Diatonic music in Greece: a reassessment of its antiquity

SEARCH FOR | RETURN ¡yavets i ALERT | OROERS » Homes Browse Results Publications Issue/ Article Mnemosyne Previous article Next article Publisher. Brill Academic Publishers ISSN: 0028-7074 (Paper) 1568-525X (Online) of ae 0 è Export Citation: RIS DO!: 10.1183/156952502320880186 nd wurde fii ra i Classical Stiftes Issue: Volume 55, Number 6 Linking Options Date: November 2002 Send this article to | Pages: 669 - 702 an email addres Quick Search Search within this pub For. Search Title/Abs Search Author DIATONIC MUSIC IN GREECE: A REASSESSMENT OF ITS | Search Fulltext Search DOI ANTIQUITY John Curtis Franklin Ne ARANKUN 9As.o Abstract This paper argues that diatonic music and the theory of its tunings were an important precursor to the musical developments of the fifth and fourth centuries, The cyclical principles of diatony were” imported to Greece in the early Archaic period as a musical aspect of the Orientalizing movement, an event which is encrypted in the tradition that Terpander Invented the seven-stringed lyre. The Terpandrian style of music persisted until the time of Phrynis in the mid-fifth century, after whom constant harmonic innovation began to obscure its Important diatonic foundation. This phase of Greek musical history has left onty oblique traces in the corpus of technical literature, since the earliest (mostly) extant treatise, the Full Text Avallable The full text of this arti view the article as (a): PDF The size of this docurr Although it may be a li is the most authoritati\ E Harmonica ofAristoxenus, presents rather an account of the Perfect System, which was designed to accommodate the innovations of the later Classical period. Local HTML (Non-Pa This offers the quickes browsing. Please note mathematical characte precisely as in PDF ve E Frequently asked questions | General information on journals and books © Springer. Part of Springer Science+Business Media | Privacy, Disclaimer, Terms and Conditions, © Copyright Ini Remote Address: 130.37.129.78 è Server. MPWEB18 HTTP User Agent: Mozilla/4.0 (compatible; MSIE 6.0; Windows NT 5.1; SV1) http://www.springerlink.com/app/home/contribution.asp?wasp=b624028d01dd40578b0... [oraria

A REASSESSMENT OF ITS ANTIQUITY JOHN CURTIS FRANKLIN Abstract This paper argues that diatonic music and the theory of its tunings were an important precursor to the musical developments of the Ž fth and fourth centuries. The cyclical principles of diatony were imported to Greece in the early Archaic period as a musical aspect of the Orientalizing movement, an event which is encrypted in the tradition that Terpander invented the seven-stringed lyre. The Terpandrian style of music persisted until the time of Phrynis in the mid-Ž fth century, after whom constant harmonic innovation began to obscure its important diatonic foundation. This phase of Greek musical history has left only oblique traces in the corpus of technical literature, since the earliest (mostly) extant treatise, the Elementa Harmonica of Aristoxenus, presents rather an account of the Perfect System, which was designed to accommodate the innovations of the later Classical period. 1. Introduction The diatonic or ‘Pythagorean’ tuning process, one of Aristoxenus’ three types or genera of tuning, is now known to have been cultivated in the Ancient Near East from the Old Babylonian period (c. 1800 BC) or earlier down through the last generations of the cuneiform scribal tradition.1) It doubtless persisted beyond as the basis for the various forms of modal heptatonic music found throughout later Near Eastern history (see e.g. Farmer [1962], 373 f.). I have recently argued (Franklin [2002] and forthcoming) that the traditional ascription to Terpander of a newly-(re)invented sevenstringed lyre—the ¥pt‹tonow fñrmigj of fragment 4 (Gostoli)—epitomizes the Greek exposure, at the height of Neo-Assyrian expansionism (c. 750-650 BC), to this Mesopotamian tradition of classical music. The Mycenaean seven-stringed lyre, which has always been the chief 1) The Mesopotamian musical system cannot be reviewed here: the best introductions (with bibliography) are Kilmer (1971) and (1997). © Koninklijke Brill NV, Leiden, 2002 Also available online – www.brill.nl Mnemosyne, Vol. LV, Fasc. 6

obstacle to crediting Terpander or his age with the invention of a ¥pt‹tonow fñrmigj—see e.g. Maas and Snyder (1989), 203—may be readily explained as a trapping of high culture that disappeared, like literacy, with the collapse of the palaces. The non-diatonic genera—the enharmonic and chromatic which were popular in the later Classical period—represent the overlay of native musical in ections (derived from an unknown variety of sources, including probably the inherited art of epic song, and perhaps the intonation of the aélñw: v. infra) on the borrowed diatonic musical art, and hence the creation of a distinctly Hellenic form of the heptatonic koinê of the Near East. For though these genera could not be tuned solely through the consonant intervals of the diatonic method, they were nevertheless consistently seen as modiŽ cations of the diatonic, and were required to conform to minimum conditions of diatony according to Aristoxenus’ cardinal rule of sun¡xeia (‘continuity’). This hypothesis calls for a reassessment of the early history of Greek tonality. It is generally assumed that the Perfect System (sæsthma t¡leion)—documented, and largely devised, in the late fourth century by Aristoxenus—was the Greeks’ Ž rst coherent theoretical structure, the culmination of Ž fth-century eVorts to Ž nd some common structural ground between various heterogeneous tuning conventions—the rmonÛai. This evolutionary view of the Perfect System, most Ž rmly established by Winnington-Ingram (1936), has since crystallized into the not quite identical belief that the earliest tunings of which we hear were actually ‘defective’, the Greeks not yet achieving the complete diatonic conception that underlies the Perfect System with its cyclical species (eàdh or tñnoi) and pitch keys (tñnoi).2) Aristides Quintilianus, for instance, a neo-Platonizing musicologist of perhaps the late third century AD (Mathiesen [1999], 521-4), preserves a collection of rmonÛai, allegedly those known to Plato himself, which show sometimes more, sometimes fewer than seven pitches.3) There is also the spondei‹zvn trñpow (‘Libation Style’) 2) For the two senses of tñnoi, v. infra and Winnington-Ingram (1936), 82 f. Henderson (1957), 347 oVered a valuable reŽ nement to our interpretation of the tñnoi, seeing them not as absolute pitch-keys but “theoretical concepts employed to deŽ ne and name the relative loci of the topography of harmonic space”. 3) Aristid. Quint. 1.9. On these scales generally see Winnington-Ingram (1936), 55 V.; West (1992), 174 f. and n. 47, with further bibliography.

studied by Aristoxenus, a melody of the Archaic period attributed to the great aulete Olympus which, unlike the contiguous scales of the Perfect System, had an intervallic or ‘gapped’ structure, as it is commonly described.4) Finally, a handful of sources, beginning in the later Ž fth century with Philolaus—the earliest extant Pythagorean— have been read as attesting ‘defective’ scales, covering an octave in seven strings and so ‘omitting’ one pitch which was later ‘Ž lled in’.5) Thus, while admitting that it was “attractive” to equate the octave species of the Perfect System with the ancient rmonÛai—for “it is clear that they were to some degree the heirs of the rmonÛai, for both the term rmonÛai and the modal names were applied to them”—nevertheless Winnington-Ingram thought it better to see them as “systematized surrogates of less uniform scales.”6) Yet Winnington-Ingram himself suspected that the knowledge of diatonic scales was probably coexistent with, and perhaps even preceded, these so-called defective structures ([1928], 84 f.). Indeed, the discovery that a cyclical diatatonic tone-system was widely known in the Near East for probably two millennia before Aristoxenus now deprives this simple evolutionary view of whatever foundation it might claim, namely the paucity of pre-Aristoxenian source material. This is not to deny the existence of pentatonic and other ‘gapped’ systems, nor to reject the historicity of the rmonÛai in Aristides Quintilianus and the Libation Style of Olympus, nor to make a simple equation of the Ž fth-century rmonÛai with the octave species, nor to turn a blind eye to the systematization which the sæsthma t¡leion clearly represents. But equally, these facts are no longer suYcient to exclude the synchronous or earlier existence of heptatonic music in a well-developed, ‘undefective’ form. If an historical connection is established between the diatonic methods of Greece and Mesopotamia, our explanation of the non-diatonic Greek structures will need to be renovated. This paper assembles evidence for the early history of diatonic music in Greece. I distinguish this from the narrower term ‘diatonic 4) Aristox. fr. 83 = ps.-Plut. de Mus. 1135a; see Winnington-Ingram (1928); Barker (1984-9), 1.255 V. 5) Philol. fr. 44B6a D-K; ps.-Arist. Pr. 19.7, 19.25, 19.32, 19.44, 19.47; Nicom. Ench. 5 (244.22-245.11), etc. 6) Winnington-Ingram (1936), 10 f.; cf. 69, 82; cf. Anderson (1994), 139 f.

genus’, since the genera as we know them bear the Peripatetic stamp of Aristoxenus (Rocconi [1998]) and the term ‘diatonic’ itself may have been a relatively late coinage (v. infra). Yet obviously the genera must have codiŽ ed existing tuning methods. It is on this living music, and on its theoretical treatment before Aristoxenus, that we must focus. 2. The Chronology of Aristoxenus Other types of tuning were more popular in the late Ž fth and fourth centuries, namely those classiŽ ed within the enharmonic and chromatic genera.7) But according to Aristoxenus, who devised the system as we know it, the diatonic was older than either: prÇton m¢n oïn kaÜ presbætaton aétÇn yet¡on tò di‹tonon, prÇton gŒr aétoè ² toè ŽnyrÅpou fæsiw prostugx‹nei, deæteron d¢ tò xrvmatikñn, trÛton d¢ kaÜ ŽnÅtaton tò ¤narmñnion, teleutaÛÄ gŒr aétÒ kaÜ mñliw metŒ polloè pñnou suneyÛzetai ² aàsyhsiw.8) ‘Now, the diatonic must be put down as the Ž rst and oldest of them [sc. the genera], for the natural state [fæsiw] of man comes across it Ž rst, and afterwards the chromatic, and third and Ž nally the enharmonic, for it is the last to which the perception grows accustomed— and with diYculty at that, after much labor.’ A persistent tradition, not limited to the Aristoxenian school, agrees in regarding the diatonic as somehow more natural than the other genera, and given its systematic dependence on the primary resonant intervals 3:2 and 4:3, this is a crucial point.9) The diatonic 7) Without going into detail, the various genera and their shades (xrñai) were catalogued by the position of pitches which were ‘movable’ between the ‘bounding’ tones of the consonant fourth (oß peri¡xontew fyñggoi): see Ž rst Aristox. Harm. 21-27. 8) Aristox. Harm. 19; the formal sequence is followed, without chronological context, by e.g. Anth. Pal. 16.220.5 f. (Antipater); Cleonid. 3 (181.12 V.); ps.-Plut. de Mus. 1142d; Adrastus ap. Theo Sm. 53.17-56.5; Gaud. 5 (331.8 f.); Boeth. De inst. mus. 1.15 (200.25 f.), 1.21 (212.25). The sequence is reversed by Bacch. 21 (298.6), Vitr. de Arch. 5.4.3, as it is (more or less) in Aristoxenus’ presentation of the xrñai (Harm. 21-7). 9) This may be inferred from Philolaus’ and Plato’s preference for the diatonic, but is made explicit by Vitr. de Arch. 5.4.3: diatoni vero, quod naturalis est, facilior est intervallorum distantia (‘indeed, because it is natural, the distance of intervals of the diatonic is easier’); Aristid. Quint. 1.9 (16.10 V.): toætvn d¢ fusikÅteron m¡n ¤sti

