatonic genus has no pyknon, he analyzes the diatonic dia tessaron last, and he does so according to the placement of the lone halftone. Similarly, he analyzes the enharmonic and chromatic species of the dia pente by the placement of both the barypykna, mesopykna, and 12AristidesQuintilianusDe musica 19.2 - 19.10 (Winnington-Ingram)and Mathiesen(supra, n. 6) 20 and 86. 3Aristoxenus #2 (166[Macran];6.14 - 7.8 and 11.2 - 11.12 [da Rios]). 4See the diagramscited supra, n. 11. 15Thepyknon is, accordingto AristidesQuintilianus9.15 - 9.16 (Winnington-Ingram),an arrangement of three notes, but the term is used only with the lower three notes of a distinct enharmonicor chromatictetrachord.

oxypykna and the disjunctivewholetone, and he analyzes them before the species of the diatonic dia pente. In all likelihood, Cleonides, following Aristoxenus, bases his analyses of the dia tessaron and dia pente species on the traditional,pre-Aristoxenianspecies of the dia pason. What, then, might be the relationshipbetween Cleonides' octave species and his tonoi, the formerelaboratelyanalyzed and geographicallylabeled, the lattersimply listed and geographicallylabeledwithoutelaboration? It seems to me that the octave species (and with them of course the dia tessaron and dia pente species) are analytical, the tonoi practical in conception. The very concept of the "species" (eidos, skema)is not developed until late in the fifth century or early in the fourth century in Academic (Platonic)terminology. In the late-fifthcentury, for example, for the comic playwrightAristophanesthe word skema is a "figure" of a dance; for the historian Thucydides it is a "figure" or "characteristic"of a city-state. For the late-fifth-centuryHippocraticmedicalcorpus, skemais a "position" of the body. Within one generation,however, in the early-fourthcentury, Plato is using both eidos and skema to refer to figures, types, Forms; with Aristotle in the next generationthe words are canonized as peripateticcategories.'6 Eratocles probablyused the words in the same sense as Aristophanes,Thucydides,and [Hippocrates],thatis, in a proto-technical application of a common word, whence the peripateticAristoxenuseasily adopted it into his analyses of the "figures," i.e. species, of the dia tessaron, dia pente, and dia pason. For Aristoxenus,the terms are purely analyticaland not at all native to actual music. Informingus of this relatively recent and continuingdevelopment in music theory and terminology, Aristoxenus(#6 = 11.2-11.12 [da Rios]) tells us that Eratoclesalone investigatedthe figures (species) of the octave, that "none of his [Aristoxenus']predecessors"did so [169 Macran];10.1810.19 [da Rios]: TWOv8' '6XXov Ka(xo6XouvLEv KOAdh6TrepE_iTrpoOIev e '(TTOEpEV oEi6s q; TTrOL),and that he, Aristoxenus, was first to analyze the species of the dia tessaron and dia pente, which he emphasizes should be done first. Aristoxenus' dia tessaron and dia pente divisions have not survived. Cleonides', of course, have, and following Aristoxenus' guidelines he begins with the species of the dia tessaron and proceedsto the dia pente and then the dia pason. It is no accidentthatCleonides, following the tradition,in this instance Aristoxenus, analyzes the species of the enharmonicand chromaticfirst, the diatonic last. This preserves the order of things passed down from Eratocles, with his lost analysis of the enharmonicoctave species, to Aristoxenus, with his lost analysesof the enharmonic,chromatic,and diatonic dia tessaron and dia pente species, to Cleonides, about whom everything but his name and treatise is lost. (One sees here from the gaps in our evidence anotherreason that a complete and coherent analysis of ancient Greek music tonal theory is so elusive.) 16Theseand other examples can be found in L.S.J., q.v. crXilJxt.