basis of the other genera, seen in the precepts of sun¡xeia , is corroborated by Aristoxenus’ appeal elsewhere to ‘the nature of melody’ (t¯n t°w melÄdÛaw fæsin) as the foundation of the proper heptatonic tone structures governed by this rule (Harm. 28). Thus he states that there is ‘a certain nature of the cohesive/continuous in melody’ (tiw fæsiw . . . toè sunexoèw ¤n t» melÄdÛa, Harm. 27). Likewise, he criticized his predecessors for not showing which sequences would be ‘contrary to nature’ (parŒ fæsin), in other words, for not formulating the rule of sun¡xeia (v. supra). Nicomachus too described the diatonic progression as dictated by ‘a certain natural necessity’ (Žn‹gkú tinÜ fusik»).10) There is good reason to accept the Aristoxenian chronology as historical. Obviously we cannot expect Aristoxenus to have had a perfectly accurate picture of the state of Greek music from three centuries earlier. Nevertheless, if the diatonic was in fact of great antiquity, one may at least credit the musicians of the fourth century with a general awareness of the fact. A number of arguments conŽ rm this view. 3. The Seven-Stringed Lyre Terpander’s ¥pt‹tonow fñrmigj tells an important tale of its own, since the term tñnow, with eight distinct layers of meaning, has clear diatonic overtones.11) At its most basic, tñnow designated merely a tò di‹tonon k.t.l. (‘Of these, the diatonic is more natural’ etc.); Boeth. De inst. mus. 1.21 (212.26): diatonum quidem aliquanto durius et naturalius. Plato Lg. 657a4-c4 calls for music which follows the laws of nature (m¡lh tŒ t¯n ôryñthta fæsei parexñmena), and this can be loosely connected with the diatonic given his preference for it in the Republic and Timaeus; cf. Adrastus ap. Theo Sm. 56.3-5: tò d¢ di‹tonon g¡now ploèn ti kaÜ gennaÝon mllon katŒ fæsin: diò mllon toèto paralamb‹nei Pl‹tvn (‘The diatonic genus is somewhat simple and more noble by nature; for this reason Plato embraced it the more’); cf. Macr. Somn. Scip. 2.4.13 diatonum mundanae musicae doctrina Platonis adscribitur. 10) Nicom. Ench. 7 (249.1-3): t¯n d¢ prñbasin Žn‹gkú tinÜ fusik» . . . katŒ toèto tò diatonikòn g¡now (‘the progression by some physical necessity . . . along this diatonic genus’). 11) The musical writers vary in the number of meanings they report: see for example Cleonid. 12 (202.6 V.); Aristid. Quint. 1.10 (20.1 V .); Porph. in Harm. 4 (82.1 V.); Theo Sm. 70.7 V. From these and other sources I have compiled the following: 1. t‹siw; 2. fyñggow; 3 di‹sthma generally; 4. the di‹sthma of a whole tone speciŽ cally; 5. tñnow as a whole tuning; 6. the speciŽ c tuning of the diatonic

stretched string of any pitch, and was synonymous with t‹siw; to this category belong its various uses in rhetorical contexts, of the voice’s ‘pitch’. But naturally the Greeks tuned their instruments to purposeful tñnoi, and not randomly, whence the secondary equation of the term with fyñggow, the musical ‘note’. Cleonides cites ¥pt‹tonow in the Terpander fragment and Ion of Chios (v. infra) as an illustration of this sense, asserting that this was the normal force of the word, which thus comes close to being a technical term;12) we also Ž nd the form ¥pt‹fyoggow (Nicom. Ench. 6 [277.9-10]). If this is right, ¥pt‹tonow should imply a speciŽ c set or means of relating seven fyñggoi. Where there are purposeful pitches, there are also purposeful intervals; accordingly, some sources record a tertiary meaning of tñnow as the interval or ‘stretch’ between two tuned strings.13) Cleonides, whose third semantic level is merely Éw di‹sthma (‘as an interval’), may also be taken to mean this, but as the sequel shows, it was usual to understand tñnow as the speciŽ c interval of a wholetone—in the words of Aristoxenus, ‘that by which a perfect Ž fth is greater than a perfect fourth’.14) This fourth layer of meaning must point to a time when the wholetone was the interval which typically occurred between two strings; and this clearly requires the diatonic method. It is true that a diatonic scale also contains one or (for 5 and 6 v. infra); 7. tñnow as octave species (deriving perhaps from 5 and 6); 8. tñnow as pitch key, to which we may refer Cleonid. 1 (180.4 f.): tñnow d¡ ¤sti tñpow tiw t°w fvn°w dektikòw sust®matow Žplat®w (‘and tñnow is some place in pitch, without width, which can receive a system’; cf. Aristox. Harm. 37: p¡mpton dƒ ¤stÜ tÇn merÇn tò perÜ toçw tñnouw ¤fƒ Ïn tiy¡mena tŒ sust®mata melÄdeÝtai (‘The Ž fth subtopic [of rmonik®] is that which concerns the tñnoi, upon which the systems which are sung are placed’); cf. Porph. in Harm. 4 (82.3 V.). For meanings 7 and 8, v. infra. 12) Cleonid. 12 (202.8 V.): ¤pÜ m¢n oïn toè fyñggou xrÇntai tÒ ônñmati oß l¡gontew ¥pt‹tonon t¯n fñrmigga kay‹per T¡rpandrow kaÜ …Ivn. For Ion of Chios fr. 32 (West), v. infra. 13) Aristid. Quint. 1.10 (20.1-4): tñnon . . . kaloèmen . . . m¡geyow poiòn fvn°w, oåon Ú tò diŒ p¡nte toè diŒ tess‹rvn êper¡xei (‘We call a tñnow a certain interval [lit. ‘size’] of the voice, as for example that by which the Ž fth is greater than the fourth’); schol. ad Ptol. Harm. 1.4 (10.3): tñnow l¡getai kaÜ tò Žpò tñnou eÞw tñnon di‹sthma ; Porph. in Harm. 82: tñnow gŒr l¡getai kaÜ tò di‹sthma , oåon m¡tron ti toè t°w fvn°w tñpou, kayƒ ù l¡getai meÝzon eänai tò diŒ p¡nte toè diŒ tess‹rvn <tñnou> lñgÄ. 14) Aristox. Harm. 46: tñnow dƒ ¤stÜn Ú tò diŒ p¡nte toè diŒ tess‹rvn meÝzon, et alibi.

two semitones,15) so that not every interval can be a tñnow in this sense. But since wholetones far outnumber semitones, it was possible to understand these tone structures as proceeding ‘through tones’ (dia-ton-ically), and the genus is in fact so deŽ ned in a persistent tradition of non- and probably pre-Aristoxenian pedigree.16) Thus Plato uses tñnow to describe each and every ‘tone’ in the cosmic, Sirensung diatonic scale in the Myth of Er.17) A ‘heptatonic’ lyre should therefore mean precisely a ‘diatonic’ lyre; for the history of the term tñnow, with all its layers, points unambiguously to the word’s deep involvement with the diatonic tuning method. Terpander’s ¥pt‹tonow is meaning-laden, i.e. signiŽ cant, and consequently implies a particular style of music. In fact, the Lesbian poet was not merely an organological innovator. He was remembered for kainotomÛa generally—his radical, trail-blazing changes to musical idiom.18) If it is right to associate these changes with diatony, it need not be literally true that Terpander’s fñrmigj had seven strings, although this is the standard representation during the Archaic period. The actual tunings used in the new music would always be ¥pt‹tonow, regardless of the instrument used to render them—though a minimum of seven strings would be needed. In Mesopotamia, the ‘heptatonic’ system was expressed in terms of the nine-stringed sammû. Thus, according to one tradition, the salient 15) Depending on its species, and whether the structure is repeated at the octave. 16) Adrastus ap. Theo Sm. 54.12-15: kaleÝtai d¢ tò toioèton g¡now t°w melÄdÛaw di‹tonon . . . ÷ti diŒ tÇn tñnvn tò pleÝston diodeæei (‘This type of melody is called diatonic . . . because it progresses for the most part through tones’); Nicom. Ench. 12 (262.14 V.): kaÜ ¤k toætou ge diatonikòn kaleÝtai, ¤k toè proxvreÝn diŒ tÇn tñnvn k.t.l.; [Aristid. Quint.] 2.19 (92.22 f.): di‹tonon d¢ kaleÝtai diñti pepæknvtai toÝw tñnoiw katŒ tŒ diast®mata (‘It is called ‘diatonic’ because it is packed with tones in its intervals’)—Meibom recognized this passage as an interpolation; it is closely followed in this and other details by Anon. Bell., here 2.26 (7.14-16): di‹tonon m¢n oïn l¡getai , ¤peid¯ katŒ tò pleÝon diŒ tÇn tñnvn yevreÝtai tò di‹sthma (‘it is called diatonic since for the most part the interval is observed through tones’); Mart. Cap. 9.956: diatono vero [sc. dicitur], quod tonis copiosum; Boeth. De inst. mus. 1.21 (213.7): ideoque vocatur diatonum, quasi quod per tonum ac per tonum progrediatur. On the probable pre-Aristoxenian antiquity of this tradition, see Franklin (forthcoming). 17) Pl. Resp. 617b5 f.: Seir°na sumperiferom¡nhn, fvn¯n mÛan ßeÝsan , §na tñnon; cf. Philostr. Im. 1.10.15. 18) Ps.-Plut. de Mus. 1135c: ² Terp‹ndrou kainotomÛa; cf. Jacoby’s restoration to Marm. Par. FGrH 239A34: T¡rpandrow . . . toçw nñmouw toç[w kiy]a[r]v id [ik]oçw . . . [¤kainotñm]hse kaÜ t¯n ¦mprosye mousik¯n met¡sthsen.

fact is that Terpander ‘invented the heptatonic tuning’ (t¯n ¥pt‹tonon rmonÛan eêreÝn).19) This subtle distinction, between the seven-stringed lyre and ² ¥pt‹tonow rmonÛa, is eVectively glossed in the Hymn to Hermes, the standard mythological account of the instrument’s invention, dating to the sixth century or earlier—though naturally the myth itself may well be older than our text.20) The concluding lines of a technical set-piece read: kaÜ p®xeiw ¤n¡yhkƒ, ¤pÜ d¢ zugòn ³raren ŽmfoÝn, ¥ptŒ d¢ sumfÅnouw ôývn ¤tanæssato xord‹w.21) ‘And he put in the arms, and joined a yoke upon them both, / And stretched seven consonant strings of sheepgut.’ This is the Ž rst appearance of sæmfvnow (‘consonant’) in Greek literature. So much earlier is it than the next attestations that some scholars are reluctant to see here any of the word’s later technical sense (Barker [1984-9], 1.43 n. 18, cf. 1.295 n. 177). To be sure, this is not a passage of music theory. And yet Apollo, hearing the new sound, explicitly inquires of his brother ‘What is this t¡xnh?’ (H. Merc. 447, cf. 482 sqq.). We must not fail to give the word its due weight. In Stravinsky’s deŽ nition, t¡xnh is ‘the knowledge and study of the certain and inevitable rules of the craft’ ([1942], Lesson 1). This is what Alcman described concisely as tò kalÇw kiyarÛsdhn (‘to play the kiy‹ra beautifully’, Alcm. 41 PMGF ), while Terpander was 19) Georg. Syncell. Chronog. 403 (253.21 Mosshammer). Note that rmonÛa may be anachronistic here, not being certainly attested in the sense ‘tuning, scale’ before Lasus of Hermione (fr. 1 PMG 702) in the late sixth century (but see Sapph. fr. 70.9-11 [ Voigt], often overlooked). 20) The Hymn to Hermes has been variously dated, to as late as the end of the sixth century: see Janko (1982), 143; he is, however, receptive to a date as early as the second half of the seventh century, but not earlier because there is false archaism (communication). 21) H. Merc. 50 f. The key defense of the reading sumfÅnouw over the variant yhlut¡rvn is that Sophocles Ichn. 326 (Maltese) used sæmfvnon in his adaptation of the myth, which is in fact one of the next attestations of the word (preceded by Pi. P. 1.70, followed by Ion of Chios fr. 32 [West] and Ar. Av. 221, 659). It is true that yhlut¡rvn is the diYcilior lectio. But either Sophocles adopted sæmfvnon from the Hymn, or sumfÅnouw was later introduced into the Hymn under the in uence of Sophocles. The former is the more economical solution, and the alternation of sumfÅnouw with yhlut¡rvn might be accounted for by the complex ‘textual’ transmission of the Archaic oral repertoire.

remembered as ¤nt¡xnvw kiyarÛsaw (‘playing the kiy‹ra in accord with the t¡xnh’, Diod. Sic. 8.28 ap. Tz. H. 1.389). Far from being untechnical, this early passage is of chief importance, attesting that consonance was the key feature of the new seven-stringed instrument. ‘Beautiful musicianship’, tò kalÇw kiyarÛsdhn, required each string ‘to be well and knowledgeably tuned’ (tò “eï kaÜ ¤pistam¡nvw” eänai t¯n neur‹n), the most basic musical deŽ nition of rmonÛa.22) According to the Hippocratic de Victu, the ‘beautifully tuned voice’ comes through the use of consonance (kalÇw d¢ ²rmosm¡nhw glÅsshw t» sumfvnÛ&)—and here the diatonic is assumed.23) Indeed, with every string described as sæmfvnow in the Hymn to Hermes—sæmfvnoi xordaÛ—it is natural to understand consonance as operating mutually throughout. The tuning is consonant as a whole, with the seven resonating strings which are the prerequisite of diatony. Thus sumfvnÛa or sumfvneÝn could be used collectively to describe a tuning, where the diatonic is often assumed.24) For the enharmonic and chromatic genera used a number of relations which could not be established by the process of consonant tuning, ² l°ciw diŒ sumfvnÛaw.25) Diatony was thus the heptatony par excellence. For Terpander, ¥pt‹tonow may well have been synonymous with the later di‹tonow. First attested only in Aristoxenus, this term must have owed its existence to the need for distinguishing between several types of scales— heptatonic scales—some of which did not proceed ‘through tones’, were not ‘tuned throughout’ or ‘cross-supported’, or whatever di‹tonow originally meant in this context—for tñnow and di‹tonow, like rmonÛa and Akkadian pitnu, may all have belonged to an ancient metaphor of tonal ‘construction’.26) Likewise the term sæntonon, which in and 22) Schol. ad Ar. Eq. 994 = Suda s.v. rmonÛan; note the dactylic quotation, which suggests that the deŽ nition derives substantially from the Archaic period, a sort of technical fragment in oral diction. 23) Hp. Vict. 1.18. On the assumption of diatony here and in 1.8, v. infra. 24) Pl. Resp. 617b6 f.: ¤k pasÇn d¢ ôktÆ oésÇn mÛan rmonÛan sumfvneÝn; Nicom. Exc. 3 (242.15 f.): t°w kosmik°w sumfvnÛaw; 6 (277.9-10): ¥ptafyñggÄ . . . sumfvnÛ&. 25) Ps.-Plut. de Mus. 1145b-c, esp. tò m¯ dænasyai lhfy°nai diŒ sumfvnÛaw tò m¡geyow, kay‹per tñ te ²mitñnion kaÜ tòn tñnon kaÜ tŒ loipŒ d¢ tÇn toioætvn diasthm‹tvn (‘the magnitude [sc. of a quarter-tone] cannot be taken through consonance, as can the semitone and tone and the other such intervals’). 26) For pitnu, see Kilmer (1965), 262-265; (1971), 132.

after Aristoxenus referred to the Pythagorean tuning, presupposes a diVerent type of diatonic, the malakñn or ‘soft’. Taken together, the two terms suggest the ‘tense’ diatonic as a norm, and sæntonon describes this tuning quite well since each tñnow—whether we understand the word as an individual pitch, or the interval between two such pitches—is ‘together’ with its neighbors in the correct resonant—i.e. diatonic—place. Indeed, in less technical passages which use tñnow to mean ‘tuning’, the diatonic can be implicit or explicit.27) This peculiar usage, which had disappeared from the language of the theorists by the fourth century, continuing only in the sub-technical vernacular, suggests that the ‘normal’ tuning designated by tñnow was diatonic for non-professionals of basic musical education, even as professional musicians were expanding their horizons. Hence, according to Aristides Quintilianus, ‘[sc. the diatonic] can be sung by everyone, even those who are altogether untrained’ (psi gŒr kaÜ toÝw Žpaideætoiw pant‹pasi melÄdhtñn ¤sti, Aristid. Quint. 1.9 [16.1115]). This is important for understanding the Archaic background of the Classical yevrÛa, for it lets us assume, in the absence of qualiŽ ers, that the seven-stringed lyres which are ubiquitous in vase paintings of the seventh and sixth centuries were for the most part, like Terpander’s ¥pt‹tonow fñrmigj, tuned ‘normally’, i.e. diatonically. Compare the Akkadian tuning iÒartu (‘upright, normal’), found at one end of the diatonic cycle, with rmonÛhw ôry°w in the de Victu; Apollo’s mousikŒn ôry‹n at the wedding of Cadmus and Harmonia; and Plato’s insistence on ‘melodies which evince the correctness (ôryñthta) of nature’.28) To Terpander was attributed ‘the orthian style of melody’ (tòn t°w ôryÛou melÄdÛaw trñpon, ps.-Plut. de Mus. 27) Ar. Eq. 532: toè tñnou oék¡tƒ ¤nñntow shows tñnow as a ‘tuning’ generally; Hp. Vict. 1.8 also refers to a whole tuning as tñnow, and states that without rmonÛa it cannot exhibit the consonances of fourth, Ž fth and octave; based on the linguistic parallels to Philol. fr. 44B6a D-K, this passage must assume the diatonic— which most consistently employs these intervals; tñnow is expressly equated with ‘diatonic tuning’ at Anth. Pal. 16.220.5 f. (Antipater), where it is contrasted with the other genera: Žllƒ  m¢n kr‹nteira tñnou p¡lei,  d¢ melÄdñw / xrÅmatow,  d¢ sofw eêr¡tiw rmonÛaw (‘But the one [sc. Muse] is master of the diatonic, the next is a singer of the chromatic, and the last is inventor of the clever enharmonic’); three Muses, one per g¡now, are likewise attested at Plut. Quaest. conviv. 744c: treÝw ¾desan oß palaioÜ Moæsaw . . . aÞtÛa dƒ oéx Éw ¦nioi l¡gousi tŒ melÄdoæmena g¡nh, tò di‹tonon kaÜ tò xrvmatikòn kaÜ tò ¤narmñnion. 28) Pi. fr. 32 (S-M), v. supra; Hp. Vict. 1.8, v. supra; Pl. Lg. 657a7 f.

1140 f.). High-pitched music is described as ‘orthian’ elsewhere,29) but here the word, which has both meanings of iÒartu, seems to designate something more general. We do indeed Ž nd early hints of enharmonic and chromatic music, but these exceptions mark the rule (Franklin [forthcoming]). Terpander’s ¥pt‹tonow fñrmigj is therefore of much greater signiŽ cance than at Ž rst meets the eye. Appearing in the right place at the right time, and with the needed technology of seven resonating strings, it was the instrument by which the Archaic melic was achieved. 4. The Tonoi and the Perfect System While the diatonic tuning method may have shared the Classical stage with the chromatic and enharmonic genera, it must have provided the foundation of the later sæsthma t¡leion. The tñnoi or ‘pitch keys’—by which Aristoxenus organized and interrelated the various octave species (sx®mata) of each genus and the smaller fragments (sust®mata) thereof for the purposes of modulation and interconnection (metabol® )—were essentially diatonic in nature. This follows from the fact that the term tñnow in this usage must derive from its more basic meaning (v. supra), ‘the diVerence between a perfect fourth and a perfect Ž fth’. As may be seen in the Mesopotamian system, it is through the continuous alternation of these two intervals that the diatonic scale is generated, and consequently a series of tñnoi in the earlier sense of the word. Since these pitches were the same tñnoi ‘upon which systems are placed and sung’,30) we may exclude a direct etymology from tñnow as t‹siw (‘pitch’). Ptolemy considered this a likely explanation of the ancients’ coinage, though the exact derivation of this layer of meaning had been forgotten by his time.31) There were in fact thirteen tñnoi (and later 29) References to ‘orthian’ of high-pitched music, including the so-called öryiow nñmow, as well as ‘orthian’ rhythm, are collected by Barker (1984-9), 1.251 V. 30) Cf. Aristox. Harm. 37: p¡mpton dƒ ¤stÜ tÇn merÇn tò perÜ toçw tñnouw ¤fƒ Ïn tiy¡mena tŒ sust®mata melÄdeÝtai (‘The Ž fth subtopic [sc. of rmonik®] is that which concerns the tñnoi, upon which the systems which are sung are placed’). 31) Ptol. Harm. 2.10 (62.21 f.): tñnÄ diaf¡rontaw Žll®lvn êpoy¡menoi, kaÜ diŒ toèto àsvw tñnouw aétoçw ônom‹santew (‘assuming these to diVer from each other by a tñnow, and perhaps for this reason naming them tñnoi’).

Ž fteen), rather than seven or eight, in the sæsthma t¡leion .32) But this came about merely as an extension of the diatonic process through two cycles of alternating Ž fths and fourths, rather than one, so that all possible modulations could be accommodated by an underlying grid of semitones (hence the temptation to draw comparisons with equal temperament: see Laloy [1904], 251-5). Thus tñnow in this sense derives from the wholetone’s function as a useful unit of sonic measurement.33) Ptolemy himself, of course, recognized only seven tñnoi, which were not pitch-keys but octave species, and this shows him a more faithful heir to the Archaic heptachordal music than Ž fth-century modernists like Phrynis and Timotheus, or their successors who used the pitch-keys of Aristoxenus (Laloy [1904], 252; Winnington-Ingram [1936], 82 f.). 5. Interval Rotation and the Predecessors of Aristoxenus That the sæsthma t¡leion had a theoretical precursor in the diatonic has been further obscured by a passage of the Elementa Harmonica in which Aristoxenus, in criticizing the diagrams of his predecessors, says that they concerned themselves only with octachords in the enharmonic genus.34) This allusive and punning account was 32) Aristoxenus’ theory of the tñnoi is alluded to by Cleonid. 12 (203.4-204.15); Aristid. Quint. 1.10 (20.5 V.); cf. ps.-Censor. de Mus. 6.609.17 V.; Isid. Etym. 3.20.7; see also the criticisms of Ptol. Harm. 2.9-11. 33) Aristox. Rhythm. 2.21 gnÅrimon katŒ m¡geyow, ³toi Éw t‹ te sæmfvna kaÜ õ tñnow µ Éw tŒ toætoiw sæmmetra (‘. . . intelligible in magnitude, either like the consonant intervals and the tñnow, or like those intervals commensurate with these’); Adrastus ap. Theo Sm. 53.3 V.: kay‹per õ p°xuw toè kurÛvw topikoè diast®matow . . . ¦sti d¢ gnvrimÅtaton tò toniaÝon di‹sthma , ¤peid¯ tÇn prÅtvn kaÜ gnvrimvt‹tvn sumfvniÇn ¤sti diafor‹ (‘just like the cubit for literally spatial intervals . . . the tñnow is the most intelligible interval, because it is the diVerence between the Ž rst and most intelligible consonances’); cf. 66.19-67.3: oß d¢ palaioÜ prÇton di‹sthma t°w fvn°w ¦labon tòn tñnon . . . ÷ti m¡xri toætou katabaÛnousa ² fvn¯ toè diast®matow Žplan° t¯n Žko¯n ful‹ssei. tò d¢ metŒ toèto oék¡ti oáa te ² Žko¯ pròw ŽkrÛbeian labeÝn tò di‹sthma (‘and the ancients took the tone as the Ž rst interval of the voice . . . because, as the voice proceeds, it safeguards the hearing as far as this interval, but after this [i.e. with smaller intervals] the hearing is no longer able to take the interval with precision’). 34) Aristox. Harm. 2-3: toçw m¢n oïn ¦mprosyen <²mm¡nouw t°w rmonik°w pragmateÛaw sumb¡bhken Éw ŽlhyÇw, restituit Marquard ex Procl. in Ti.> rmonikoçw eänai boælesyai mñnon, aét°w gŒr t°w rmonÛaw ´ptonto mñnon, tÇn dƒ llvn genÇn oédemÛan pÅpotƒ ¦nnoian eäxon (‘Now it happens that those who previously set