Surely something is different and irregularabout Cleonides' direct or indirect source here, for elsewhere Cleonides normally begins with the diatonicand then proceedsto the chromaticand then last to the enharmonic. He introducesthe three generain this order(181.12). He analyzes the three genera in this order (181.13).17 He lists the names of the notes (182.4 184.10) in the same order, and he reintroducesthe three genera (189.10) in the same order-diatonic, chromatic,enharmonic. The species he treatsdifferently, as we have seen-enharmonic, chromatic, diatonic. So far as we can tell, the octave species is an analytical device developed by Eratocleswho, accordingto Aristoxenus,with or without the Harmonistsdivided the entiredia pason system of notes into twentyeight quartertonedieses. 18 It looks as if the octave species is an analytical contrivance devised by Eratocles to assist him in maneuveringhis music up and down his impossibly close-packed quartertonesystem and that the species of the dia tessaron and dia pente are then additionalspecies devised and developed by Aristoxenusto conformto his notion thatall Greekmusic consists of regularizedconjunct and disjuncttetrachords.19 The tonoi, on the other hand, representreal music for these earlier theorists. When Aristoxenus discusses them, he compares (#37) the confusion about the number, make-up, and relationshipof the tonoi with the confusion about the ancient Greek calendar.The tenth day of the month at Corinthfalls on the same day as the fifth day of a differentmonthat Athens and this same day is the eighth day of some othermonthsomewhereelse.20 Indeed, this example offered by Aristoxenusillustratesfurthersome of the problemsI outlined at the beginningof this paper, and it shouldbe considered not at all unique to ancient Greek music. Be it in the distributionof the 365V4days of the year, the tonoi of ancientGreekmusic, ancientGreek political systems, ancient Greek philosophical schools, or ancient Greek genres of poetry, ancient Greece is almost never a unified entity but a collection of city-states each steeped in its own habits, culture, traditions, and music. In the archaic period-the seventh and sixth centuries B.C.-these differences surely provided the climate for the creation of the different harmoniai-the Dorian from the austeretribe of southernGreece, the Lyd17Hedoes so (181.13 - 181.16) in the same, colorless, detailed, peripateticfashion as the rest: "The diatonicconsists of a wholetoneplus wholetoneplus halftonedescending, ascending,the opposite, halftone plus wholetone plus wholetone. The chromaticconsists of a trihemitoneplus halftone plus halftone descending," etc. 18Thiscould well be an argumentumex silentio, but Aristoxenusfor one says that "none of the others" describe or analyze the octave species. Aristoxenus could be misrepresentingthe truth, of course. Ancient authors often misrepresentanother's theories, particularlyin that age in which legal recoursefor such misrepresentationwas unavailable. 19Aristoxenus,Book III (passim), discusses this. See 209 - 222 (Macran)or 73 - 92 (da Rios). 20Aristoxenus#37 (46.20 - 47.1 [da Rios]): &Xkta Trtav'reX)S; olov br a &y/to-y' Tb)V apPLOVLK6)Vh Irept T6V TOVwV Trr68ocrLs, 5'yoo'LV AJqnvaLOL 8E 7rxL7TTOV 'T'EpoL e8 TLVES6O'86'qV. OLKET'l TO)ViLEpWV 8EK6Trlu KOp0UOUOL ELPV "But the situation with the tonoi is very much like the arrangementof days, whereby the tenth day for the Corinthiansis the fifth for the Atheniansand the eighth for others."

ian from the affluent, haughty, orientalsociety of the Asian coast, and the Phrygianfrom the unbounded, ecstatic peoples of the wild, mountainous regions of the Anatolian highlands. By "different" I do not mean just differenttonoi, i.e. "scales," but entirelydifferentethnomusicalsystemsscales, instruments,subject matter,dance, poetry, and ethos. Of course we have no external examples of analytical music theory from the seventh, sixth, or fifth centuriesB.C., and it is only in the fourth century that Plato and Aristotle give us their brief, descriptive, that is, ethical, musical philosophies.21By this time the national harmoniaiseem to have become rather standardized.This probably begins to happen as early as the time of Damon, and it continuedsurelyin fifth-centuryAthenian tragedy. It is not entirely a "national" matter when Plato and Aristotle admitand rejectcertain"harmoniai"in establishingtheirideal states. They rejectnot Lydianmusic but Lydian-stylemusic. Roughlycontemporarywith Plato and Aristotle, however, are Eratocles'regularizingtheories and those of the Harmonists.They continue to break down the old harmoniaiwhich are now rapidlybecoming tonoi with more regularizedconstituentpartsand more compatible interrelationships.Finally with Aristoxenus one or two generationslater we get our first complete, unified, and all-encompassing analyticaltheory. We have two musical examples from fifth-centuryGreek lyric music, and the music of the Orestes papyrusat least can be shown to belong to the Phrygian (or Dorian) harmonia (as described in Aristides Quintilianus).22This Euripideantragedyof the very late fifth century,the Orestes, predatesAristoxenus by nearly a century, so I would not be surprisedto find it not competely analyzableby Aristoxeniananalysis. After all, Euripides wrote his music within the systems of the nearly standardizedharmoniai of the fifth century;Aristoxenus analyzed in a peripateticfashion the music theory of the fourth. Aristoxenus'tonoi do not necessarilytherefore belong to the practicalmusic of a centurybefore his day (in a city not native to him; he was not an Athenian). The tonoi he discusses are instead the variegated and separate but slightly modified musical systems of his own era. He recognized the irregularnational systems. He was disturbed by the previous attemptsby Eratocles and the Harmonistsat regularizing them, so his solution was to contrive the GreaterPerfect System to admit all the notes in the varioustonoi. This GreaterPerfectSystem was somewhat like Eratocles' shifting enharmonicsystem, but it accommodatedthe diatonic and chromaticas well as the enharmonicgenera. Aristoxenusno doubt had to squeeze some of the intervallicleaps used originally in the native, tribal harmoniai and then in the tonoi into or out of the great system, but such is the universallycompromisingforce of standardization.The difference between our own temperedand non-temperedsystems provides somewhat of a parallel. 21Plato Rep. 398 C - 399 E; Arist. Pol. 1340a38- 1340b10. 22Supra,n. 12. The intervalswould be (in the enharmonic):1 + 1/4 -+ /4 + 2 + 1 + 1/4 + 1/4 + 2 in the Dorian. Only the final intervalwould be differentin the Phrygian( + 1). It is not impossible that the music modulatesin line 5 (8etvvv ir6vov) from one to the other.

The end resultof Aristoxenus'efforts at standardization was apparently the list of tonoi found now in Cleonides. Aristoxenusnever lists the tonoi in the extant works. He does in section 37 mention several of them, but this is to illustratethe confusion.23It must have been elsewhere that he or Cleonides or an intermediatetheorist standardizedthese tonoi completely to fit into the GreaterPerfectSystem with each of the thirteentonoi standing one halftone above the preceding, e.g. beginning on A, A#, B, c, c#, d, d#, e, f, f#, g, g#, and a again in the next octave. Someone finding hypocrisy in my stating that the species of the dia tessaron, dia pente, and dia pason were merely analytical contrivances could easily jump in here to claim that "you yourself in your tedious analysis of the Seikilos inscriptiontry to prove that the piece is built upon the modulationof variousspecies of the dia tessaronanddia pente." Indeed I did try to prove that the species of the dia tesseron and dia pente were integral parts of the composition of the Seikilos inscription, and I still believe that to be the case. But I now clarify this: Some of the music, including the Seikilos inscription, written well after the promulgationof Aristoxenus' theories-and his work was well-known all over the GrecoRoman world24-was writtenin compliancewith