already confusing in antiquity. As Proclus commented, ‘Aristoxenus is saying something incredible here, that the ancients did not know the diatonic diagram,’35) reporting also the older gibe of Adrastus, elicited by this same problem, that Aristoxenus was generally ‘concerned to seem to say something brand new’ (÷pvw ’n dñjú ti kainòn l¡gein pefrontikÅw).36) For the diatonic had been the subject of close scrutiny by Philolaus, Plato, and—in his wish to make it conform more closely to the higher superparticular (i.e. resonant) ratios— Archytas.37) Indeed, the statement, according to the usual interpretion, would scarcely accord with Aristoxenus’ own chronology of the genera. The solution to the riddle must be that Aristoxenus, in focusing on the new system he was forging, neglected an older, established yevrÛa as not needing any redress, and saved his criticism for the architects of its change. Aristoxenus brought to completion what had long been sought, a new system which could accommodate the innovations of the late Ž fth and fourth centuries. What he has taken for granted, then, is the phase of music and its theory preceding these trends, which, relative to the New Musicians, will have been classical forms. Thus, when he complains that ‘Eratocles attempted to enumerate the octave-schemes of one genus [sc. the enharmonic], showing it, without formal demonstration, by the rotation of the intervals’ (ƒEratokl°w ¤pexeÛrhse kayƒ ©n g¡now ¤jariym°sai tŒ sx®mata toè diŒ pasÇn ŽnapodeÛktvw t» perifor˜ tÇn diasthm‹tvn deiknæw, Aristox. Harm. 6), we should not conclude that the enharmonic genus was the Ž rst melodic style ever subjected to theoretical scrutiny. It was rather the Ž rst to be analyzed with an eye towards comprehending in a single system the innovative practices that were themselves to the endeavour of rmonik® truly wanted to be only ‘rmonikoÛ’, for they grasped only the enharmonic [rmonÛa] itself, but never yet had any thought for the other genera’); cf. the summary, with some additions, in ps.-Plut. de Mus. 1143e-f. 35) Procl. in Ti. 3.192a (2.169.21-29 Diehl): ¤n oåw kaÜ l¡gei ti yaumastòn õ ƒAristñjenow, ÷ti tò diatonikòn di‹gramma oék ¾desan oß palaioÛ . . . pÇw oïn taèta l¡gei kaÛtoi kaÜ toè Pl‹tvnow katŒ tò diatonikòn g¡now ¤kyem¡nou tò di‹gramma kaÜ tÇn ŽmfÜ tòn TÛmaion, yaum‹sai jion. 36) Aristox. fr. 8 = Adrastus ap. Procl. in Ti. 3.192a (2.169.29 V. Diehl). 37) Philol. fr. 44B6a D-K; Archyt. fr. 47A16; Pl. Ti. 35b1-36b5. Cf. WinningtonIngram (1932); Burkert (1972), ch. 5 sec. 2; Barker (1978), 3; (1984-9), 2.59 f.; West (1992), 165.

then (in the second half of the Ž fth century)38) being developed, what would eventually culminate in the sæsthma t¡leion. Eratocles is criticized for not having done this well or completely enough, and for doing it ŽnapodeÛktvw, that is, without “the logical derivation of propositions from appropriate principles” (Barker [1984-9], 2.130 n. 25.). The phrase t» perifor˜ tÇn diasthm‹tvn is crucial. This ‘interval rotation’ has always been seen as Eratocles’ great achievement, a breakthrough in the cyclical synthesis of disparate tunings. But given the opprobrious tone, it is equally possible to understand the phrase as belonging to the complaint of ŽnapodeÛktvw. Since Aristoxenus criticized his predecessors for not producing suYcient diagrams, ² perifor‹ would then be a means of demonstrating the species without recourse to diagrams, and so presumably could be executed on the instrument itself, i.e. with one tuning succeeding another in a visibly and/or audibly coherent sequence (deiknæw, ‘showing’). It was a processual cycle which ‘brought one back around’ to the starting point, exactly as perifor‹ suggests; the similarity to the diatonic tuning cycle of UET 7/74 is striking (for which see Gurney [1968]; Wulstan [1968]; Gurney [1994]). Thus the rotation of intervals was a familiar technique that could be used without the more rigorous methods required by Aristoxenus—not needing, for example, the linear interval map of the sæsthma t¡leion. The underlying principle of scales related cyclically would have been the same in both systems, but the two forms of presentation were quite distinct. To take full account of complex musical developments, a more graph-like approach was needed to assist the ears in the analysis of music. This was the function of the musical diagram, as Bacchius explains: Di‹gramma d¢ tÛ ¤sti;—Sust®matow êpñdeigma . . . diagr‹mmati d¢ xrÅmeya, ána tŒ t» Žko» dæslhpta prò ôfyalmÇn toÝw many‹nousi faÛnhtai. (Bacch. 62 [305.16-20]; cf. Rocconi [1999], 101) ‘And what is a diagram? A representation of a (sc. musical) system. And we use a diagram so that, for students of the subject, matters which are hard to grasp with the hearing may appear before their eyes.’ 38) The resonance between his theory of road-junctions and Ion of Chios fr. 32 (West)—for which v. infra and cf. West (1992), 226—as well as his use of octachords, lets Eratocles be dated approximately to the second half of the Ž fth century.

Thus Eratocles did not produce a suYcient account by Aristoxenus’ latter-day standards, but merely used a rotational process which did little to transform a no-longer-adequate method of musical analysis. Given that the sæsthma t¡leion reveals a diatonic substructure in the tñnoi, and that Aristoxenus accepted the diatonic as the oldest of the genera, the easiest solution is to suppose that ² periforŒ tÇn diasthm‹tvn reveals a thorough familiarity with the cyclical properties of the diatonic method as the basis of pre-Aristoxenian yevrÛa—a long-familiar, not novel, approach. It is important, then, that Bacchius deŽ nes a diagram as ‘a  at chart on which all the genera could be sung’ (sx°ma ¤pÛpedon, eÞw ù pn g¡now melÄdeÝtai).39) Plato, who was only interested in the diatonic, serves to unite this tuning method with the cyclical in his elaborate Myth of Er, where the eight tones (tñnoi) all partake in a cyclical cosmos (Pl. Resp. 616b1-617d5). The old usage of tñnow as ‘tuning’ clariŽ es the word’s later meaning of ‘octave species’: that is, these tñnoi were ‘the tunings’—i.e. the standard tunings—and they were created by cyclical transformation; compare the synonymous term trñpoi, which may thus be rendered as ‘turnings’ of the musical circle.40) The link between these cyclical tñnoi and the diatonic method is established by the intermediate application of tñnow, ‘tuning’, to mean ‘diatonic tuning’ speciŽ cally—an ancient and somewhat untechnical usage documented for the Classical period (v. supra). Eratocles therefore showed how the enharmonic could be schematized according to a classical, diatonic, and fundamentally circular approach. In the light of the foregoing, one can see, in a criticism of his predecessors where Aristoxenus’ new, unaddressed harmonic concerns dwarf those of an earlier period, the strata of the evolutionary process which led to the sæsthma t¡leion : 39) Bacch. 62 (305.16-20). A diagram with all the genera is found at e.g. Nicom. Ench. 12 (264.6 V.). 40) For trñpow as tñnow, see e.g. Plut. An seni 793a: tñnvn kaÜ trñpvn . . . oîw rmonÛaw oß mousikoÜ kaloèsi; De E Delph. 389e: eàte tñnouw µ trñpouw eàyƒ rmonÛaw xr¯ kaleÝn: cf. West (1992), 188 n. 103; ps.-Plut. de Mus. 18.1137b: polutrñpÄ; Bacch. 46-7 (303.3 V.), etc.; Gaud. 20 (347.22): trñpon µ tñnon; Aristid. Quint. 1.6 (8.20), 1.10 (20.1-4): tñnon . . . trñpon susthmatikñn, oåon lædion µ frægion, etc.; Alyp. 3 (367.20): trñpouw te kaÜ tñnouw.

t¡tarton dƒ n eàh m¡row tŒ sust®mata yevr°sai pñsa tƒ ¤stÜ kaÜ po݃ tta kaÜ pÇw ¦k te tÇn diasthm‹tvn kaÜ fyñggvn sunesthkñta. oéd¡teron gŒr tÇn trñpvn teyeÅrhtai tò m¡row toèto êpò tÇn ¦mprosyen: oëte gŒr eÞ p‹nta trñpon ¤k tÇn diasthm‹tvn suntÛyetai tŒ sust®mata kaÜ mhdemÛa tÇn suny¡sevn parŒ fæsin ¤stÜn ¤pisk¡cevw tetæxhken, oëyƒ aß diaforaÜ psai tÇn susthm‹tvn êpƒ oédenòw ¤jhrÛymhntai. perÜ m¢n gŒr ¤mmeloèw µ ¤kmeloèw plÇw oéd¡na lñgon pepoÛhntai oß prò ²mÇn, tÇn d¢ susthm‹tvn tŒw diaforŒw oß m¢n ÷lvw oék ¤pexeÛroun ¤jariymeÝn— ŽllŒ perÜ aétÇn mñnon tÇn ¥ptaxñrdvn “ ¤k‹loun rmonÛaw t¯n ¤pÛskecin ¤poioènto—oß d¢ ¤pixeir®santew oéd¡na trñpon ¤jhriymoènto, kay‹per oß perÜ Puyagñran tòn Zakænyion kaÜ ƒAg®nora tòn MutilhnaÝon. (Harm. 36-7) ‘The fourth topic would be to observe the systems: how many they are, what type, and how they are composed from intervals and musical tones. For in neither of these ways has this topic been observed by the earlier harmonists: for the question of whether systems are composed from intervals in every manner, and whether none of these composites run counter to nature, has not met with an examination; nor have all the diVerences of the systems been enumerated by anyone. For concerning what is properly melic and what is not (perÜ m¢n gŒr ¤mmeloèw µ ¤kmeloèw ), our predecessors have simply made no account. Some made no attempt at all to enumerate the diVerences between systems, but made examination only of the heptachords themselves, which they used to call rmonÛai. Those who did try were in no way exhaustive, as for instance Pythagoras of Zacynthus and his school, and Agenor of Mytilene and his.’ The key phrase here is ŽllŒ perÜ aétÇn mñnon tÇn ¥ptaxñrdvn “ ¤k‹loun rmonÛaw t¯n ¤pÛskecin ¤poioènto. The manuscript reading ¥ptaxñrdvn must be retained against the emendation ¥ptŒ ôktaxñrdvn, adopted by Westphal, Marquard, Macran and Da Rios. In M, ¥ptŒ xordÇn had been corrected to ¥ptaxñrdvn; wishing to account for this, modern editors have seen a parallel in Aristoxenus’ criticism (v. supra) of his predecessors who ‘only spoke about enharmonic octachord systems’ (perÜ susthm‹tvn ôktaxñrdvn ¤narmonÛvn mñnon ¦legon, Harm. 2). It is generally held that the Elementa Harmonica is, as we have it, a later compilation of two independent drafts, for there are a number of parallel topics that are repeated between books 1 and 2.41) On the supposition that the two passages in question are essen41) See Da Rios (1954), CXII V.; contrast Bélis (1986).