Aristoxenianguidelines. That so many of our fragmentsof ancientGreekmusic are analyzable(with the Alypian tables) as belonging to a certainpitch-standardizedtonos (tropos) while at the same time being analyzable through a thetic shift as belonging to a certain octave species, I attributein part to this fact. Aristoxenus not only fit the music, the variegatedtonoi (once harmoniai) as well as the Eratocleanoctave species into one musical system of standardized notes and intervals, but he also createdthe standardizedsystem upon which almost all subsequentmusic in ancient Greece and Rome is based. Parallels for one man's theoreticalanalyses of music and theoreticalconstructs setting the standardfor the composed music of subsequentgenerations are apparentfrom the past few centuries, so it is highly possible that Aristoxenus, who we know was regardedas a giant in the field in antiquity, had as much an effect on ancient music theory and practice as did his contemporaryTheophrastuson ancietit botany or his teacher Aristotle on ancient, medieval, and Renaissancepoetic theory. I mentioned earlier the phenomenon which appears in most of our forty-two Greek musical fragments,that the tonos (tropos) as analyzed via the notation used in the Alypian tables is at the same time describableas an octave species analyzable via the Aristoxeniansystem. This same phenomenon was recognized in the early second century A.D. by Claudius Ptolemy. Never one to be stumpedby theoreticaldivergenceor contradictory data, Ptolemy (Harmonics2.5) described a mechanismfor shifting a piece of music from its notationaltonos (tropos) to its thetic, or practical, 23He says that some Harmonistslist the tonoi (ascending) as Hypodorian,Mixolydian, Dorian, Phrygian, Lydian, others as Hypophrygian,Hypodorian,Mixolydian, Dorian, Phrygian, Lydian, and others with different intervalsbetween these five or six tonoi. 24Thereis ample evidence for this in the testimoniafound in Rosettada Rios. AristoxeniElementa harmonica (Rome, 1954) 95-136.

octave species. The Mesomedes Hymns to the Muse and to Calliope (II A.D.) are in the Lydiantonos (by notation)but in the Dorianoctave species by thetic shift. The Seikilos inscriptionof the first century A.D. is in the Ionian tonos (by notation)but in the Phrygianoctave species by the thetic shift. The Berlin paean is in the Hyperioniantonos by notation but in the Hypodorianoctave species by thetic shift. Since Aristoxenus refused to employ the notational system(s) developed most probablyas early as the fifth century B.C.-he despised the use of notation as a pedagogical device-his theoretical, perfect systems were developed apart from the notational,and the two needed at some point to be reconciledin the theoretical treatises. This was part of Ptolemy's contribution. What I have done here amountsprobablyto an inferiorChailleyesque stab at establishing a chronological development for various systems of musical theory possibly so complex that any ancient theorist or musician would simply dismiss my summaryof theirdevelopmentalhistoryas typical neo-neo-Aristoxeniannonsense. But my belief that the world of ancient Greek music is, characteristicallyfor all of ancient Greek culture, a confusing, inconsistent, contradictoryone, especially in the sixth, fifth, and fourthcenturies, B.C., is strong. It is so strongthat I am able to reconcile all the harmoniai, tonoi, and octave species only so far as I can reconcile the calendarsof Athens and Corinthor the republicandemocracyof Athens and the dual monarchyof Sparta. There is no doubt that ancient theorists of governmentrecognized such differences and tried to reconcile them as partof a great cycle of governmentrevolving throughdemocracy, tyranny, and oligarchy.25I thereforeassume that ancient theorists of music recognized a similar difference between the various musics of Greece-Aristoxenus (#37) says as much in introducingthe varieties of tonoi-and that they then tried to reconcile these differences. Their solutions differ greatly, and most of the music and theoreticalevidence is lost. We do the best we can with a fraction of the total music that was actually written down in antiquity. But to judge from what evidence we do have, I would hazarda guess that the tonos and the octave species in Cleonides (ex Aristoxeno) were two very differententities, one an attemptedstandardizationof actual national musics, the other an analytical device developed from Eratocles but which became part of the standardizedmusic for subsequentgenerations. University of Arizona 25As described, for example, in Book 8 of Plato's Republic.