tially the same critique, it is suggested that ôkta- was omitted in a sort of numerical haplography, whereupon an editor of M closed the gap between ¥ptŒ and xordÇn in a false emendation. But this cannot be right. First, ¥ptŒ xordÇn is more economically explained as an erroneous division of EPTAXORDVN at the time when word breaks were Ž rst introduced to a text without accents, a very simple error for which there is an exact (but inverted) parallel in the tradition of Nicomachus (Exc. 1 [266.7]). Second, with “ ¤k‹loun rmonÛaw (‘which they used to call rmonÛai’), Aristoxenus is evidently drawing a distinction between an older use of the term and that of his own day. Now, with the exception of this passage, Aristoxenus always uses rmonÛa to mean a scale in the enharmonic genus; the enharmonic, so popular in the late Ž fth and early fourth centuries, had become the ‘tuning’ par excellence.42) Thus the predecessors criticized here cannot have been talking about the enharmonic. Consequently the Ž rst passage cannot be adduced as a parallel, and the supposed haplography vanishes. With this reading, the passage lets us glimpse the earlier practical and theoretical norm of the seven-stringed lyre which had been current in the Archaic period and well into the Classical. It is clear from the phraseology that Aristoxenus saw these heptachords as a Ž xed, Ž nite set, as shown both by the deŽ nite article and still more so by the intensive pronoun (perÜ aétÇn mñnon tÇn ¥ptaxñrdvn, ‘only about the heptachords themselves’). This would naturally precede the work of Eratocles and others, whose octachord diagrams were the Ž rst steps towards the sæsthma t¡leion . Moreover, these ancient rmonÛai must have been more orderly than the odd tunings, seemingly from the high enharmonic period, preserved by Aristides Quintilianus, which show sometimes more, sometimes fewer than seven pitches.43) For they did in fact have seven pitches—exactly as we 42) Adrastus ap. Theo Sm. 55.15-56.1: kaleÝsyai d¡ fhsin ƒAristñjenow toèto tò proeirhm¡non g¡now rmonÛan diŒ tò eänai riston , Žpenegk‹menon toè pantòw ²rmosm¡nou t¯n proshgorÛan (‘And Aristoxenus says that this, the aforementioned genus, is called rmonÛa because it is best, taking this title away from tò ²rmosm¡non as a whole’); ps.-Plut. de Mus. 1143e-f. See also Henderson (1957), 388 f.; West (1992), 164 f. 43) Aristid. Quint. 1.9. On these scales generally, see Winnington-Ingram (1936), 55 V.; West (1992), 174 f. and n. 47 with literature cited there.

should expect from early literary evidence and the consistent representation of seven-stringed lyres throughout the Archaic period.44) This ancient heptachordy began to undergo a permanent change at the professional level in the Ž rst half of the Ž fth century (probably c. 480-460),45) an important landmark being Phrynis’ victory at the Panathenaea in 446/5 with his modern poluxordÛa.46) Yet the heptachordal norm must have persisted at the popular level and in the music lesson, for non-professional lyres are still commonly so depicted throughout the period of the New Music and beyond, and the seven strings of the ancients are still clearly recalled in much later sources.47) Aristotle treats it as a matter of fact that there were seven strings in the old rmonÛai, while the Aristotelian Problems, 44) Terp. fr. 4.2 (Gostoli); h. Merc. 51; Pi. N. 5.22: fñrmiggƒ . . . ¥pt‹glvssan; P. 2.70 f.; Ion of Chios fr. 32 (West), v. infra. For the ceramic evidence, Maas/Snyder (1989). 45) This crucial issue has not been adequately addressed; see Ž rst West (1992), 63 f. A thorough study of the ceramic evidence is needed; initial indications of my own ongoing survey are that eight-stringed instruments become a common conŽ guration in professional contexts between 480-460; but note that an accurate typology, could it be established, might itself provide a dating criterion. Corroborative literary evidence is Pliny Nat. 7.204, who credits Simonides (traditionally c. 556468: see West [1971]) with the eighth string—or tòn trÛton fyñggon as the Suda puts it (s.v. SimvnÛdhw)—while ps.-Plutarch reports that Lamprocles added a disjunctive tone at the top of the conjunct heptachord (de Mus. 1136c-d). Nicomachus’ attribution of the eighth string to Pythagoras in Ench. 5 (244.14 V.) was in his time already an old tradition, which may be dismissed as having the ulterior motivation of glorifying the master. The tradition of Terpander’s eighth string is equally false, as I will show in a future publication. 46) Ister FGrH 334F56 = schol. a ad Ar. Nub. 971: õ Frèniw kiyarÄdñw . . . dokeÝ prÇtow kiyarÛsai parƒ ƒAyhnaÛoiw kaÜ nik°sai Panay®naia ¤pÜ Kalli<m‹x>ou rxontow (for the emendation, see West (1992), 360 n. 15. 47) E. Alc. 446 f.: ¥pt‹tonñn tƒ ôreÛan / x¡lun; Ion 881; Call. Del. 253 V.: ¦nyen õ paÝw toss‹sde lærú ¤ned®sato xord‹w / ìsteron, õss‹ki kæknoi ¤pƒ ÈdÛnessin eisan: ögdoon oék¡tƒ eisan (‘Hence the child [sc. Apollo] later bound that number [sc. seven] of strings to the lyre, as often as the swans sang upon his birth; an eighth time they did not yet sing’); forged Laconian decree, Boeth. De inst. mus. 1.1 (182.7 V.); Verg. Aen. 6.646; Thrasyllus wrote a work called PerÜ toè ¥ptaxñrdou probably in the early Ž rst century AD (Porph. in Harm. 5 [91.14]; for dates see Barker [1984-9], 2.209 f.); Anth. Pal. 9.250 (Onestes); Nicom. Ench. 3 (242.5): ¦n ge t» ¥ptaxñrdÄ katŒ tò palaiòn, cf. 5 (245.4), 7 (249.15), 9 (253.4), 11 (256.5 f.): t» toÛnun ŽrxaiotrñpÄ lær&, tout¡sti t» ¥ptaxñrdÄ; Exc. 1 (266.3), 6 (277.9-10); Paus. 3.12.10: xordaÝw ¥ptŒ taÝw ŽrxaÛaiw; Lucian Astr. 10; ps.-Plut. de Mus. 1141c: ¥ptafyñggou t°w læraw êparxoæshw §vw eÞw T¡rpandron; Exc. Neap. 23 (418.10 V.); Procl. Chr. ap. Phot. Bibl. 320a33-b11; Alex. Aphr. In Metaph. 1093a13; Clem. Al. Strom. 6.16.144; Isid. Etym. 3.22.4; Suda s.v. T¡rpandrow; etc.

compiled well into the octachord period, nevertheless report heptachords as standard in an earlier yevrÛa.48) Nicomachus clings stubbornly to the memory, loyally (if wrongly) attributing the eighth string to Pythagoras (Ench. 5 [244.22-245.11] et passim). We are thus justiŽ ed in regarding ‘the heptachords’ of Aristoxenus as comprising a coherent collection of some sort associated with this ancient phase of Greek music, just as the Aristotelian problems cited refer in the plural to heptachordal rmonÛai. Aristoxenus remembered that the term rmonÛa was closely associated with the tunings of this heptachordal ‘system’, not used as ‘attunement’ in some more generic sense which might include a variety of other tunings with more or fewer than seven strings, such as those in Aristides Quintilianus. For Aristoxenus, these heptachordal tunings were the rmonÛai. Thus two broad groups of rmonikoÛ may be detected in Aristoxenus’ critique. Like Eratocles, the schools of Pythagoras of Zacynthus and Agenor of Mytilene, while aware of the subjects which needed discussion, addressed them inadequately. But the unnamed adherents of seven-stringed classical music never even attempted an investigation. It was not the concern of the earlier, codiŽ ed heptachordy, which was widely taught in the paideÛa, to incorporate new features which would catalyze a breakdown of rules and conventions which had been handed down from the Archaic period. 6. The Two Classical Styles This conservative force, and the coexistence in the Ž fth century of an old heptachordal discipline with its modiŽ cation by avantgarde musicians, is well illustrated by Right Logic’s resentful account of the ‘contemporary’ music lesson in Clouds. Scandalously, young students were introducing fashionable modulations—kampaÛ or ‘bends’,49) a term which derives its meaning from the ancient image 48) Arist. Metaph. 1093a14: ¥ptŒ d¢ xordaÜ ² rmonÛa; ps.-Arist. Pr. 19.7: oß ŽrxaÝoi ¥ptaxñrdouw poioèntew rmonÛaw (‘the ancients, making their heptachordal rmonÛai’); 19.47; 19.25: ¥pt‹xordoi ·san aß rmonÛai tò palaiñn; 19.32: ¥ptŒ ·san aß xordaÜ tò ŽrxaÝon; cf. 19.44. 49) For the term, cf. Ar. Nub. 333: frr. 753, 953 K-A; Pherec. fr. 155.15 K-A; Eup. fr. 366 K-A; Tim. fr. 26.3 (PMG 802) of Phrynis; Poll. Onom. 4.66.

of the melodic ‘road’50)—into the older style on oVer from the kiyarist®w: eäta badÛzein ¤n taÝsin õdoÝw eét‹ktvw eÞw kiyaristoè . . . eätƒ aï promayeÝn Ÿsmƒ ¤dÛdasken tÆ mhrÆ m¯ jun¡xontaw . . . ¤nteinam¡nouw t¯n rmonÛan ¶n oß pat¡rew par¡dvkan. eÞ d¡ tiw aétÇn bvmoloxeæsaitƒ µ k‹mcei¡n tina kamp®n oáaw oß nèn, tŒw katŒ Frènin taætaw tŒw duskolok‹mptouw, ¤petrÛbeto tuptñmenow pollŒw Éw tŒw Moæsaw ŽfanÛzvn. (Ar. Nub. 964-72) ‘And then [sc. they had] to walk in good order in the streets to the citharist’s . . . / And then in turn he taught them to learn a song by heart, not holding their thighs together . . . / Tuning the rmonÛa which our fathers handed down. / But if one of them played the fool or eVected some modulation— / Like musicians nowadays do, those diYcultly-bent modulations à la Phrynis— / He got a good long thrashing for doing away with the Muses.’ Actually, the humor of the passage lies in the anachronism of the complaint, for Phrynis was already old news in Aristophanes’ day, having been radical only when the men who fought at Marathon had reached middle or old age (Dover [1968], ad 971); only a few codgers could have lived to see Clouds. We are dealing then with a musical education that was traditional already in the early Ž fth century—in other words, an inheritance from the Archaic period. Note that here in the music lesson, where we must assume a sevenstringed lyre, the term for the tuning is again rmonÛa, as in Aristoxenus. The conservative musical tastes underlying this passage—probably not entirely shared by Aristophanes, who indulged in New Music himself (and no doubt not always ironically)—is found again in Frogs. When Dionysus brings Aeschylus back to earth as the greatest tragedian, and not Euripides, it is the return of an old celebrity who had learned his craft in the classical seven-stringed phase of music. As another Aristophanic character complained elsewhere, ‘they sang everything all alike—on seven strings’ (Âdon ¥pt‹xorda p‹nyƒ õmoÝa, fr. 467 K-A). Thus, in Frogs, Euripides charges Aeschylus with ‘always composing the same things’ (poioènta taëtƒ ŽeÛ, Ran. 1250), while 50) For the road image, cf. West (1992), 227 and n. 25; Rocconi (1999), 99 f. The image survives into modern Greek, where drñmow designates ‘mode’ (Beaton [1980], 9). It is also found in ancient Indian music theory, where antaramarga is ‘the path between the notes’: see e.g. Widdess (1995), 264-7.

Psellus attributes to Euripides the introduction of poluxordÛa in tragedy.51) The well-known vase-painting by Duris, showing the music lesson in its classical form with boys studying the lyre and epic poetry at the house of the kiyarist®w—and no fewer than four carefully rendered seven-stringed instruments—is from this same Aeschylean period (Berlin F 2285: see West [1992], plate 11). One boy is shown with a tablet on which he has written a hexameter invoking the Muse; it belongs to the traditional prelude style attributed to Terpander—the Aeolic form MoÝsa is therefore not accidental (West [1971], 308). This ‘rmonÛa which our fathers handed down’ does not suggest the usual picture of chaotic evolution used to explain the apparently aberrant evidence of Philolaus fr. 6a, the Libation Style of Olympus, and the rmonÛai of Aristides Quintilianus. On the contrary, since rmonÛa and ¥pt‹xorda in the Aristophanic passages clearly do not presuppose one tuning only, it indicates a well-deŽ ned convention of tuning which had been stable for generations.52) This is conŽ rmed by another music lesson scene where Aristophanes recounts how the boorish Cleon made little progress because he would learn only the Dorian rmonÛa (Eq. 985-96); the implication is that mastery of the Dorian led on to a more involved knowledge of tuning. Hence these passages, taken together, refer to a tradition of tuning which was formal, ancient, had several stages of which the Dorian had had some primacy for generations before Aristophanes, and was properly heptachordal. What role did diatony play in this period of the classical—i.e. Archaic—heptachord? Was the diatonic, as in the later Ž fth century, largely overshadowed by what would become known as the enharmonic and chromatic genera, or by some other tunings of which we have no notice, like those of Aristides (though these themselves are predominantly enharmonic in character)? Or was the Terpandrian heptachord proper to a classical form of diatonic music which endured throughout the Archaic period? A scholiast, commenting on the ‘rmonÛa which our fathers handed down’, asserts 51) Psell. De trag. 5: sust®masi d¢ oß m¢n palaioÜ mikroÝw ¤xrÇnto, EéripÛdhw prÇtow poluxordÛ& ¤xr®sato. 52) Cf. Hp. Vict. 1.18: rmonÛhw sunt‹jiew (‘the arrangements of rmonÛa’).

that ‘the ancient tuning was sæntonow53)’—the very term used by Aristoxenus to describe the diatonic in its normal form.54) In the music lesson the diatonic was surely the Ž rst method to be learned, if it was regarded as the oldest and, as Aristoxenus held, most open to human discovery (v. supra). It would have been easiest to master, since, as Aristoxenus asserted elsewhere, the ear can readily trust the consonant intervals, and the diatonic was tuned by a very regular progression of these prÇtai sumfvnÛai.55) The enharmonic, by contrast, could not be established solely through ² l°ciw diŒ sumfvnÛaw (v. supra). Requiring years of practice, it belonged to the art of the professional musician.56) The citizen-choruses of the tragic stage, with twelve or more voices, would have needed much practice to make these quarter-tone discriminations nicely.57) Indeed, though the enharmonic was considered proper to tragedy in the 53) Schol. ad Ar. Eq. 968, glossing ¤nteinam¡nouw t¯n rmonÛan: Éw suntñnou oëshw t°w palaiw rmonÛaw. 54) Cf. Psell. De trag. 12 proshæloun aétaÝw oß kr‹tistoi aélhtaÛ, õ m¢n t¯n xrvmatik¯n perÛodon, õ d¢ t¯n ¤narmñnion, õ d¢ t¯n sæntonon; Winnington-Ingram, ap. Browning (1963), 71, wished to supplement this as sæntonon <di‹tonon>. 55) Cf. Aristox. Harm. 55: polç mllon toÝw tÇn sumfÅnvn meg¡yesi pisteæei ² aàsyhsiw µ toÝw tÇn diafÅnvn: Žkribest‹th dƒ ’n eàh diafÅnou diast®matow l°ciw ² diŒ sumfvnÛaw (‘our perception is much more trusting of the consonant interval sizes than the non-consonant, and the tuning of a nonconsonant interval would be most precise when it is taken through consonance’); cf. Vitr. de Arch. 5.4.3, v. supra; Adrastus (ap. Theo Sm. 53.3 V.), v. supra. 56) Aristox. Harm. 19: trÛton d¢ kaÜ ŽnÅtaton tò ¤narmñnion, teleutaÛÄ gŒr aétÒ kaÜ mñliw metŒ polloè pñnou suneyÛzetai ² aàsyhsiw (‘Third and last comes the enharmonic, for the perception becomes accustomed to it last and with diYculty after much labor’); cf. Adrastus ap. Theo Sm. 56.1 V.: ¦sti d¢ dusmelÄdhtñtaton kaÜ, Éw ¤keÝnñw fhsi, filñtexnon kaÜ poll°w deñmenon sunhyeÛaw, ÷yen oédƒ eÞw xr°sin =&dÛvw ¦rxetai (‘it is very diYcult to sing and, as he [sc. Aristoxenus] says, artistic and requiring much habituation, whence it does not come easily into use’). Consider Plato’s portrait of musicologists straining to distinguish between such closely-packed intervals (Resp. 7.530e5-531b8); as Barker (1978), 8, points out, puknÅmatƒ tta ônom‹zontew provides a verbal link to the katapæknvsiw (‘interval compression’) mentioned by Aristoxenus (Harm. 7, 28, 38, 53), which relied on quarter-tone discriminations and seems to have acted as musical graph paper for measuring very Ž ne intonational shades. 57) Cf. Aristid. Quint. 1.9 (16.11-5) fusikÅteron m¡n ¤sti tò di‹tonon (psi gŒr kaÜ toÝw Žpaideætoiw pant‹pasi melÄdhtñn ¤sti) . . . Žkrib¡steron d¢ tò ¤narmñnion: parŒ gŒr toÝw ¤pifanest‹toiw ¤n mousik» tetæxhke paradox°w, toÝw d¢ polloÝw ¤stin Ždænaton (‘The diatonic is more natural, for it can be sung by everyone, even those who are altogether untrained . . . But the enharmonic is more exacting; for it has won acceptance from the most illustrious men in music, and is impossible for most people’); cf. Vitr. de Arch. 5.4.3.

Classical period (PHib. 13.20 sq., v. infra; cf. West [1992], 164), its original deŽ ning feature was not the diYcult quarter-tone puknñn, but the consonance-derived ditone, which even a second-rate, underrehearsed chorus could have sung with ease. Thrasyllus still treated this as the essential form of the enharmonic (ap. Theo Sm. 92.2793.2). As Aristoxenus believed, it had been drawn by Olympus centuries earlier—in the Orientalizing period in fact—from the diatonic.58) There is no problem, then, in allowing the enharmonic its attested place in tragedy, while at the same time conceding that the further reŽ nement of the quarter-tone discriminations was less essential to its popular character than the underlying diatonic substrate. In fact, this three-pitched version of the enharmonic is attested in the Paean of Athenaeus, one of the Delphic hymn inscriptions of the Hellenistic period,59) thus showing the enduring and popular appeal of this style over the centuries since its ‘invention’. It is no accident, then, that Aristoxenus made the diatonic the oldest of the genera . It formed the core of an earlier system, before the modulating and chromatic New Music, before the challenging enharmonic in its heyday. This must be what lies behind his distinction of two ancient phases in Greek musical history: ÷ti dƒ ¦sti tiw melopoiýa ditñnou lixanoè deom¡nh kaÜ oéx ² faulot‹th ge ŽllŒ sxedòn ² kallÛsth, toÝw m¢n polloÝw tÇn nèn ptom¡nvn mousik°w oé p‹nu eëdhlñn ¤sti, g¡noito ment’n ¤paxyeÝsin aétoÝw: toÝw d¢ suneiyism¡noiw tÇn ŽrxaókÇn trñpvn toÝw te prÅtoiw kaÜ toÝw deut¡roiw ßkanÇw d°lñn ¤sti tò legñmenon . . . m‹lista m¢n gŒr kaÜ pleÝston xrñnon ¤n tÒ xrÅmati diatrÛbousin, ÷tan dƒ ŽfÛkvntaÛ pote eÞw t¯n rmonÛan, ¤ggçw toè xrÅmatow pros‹gousi sunepispvm¡nou toè m¡louw. (Harm. 23) ‘But that there is a certain style of melic composition [melopoiýa] which needs a ditonic lixanñw, and that it is not the worst melopoiýa but quite the best, is entirely unclear to the many who undertake music these days, but would be if they applied themselves. But what I am saying is clear to those who are accustomed to the Ž rst and second ancient styles . . . For they [sc. musicians today] spend most of their time in the chromatic, and if at some point they end up in the 58) Aristox. fr. 83 = ps.-Plut. de Mus. 1134f-1135b: Žnastrefñmenon tòn …Olumpon ¤n tÒ diatñnÄ k.t.l. (‘Olympus was roaming about in the diatonic,’ etc.); cf. Franklin (forthcoming). 59) DAGM 20; see also Hagel (2000), 38-89; cf. West (1992), 288 V.

enharmonic, they lead it near to the chromatic, the melody being drawn along.’ Of the two archaic styles, one is associated with the enharmonic genus, thought to be the most lofty and beautiful by those who were familiar with both and with contemporary practice. What distinguished the other ancient style? Certainly not exclusive chromaticism, since this was practiced by those who were unfamiliar with and intolerant of the older styles—eVeminate louts who would vomit bile when they heard true enharmonic music, as Aristoxenus memorably expressed it.60) Although he does equate one of the earlier styles with the enharmonic, it might be facile for us to associate a diVerent genus with each phase of music. It is logical to assume, however, that the diatonic played some role, since it is not otherwise assigned by Aristoxenus. In fact, it is said that the chromatic was Ž rst introduced into tragedy by progressive musicians of the later Ž fth century like Euripides and Agathon, earlier composers using either the enharmonic on its own—or combining it with the diatonic.61) It appears then that the diatonic occurred in one or both of the two earlier styles, and this is hardly surprising given Aristoxenus’ assertion of the diatonic’s historical priority. It is only to be expected that a more diYcult and reŽ ned style like the quarter-tone enharmonic should be a secondary development. Quite possibly the Ž rst style also saw the enharmonic in its more archaic form without the quarter-tone divisions, as established centuries earlier.62) Yet this, too, leads us back to the diatonic, which Aristoxenus believed to be older still, and the point of departure for the enharmonic. So either the Ž rst ancient style was largely diatonic; or, if it was mixed with the enharmonic—for Aristoxenus too recognized music of mixed 60) Aristox. fr. 85 = Plut. Quaest. conviv. 711c: oß dƒ nandroi kaÜ diateyrumm¡noi tŒ Îta diƒ ŽmousÛan kaÜ ŽpeirokalÛan , oìw fhsin ƒAristñjenow xol¯n ¤meÝn ÷tan ¤narmonÛou Žkoæsvsin. 61) Plut. Quaest. conviv. 645e: ƒAg‹yvnow, ùn prÇton eÞw tragÄdÛan fasÜn ¤mbaleÝn kaÜ êpomÝjai tò xrvmatikñn; Psell. De trag. 5: ² d¢ palaiŒ tragik¯ melopoiÛa g¡nei m¢n tÒ ¤narmonÛÄ ¤xr®sato ŽmigeÝ kaÜ miktÒ g¡nei t°w rmonÛaw kaÜ diatñnvn, xrÅmati d¢ oédeÜw faÛnetai kexrhm¡now tÇn tragikÇn xriw EéripÛdou; cf. West 62) As Professor West suggests (correspondence); cf. West (1992), 351 f.

genera 63)—we may suppose a still earlier phase of diatonic music, according to the Aristoxenian view of musical development. 7. The Diatonic Basis of Modulation The testimonia which concern metabol® provide further evidence that the sæsthma t¡leion was founded upon an earlier diatony, the ‘continuity’ (sun¡xeia ) of whose scales had already allowed them to be fully interrelated. According to an earlier precept which Aristoxenus attributed to Eratocles, acceptable modulation (metabol®) could only take place at consonant ‘intersections’.64) An important fragment of Ion of Chios conŽ rms that this was a standard theoretical approach to modulation not later than 422 BC, when Ion died (and probably by his oruit mid-century): ¥ndek‹xorde læra, dekab‹mona t‹jin ¦xousa tŒw sumfvnoæsaw rmonÛaw triñdouw: prÜn m¡n sƒ ¥pt‹tonon c‹llon diŒ t¡ssara p‹ntew †Ellhnew spanÛan moèsan Žeir‹menoi. (Ion of Chios fr. 32 (West) = Cleonid. 12 (202.14-7)65) ‘Eleven-stringed lyre with a ten-stepped arrangement— / The threeway, consonant crossroads of rmonÛa. / Hitherto all the Greeks played you heptatonic—two tetrachords— / Summoning up a sparse Muse.’ This is the earliest testimony bearing on the tetrachordal perspective fundamental to the later theorists (cf. Rocconi [1998], 346). It corresponds very closely, moreover, to the Eratoclean conception of metabol® as a melodic road which splits at consonant intersections, with three choices (besides the one just traveled). According 63) Aristox. Harm. 7: mignum¡nvn p‹lin tÇn genÇn; 44: pn m¡low ¦stai ³toi di‹tonon µ xrvmatikòn µ ¤narmñnion µ miktòn ¤k toætvn µ koinòn toætvn (‘every m¡low will either be diatonic or chromatic or enharmonic or mixed from these or the common-ground of these’). 64) Aristox. Harm. 5 Žpò toè diŒ tess‹rvn ¤fƒ ¥k‹tera dÛxa sxÛzetai tò m¡low (‘From the fourth the m¡low splits in two in either direction’); Aristox. Harm. 67 Žpò puknoè dƒ ¤nantÛvw ¤pÜ m¢n tò barç dæo õdoÛ, ¤pÜ d¢ tò ôjç mÛa (‘After the puknñn [sc. when descending] there are, in opposite directions, two roads continuing the descent and another one that goes back up’). 65) See the discussion of West (1992a), 25 f., adducing the Aristoxenus-Eratocles passages (v. supra).

to the rule of melodic ‘junctures’, modulation in the enharmonic and chromatic genera can only take place at the consonant ‘bounding’ notes of each tetrachord (oß peri¡xontew fyñggoi), not from the variable, ‘moving’ inner notes (oß kinoæmenoi) whose intonation was so often microtonal. In the di‹tonon g¡now, however, each fyñggow is by deŽ nition such an intersection, and so each can serve as a departure point for metabol®. Created by the strictest application of sun¡xeia—Ptolemy’s diatonikoè sunexoèw (Harm. 2.6 [55.12-15])— the diatonic species served as the skeleton of the sæsthma t¡leion, regulating, indeed enabling, modulation between the various sust®mata of the enharmonic and chromatic in all their shades. Thus the fragment implies knowledge of the complete diatonic connectability of all the species, at approximately the same time that Eratocles was rotating the enharmonic octachords. Once again his researches are seen against a diatonic background. Given that Aristoxenus was musically conservative, railing against the practices of his day and prepared to sacriŽ ce popularity for purity of technique (frr. 70, 76, 85), it follows that his contemporaries, for whom the New Music was now becoming mainstream (West [1992], 371 f.), were pursuing modulations and joining pitch systems that transgressed the rule he lays down. If this is right, his positive allowance for modulation represents an older, classical practice, known to Ion and Eratocles, and acceptable to the musician of conservative taste and traditional training. What is surprising about this is that scholars generally assume that the New Music was objectionable because it involved modulation. It now appears that modulation was a regular part of music prior to this movement, and that the New Music was controversial because it used too much modulation, and/or modulations which were improperly constituted. In fact, as early as the early sixth century (!), according to Heraclides of Pontus, the aulete Sacadas of Argos—a renowned musician from a musical city, with three consecutive Pythian victories under his belt—was modulating with each strophe of his trimel¯w nñmow (‘Etude in Three Tunings’).66) Lasserre (1998) made much of this, noting 66) Ps.-Plut. de Mus. 1134b. Sacadas’ victories began in the third year of the forty-eighth Olympiad (thus 586, 582 and 578): Paus. 10.7.4-5; ps.-Plut. de Mus.

that, despite the fact that the ethnic names Dorian, Lydian and Phrygian suggest, prima facie, independent geographical origins for these tunings, they must nevertheless have been somehow mutually compatible, implying a uniŽ ed musical system which could accommodate diverse tunings.67) We cannot say certainly what Dorian, Lydian and Phrygian mean in this context.68) Nor do we have any precise understanding of the ‘multiplicity of aélñw notes’ (t» tÇn aélÇn polufvnÛ&) used in the late sixth century by his countryman Lasus of Hermione (ps.-Plut. de Mus. 1141c). But both testimonia are clear evidence that the particular acoustic properties of the aélñw aVected the course of Greek tonality, since according to the traditional Terpandrian practice of the Archaic period, only one rmonÛa was used in a given composition (v. infra). (One should also note that the peculiar intonation of the aélñw could have left some further mark in the microtonal shadings of the genera. For all the philological shortcomings of the work, should Schlesinger [1959] be entirely ignored? The structures she discusses might provide, if not the basis of the rmonÛai [as she saw it], at least a practical foundation for the higher superparticular ratios which appear in so many theorists outside of Aristoxenus, beginning with Archytas.) A lyre used for such ‘polyphonic’ pieces, if it were to avoid retuning between strophes or elaborate mechanisms like the ‘tripod’ of Pythagoras of Zacynthus (Ath. 14.637c-f ), would require more strings than the traditional seven—nine in the case of the trimel¯w nñmow. In fact, 1134a; cf. West (1992), 212. Herodotus (3.131-2) reports that, in the time of Polycrates, ‘the Argives were held to be Ž rst among the Greeks in music’ (ƒArgeÝoi ³kouon mousik¯n eänai „Ell®nvn prÇtoi). 67) Lasserre (1988), 82: “[sc. the trimel¯w nñmow] presuppone, accanto ad una tecnica relativamente facile da mettere a punto sull’aulo, una teoria della scala musicale che identiŽ cava già perfettamente la funzione degli intervalli nella trasposizione. Questa teoria presuppone a sua volta una struttura comune ai tre modi armonizzati da Sacada, in altri termini un’origine comune”. 68) It is not clear whether these three names were preserved with the original tradition, or have been introduced anachronistically. Ps.-Plut. (de Mus. 1134a) claims that these were the only three tunings known at the time, a belief attested in other late sources, e.g. Ptol. Harm. 2.6 (56.4 V.), 2.10 (62.19 f.). Thus these speciŽ c tunings may be mere inference from the name trimel¯w nñmow. Curiously enough, Heraclides of Pontus, who seems to be the source here, insisted elsewhere that the three true rmonÛai should correspond to the three Hellenic races, Dorian, Ionian and Aeolian: see Ath. 14.624c.

such an instrument is already attested in the mid-sixth century,69) though literary traditions of dubious value variously assign an eighth and/or ninth string to Phrynis or Timotheus (West [1992], 64). At any rate, we have here good evidence for modulation well back into the Archaic period. It would seem then that Pindar—who also celebrated the pamfvnÛa or polufvnÛa of the aélñw70) and musical poikilÛa (a word glossed as poluxordÛa in ps.-Plutarch de Mus. 1137a), and was said to have been a student of Lasus (West [1992], 344 n. 68)—was no stranger to metabol®. This would have been under certain welldeŽ ned conditions at Ž rst, between strophes for instance (following the example of Sacadas), and perhaps limited to the dithyrambic genre—or at least eschewed by the heptachordal Aeschylus and his contemporaries until such polufvnÛa was introduced in the time of Euripides (v. supra). In the well-known fragment of Pherecrates, Music complains of the progressive indecencies she has suVered during the course of the Ž fth century from the likes of Melanippides, Cinesias, and Phrynis—with her ultimate violation at the hands of Timotheus who, with Philoxenus, marked the furthest progress of the New Music. Of Cinesias, the eVeminate dithyrambist of the later Ž fth century, she says: KinhsÛaw d¡ <mƒ> õ kat‹ratow ƒAttikñw, ¤jarmonÛouw kampŒw poiÇn ¤n taÝw strofaÝw, ŽpolÅlexƒ oìtvw, Ëste t°w poi®sevw tÇn diyur‹mbvn, kay‹per ¤n taÝw ŽspÛsin, Žrist¡rƒ aétoè faÛnetai tŒ deji‹. (Pherec. fr. 155.8-12 K-A) ‘And Cinesias, that damned Athenian, / Making exharmonic bends in his strophes, / So destroyed me that in the composition / Of his dithyrambs—as with [sc. the re ection of ] shields [or ‘as with snakes’?]— / The left appears in the same spot as the right.’ It is universally acknowledged that ¤jarmonÛouw kamp‹w are modulations; as ‘exharmonic’ suggests, these are pitches which do not occur within a given rmonÛa. If interstrophic modulation was accepted practice since the time of Sacadas, the criticism ¤n taÝw 69) Paris E643; cf. Maas/Snyder (1989), 38, 51 Ž g. 15a; West (1992), 62. 70) Pi. I. 5.27, O. 7.12, P. 12.19: aélÇn . . . p‹mfvnon m¡low; cf. Adesp. 29b (PMG 947): polæxordow aélñw; Pl. Resp. 399d2 V.

strofaÝw becomes intelligible as a violation of the convention.71) Moreover, the images of invertibility and re ection—or the coils of snakes—Ž t well enough with a circular conception of metabol® and sun¡xeia. In Birds, Aristophanes brings together the image of road and circle in his travesty of Cinesias and the modern dithyrambic style: KIN.: PEIS .: p¡tomai dƒ õdòn llotƒ ¤pƒ llan mel¡vn . . . Žspazñmesya filærinon KinhsÛan. tÛ deèro pñda sç kullòn ŽnŒ kæklon kukleÝw; (Ar. Av. 1374-9; cf. Anacr. fr. 33 [PMG 378]) cin.: ‘I  y on Ž rst one and then another road of m¡lh’ . . . / peis.: ‘We welcome thee, lime-wood Cinesias. / Why do you come here circling your lame foot round the circle?’ The language is complex. Though the primary reference of tÛ deèro pñda sç kullòn ŽnŒ kæklon kukleÝw—with the punning language of kullòn (‘lame’) and kæklon (‘circle’)—may be the halting, modernist dance of a circular dithyrambic chorus (Dunbar [1995], ad 1379), it combines with õdòn mel¡vn (the melodic path) to form a gloss on the modulatory nature of the music (p¡tomai dƒ õdòn llotƒ ¤pƒ llan ). This serves to support the interpretation of Pherecrates’ kay‹per ¤n taÝw ŽspÛsin, / Žrist¡rƒ aétoè faÛnetai tŒ deji‹, and conŽ rms the familiarity of cyclic modulation prior to Aristoxenus, as emphasized by the pleonastic and frequentative ŽnŒ kæklon kukleÝw. Thus what distinguished the interstrophic modulation of Sacadas from the metabol® of the later Ž fth century was not the basic principle of an interrelationship between two tunings, but the reckless abandon with which the New Musicians crossed from one to the next, breaking down all distinctions in the rmonÛai. Sacadas moved slowly from one rmonÛa to another, so that each was identiŽ able; 71) Cf. D. H. Comp. 19 (194.5-196.7 Roberts): toÝw d¢ tŒ m¡lh gr‹fousin tò m¢n tÇn strofÇn te kaÜ Žntistrñfvn oéx oåñn te Žll‹jai m¡low, Žllƒ ¤‹n tƒ ¤narmonÛouw ¤‹n te xrvmatikŒw ¤‹n te diatñnouw êpoyÇntai melÄdÛaw, ¤n p‹saiw deÝ taÝw strofaÝw te kaÜ Žntistrñfoiw tŒw aétŒw ŽgvgŒw ful‹ttein . . . oß d¡ ge diyurambopoioÜ kaÜ toçw trñpouw met¡ballon, DvrÛouw te kaÜ FrugÛouw kaÜ LudÛouw ¤n tÒ aétÒ ›smati poioèntew, kaÜ tŒw melÄdÛaw ¤j®llatton, tot¢ m¢n ¤narmonÛouw poioèntew, tot¢ d¢ xrvmatik‹w, tot¢ d¢ diatñnouw . . . oá ge d¯ katŒ Filñjenon kaÜ Timñyeon kaÜ Telest®n, ¤peÜ par‹ ge toÝw ŽrxaÛoiw tetagm¡now ·n kaÜ õ diyærambow.

but the New Music was ‘exharmonic’, not belonging to any recognizable tuning. 8. The Terpandrian Style Just as Phrynis threatened the inherited Archaic style and its honored place in education, so too we read in ps.-Plutarch that tò dƒ ÷lon ² m¢n katŒ T¡rpandron kiyarÄdÛa kaÜ m¡xri t°w Frænidow ²likÛaw pantelÇw pl° tiw oïsa diet¡lei: oé gŒr ¤j°n tò palaiòn oìtvw poieÝsyai tŒw kiyarÄdÛaw Éw nèn oéd¢ metaf¡rein tŒw rmonÛaw kaÜ toçw =uymoæw: ¤n gŒr toÝw nñmoiw ¥k‹stÄ diet®roun t¯n oÞkeÛan t‹sin.72) ‘In general, the style of citharody practiced by Terpander persisted even unto the time of Phrynis as one which was altogether simple. For in the old days it was not allowed to make citharodic compositions like today, nor to transfer the rmonÛai and the rhythms (sc. beyond their proper boundaries). For in the nñmoi they guarded the proper tuning for each.’ The practice of adhering to one diatonic tuning per piece is attested in the Middle Assyrian song catalogue VAT 10101 (= KAR 158); the same was probably true of the Hurrian hymns, to judge from the best preserved example, a cult song to Nikkal in the n“d qabli tuning.73) But though the Archaic composers were reluctant to ‘transfer the rmonÛai’, it does not follow that they were unaware of how the tunings were structurally interconnected—just as the compilers of VAT 10101 knew of seven distinct tunings, whose connectivity was celebrated in the Retuning Text (UET 7/74). Again the reference is to aß rmonÛai, the tunings. (Note too that ps.Plutarch or his source did not use the normal Aristoxenian term for modulation, metab‹llein .) Thus we read later in the same treatise: kaÜ oß palaioÜ d¢ p‹ntew, oék ŽpeÛrvw ¦xontew pasÇn tÇn rmoniÇn, ¤nÛaiw ¤xr®santo. oé gŒr ² gnoia t°w toiaæthw stenoxvrÛaw kaÜ ôligoxordÛaw aétoÝw aÞtÛa geg¡nhtai, oéd¢ diƒ gnoian oß perÜ …Olumpon kaÜ T¡rpandron kaÜ oß Žkolouy®santew t» toætvn proair¡sei perieÝlon t¯n poluxordÛan te kaÜ poikilÛan. (Ps.-Plut. de Mus. 1137a-b) 72) Ps.-Plut. de Mus. 1133b-c; for t‹sin read perhaps t‹jin, which can apply to rhythmic as well as tonal arrangement. 73) For the Mesopotamian material discussed here, with bibliography, see Kilmer (1997), 475, 477.

‘And all the ancient poets, though not without experience of all the rmonÛai, only used some of them. For it was not ignorance that was responsible for such narrow melodic range and the moderate number of strings they used, nor was it through ignorance that the circles of Olympus and Terpander, and those who followed the preference of these men, rejected a large number of strings and complexity.’ Because it was long assumed that seven tunings were a necessary correlate of the traditional seven-stringed art,74) one should take seriously a curious, seven-part division of the citharodic nñmow, attributed to Terpander himself: m¡rh d¢ toè kiyarÄdikoè nñmou, Terp‹ndrou kataneÛmantow, ¥pt‹: Žrx‹, metarx‹, katatrop‹, metakatatrop‹, ômfalñw, sfragÛw, ¤pÛlogow. (Poll. Onom. 4.66) ‘The parts of the citharodic nñmow, as apportioned by Terpander, were seven: beginning, after-beginning, down-turn, after-down-turn, center (lit. navel), seal, conclusion.’ A number of sources attribute speciŽ c compositions to Terpander, allegedly named from ethnics, rhythms, and styles. 75) Like other nñmoi of which there is notice, these titles probably derive, for the most part, from the musicologists of the Classical and Hellenistic periods, on the basis of internal features or scholarly deduction (Barker [1984-9], 1.250). But this passage of Pollux is somewhat diVerent. It does not seem to be a case of individual citharodic nñmoi, for he has already mentioned some of the more familiar Terpandrian 74) Cf. the v.l. at Arist. Metaph. 1093a14 (¥ptŒ d¢ xordaÜ µ rmonÛai rather than ¥ptŒ d¢ xordaÜ ² rmonÛa), with the comment of Alex. Aphr. In Metaph. 1093a13: ¥ptŒ d¢ fyñggoi t°w diŒ pasÇn kaÜ rmonÛai tosaètai (‘Seven are the pitches of the octave, and the rmonÛai are the same in number’), which shows that, if the variant is not in fact the correct reading, the mistake was made already in antiquity, and was besides readily intelligible in its own right. Similarly, in one manuscript of Porph. in Harm. 5 (96.16), the title of Thrasyllus’ work is given as PerÜ ¥ptaxñrdvn, as against PerÜ ¥ptaxñrdou at 91.14—which itself rests upon an emendation: see further Düring’s apparatus ad 91.13. 75) Heraclid. Pont. ap. ps.-Plut. De mus. 1132d: ¤keÝnow goèn toçw kiyarÄdikoçw prñterow Ènñmase, BoiÅtiñn tina kaÜ AÞñlion TroxaÝñn te kaÜ Terp‹ndreion kalÇn, ŽllŒ m¯n kaÜ TetraoÛdion; Schol. EG ad Ar. Ach. 13: tò de BoiÅtion m¡low oìtv kaloæmenon, ÷per eðre T¡rpandrow, Ësper kaÜ tò Frægion; Suda s.v. öryion nñmon kaÜ troxaÝon: toçw dæo nñmouw Žpò tÇn =uymÇn Ènñmase T¡rpandrow, Žnatetam¡noi dƒ ·san kaÜ eëtonoi.

pieces.76 ) Nor does it seem to be a particular composition with many sections, for Pollux speaks of the citharodic nñmow, as though the sevenfold division somehow embraced the genre as a whole. These names are not attested elsewhere, but Photius also speaks of ‘the citharodic style of melody, having an ordered [sc. method of ] tuning and deŽ nite rhythm; there were seven according to Terpander’ (õ kiyarÄdikòw trñpow t°w melÄdÛaw, rmonÛan ¦xvn takt¯n kaÜ =uymòn Érism¡non: ·san d¢ ¥ptŒ oß êpò Terp‹ndrou [Phot. Lex. s.v. nñmow]). Interestingly, Photius gives only three names (öryiow, tetr‹diow, ôjæw)—all of which are attested in the other sources as titles of individual compositions. This motley collection might be accounted for by the same logic Barker used to explain the names of other nñmoi; an historically accurate sevenfold division could have been Ž lled in with terms cobbled together from incomplete information by educated guess-work. Together these sources suggest that Terpander was associated with some canonical seven-fold organization of citharodic tuning, even if the precise terminology had been largely forgotten or overwritten. Overall, then, Terpander’s seven-part citharodic nñmow could distantly attest the full cycle that would naturally have accompanied the heptatonic instrument he is said to have invented. 9. Conclusion Without going further into the development of the sæsthma t¡leion and the nature of its antecedents, we get an idea of the important role of diatony in the Ž fth century, and good evidence for it throughout the Archaic period from Terpander onwards. Diatonic tuning, an essential theoretical precursor to any more elaborate developments, appears in the earliest fragment of music theory, Philolaus fr. 6a, and was still presupposed in most of the relevant Aristotelian problems with their fundamental musical study and test questions. The process of interval rotation, mentioned in connection with Eratocles, would in fact be easiest to eVect with the diatonic for, as we see in the Mesopotamian system, this method of tuning both 76) Poll. Onom. 4.65: nñmoi dƒ oß Terp‹ndrou Žpò m¢n tÇn ¤ynÇn ÷yen ·n, AÞñliow kaÜ BoiÅtiow, Žpò d¢ =uymÇn öryiow kaÜ troxaÝow, Žpò d¢ trñpvn ôjçw kaÜ tetraoÛdiow, Žpò dƒ aétoè kaÜ toè ¤rvm¡nou Terp‹ndreiow kaÜ KapÛvn.

derives from and gives rise to cyclical properties which are latent in the phenomena of resonance. Moreover, if it is correct that this process predates Eratocles, the ‘road map’ conception (marked by Aristoxenus as an innovation) should represent an early stage of the cycle’s conversion to the graphic two-dimensionality of the sæsthma t¡leion. By contrast, ² perifor‹ was demonstrable solely with the lyre, with each species or sx°ma transformable into another in some progressive fashion. Thus there is good evidence to support the early existence of an integrated cyclical system of diatonic tunings, what Aristoxenus remembered as ‘the heptachords which they used to call the rmonÛai’, and Aristophanes as ‘the method of tuning (rmonÛa) handed down by our forefathers’. This does not necessarily exclude other approaches to practical and theoretical lyre music in the early Classical and Archaic periods; it may have been only one tributary to a complex music-stream. Nevertheless, the diatonic component at least emerges as a self-suYcient and deŽ nite t¡xnh, with the sæsthma t¡leion encrusted thereupon as being an essential substructure. Since the various microtonal tunings were themselves required to follow the diatonic principles of sun¡xeia, the achievement of the Aristoxenian system was to allow an intrinsically diatonic connection of a wide array of tone structures. Thus he succeeded in protecting the Archaic heptachordal integrity of rmonik®. American Academy in Rome Via Angelo Masina 5 00153 Roma, Italia e-mail: johncfranklin@hotmail.com REFERENCES W.D. Anderson, Music and Musicians in Ancient Greece (Ithaca and London 1994). A. Barker, Greek Musical Writings. 2 volumes (Cambridge 1984-9). ——, Hoi Kaloumenoi Harmonikoi: The Predecessors of Aristoxenus, PCPhS 24 (1978), 1-21. R. Beaton, Modes and Roads: Factors of Change and Continuity in Greek Musical Tradition, ABSA 75 (1980), 1-11. A. Bélis, Aristoxène de Tarente et Aristote: Le Traité d’harmonique (Paris 1986). R. Browning, A Byzantine Treatise on Tragedy, in L. Varcl, R.F. Willetts (ed.), GERAS: Studies Presented to George Thomson (Prague 1963), 67-81.

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