1 The Ashmolean Papyri: DAGM 5 (Sophocles Jr. Achilleus?) and DAGM 6

Most of these little papyrus scraps preserve a handful of notes each, and very few stretch to over ten consecutive notes. In spite of their highly fragmentary state, these documents outline a remarkably stable harmonic picture that is solidly anchored to the basic Dorian harmonía framework that was typical of Classical Greek music (c–f–g–c’, see Figure 1).²

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Distribution of notes featured in the Dorian Ashmolean Papyri (cf. n. 2 on the pitch of movable notes)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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Most of these fragments are notated in a key that Pöhlmann and West identify as a ‘Hypodorian or Hyperphrygian’,³ notation tónoi that overlap in the region that corresponds to the central octave of the Dorian key C₃–C₄.

The Hypodorian interpretation is, however, preferable for several reasons. First, the most frequent note in the Ashmolean fragments is Dorian mésē F₃ with 81 occurrences. In accordance with the broader Dorian record (Lynch 2022a, Figure 5), the clear melodic prominence of Dorian mésē Π F₃ in these fragments (23.4%), coupled with Dorian paramésē Ϻ G₃ (15.6%), emphasise the basic Dorian character of these pieces.⁴ For comparison, Dorian mésē Π F₃ occurs only three times in Phrygian music as a whole. The second most frequent note in these pieces, Λ A^b_3–31,⁵ is also very significant in a Dorian setting characterised by the almost complete absence of the note Θ B^b_3–27. The typically Phrygian note Θ B^b_3–27 does not occur at all in DAGM 5 and is attested only 5 times in DAGM 6 (Figure 1) but 3 out of 5 of these readings are notably doubtful, so only two properly Phrygian Θ B^b_3–27 are securely attested in these pieces.⁶ This combination of notes produces an ‘undivided’, and archaic-sounding, enharmonic division of the upper Dorian tetrachord (G₃ A^b_3–31 C₄), which Aristoxenus found especially fitting for the Dorian harmonía.⁷

Secondly, the highest note recorded in these fragments is C₄, i.e. the upper limit (nḗtē diezeugménōn) of the basic Dorian octave employed on Classical lyres and kithárai as well as the upper note of Classical modulating auloí.⁸ In contrast, a Hyperphrygian interpretation would by definition require notes higher than C₄ – that is to say, notes that were not included in the basic lyre and aulos tunings in Classical times. As shown in Figure 1, the defining tone of the Hyperphrygian key c’–d’ falls above the central Dorian octave and into the grey zone and is not attested in the Ashmolean fragments.⁹ These ‘irregular’ features tally well with the contested status of the Hyperphrygian key as a late addition to the Classical core of the Greek harmonic system that was closely related to the innovations introduced by the New Musician Philoxenus. In keeping with this, Aristoxenus coined a new term, Hypermixolydian, to identify this ‘new’ high-pitched scale – a term that reflects an attempt to bridge the gap between the traditional system of harmoníai and the new notation tónoi.¹⁰ In §2, we shall see that the defining tone of the Hyperphrygian key (C₄–D₄) plays a central role in the markedly Phrygian context of Athenaeus’ Paean. Its absence from the Ashmolean Papyri therefore points to a Hypodorian setting.

Given the highly fragmentary state of Ashmolean Papyri, however, the absence of the characteristic Hyperphrygian tone C₄–D₄ may nevertheless be accidental, so we cannot draw too firm a conclusion solely on this basis. The same point does in fact apply also to the defining tone of the Hypodorian notation key, C₃–D₃. But, unlike the Hyperphrygian key, the central octave of the Hypodorian tónos allows us to account for the note that is most frequent in these fragments after Dorian mésē Π (F₃) and Dorian trítē Λ (A^b_3–31), that is to say Hypodorian trítē Υ (E^b_3–29). As we shall see at the end of this section, the harmonic innovations embraced by the New Musicians, and in particular their penchant for modulations between Dorian and Mixolydian, will allow us to offer a cogent explanation for the frequent use of this ostensibly exharmonic note.

The background of the New Music allows us to make sense of another prominent, if seemingly ‘extraneous’ note attested in these fragments: Ν, “the odd one out … a semitone or so below the ‘standing note’ ” Ϻ G₃.¹¹ In the light of the reconstruction offered in Lynch 2018a, the ‘irregular’ pitch of this remarkably frequent note and its exharmonic status become perfectly understandable: Ν was one of the ‘chromatic’ notes that the New Musicians introduced in order to expand the harmonic repertoire of their modulating instruments. As predicted in Lynch 2018a, this chromatic note falls within the disjunctive tone of the basic Dorian harmonía (F₃–G₃) and, together with Ο and ,¹² identifies one of the ‘colourings’ that kitharodes could produce by means of the so-called ‘twister’ (stróbilos) – a modulating key that was first introduced by Phrynis and altered the pitch of one of the intermediate fixed notes of the professional kithára (F₃ and G₃). This process produced distinctive exharmonic ‘bendings’ (kampaí) that comic poets and other ancient authors singled out as hallmarks of the New Music: chromatic alterations of the basic pitch of the central pillars of the Dorian lyre harmonía, F₃ or G_3, which ‘coloured’ and ‘sweetened’ the basic diatonic structure of this mode and ‘disfigured’ its traditional noble character.¹³

But the tragic nature of the lyrics recorded in the Ashmolean papyri suggests that these songs were originally accompanied by auloi¹⁴ – instruments that were notoriously flexible in pitch and could produce different chromatic shades by small variations in fingering and embouchure.¹⁵ The unique expressive role of the chromatic note Ν in these tragic melodies is clearly illustrated in the fragments transcribed in Figure 2A–C.

DAGM 5.1 is a piece of ‘unmistakably tragic character’,¹⁶ and is especially significant in that it illustrates how exclamations typical of tragic laments such as ἰώ(ι) μοι or ἰὼ πόποι could be set to music. It may also provide some evidence about the use of recitative (parakatalogḗ) in between sung odes, a kind of performance practice that is described as ‘tragic’ (τραγικόν) in the Pseudo-Aristotelian Problems because of its ‘unevenness’.¹⁷ In this context, the prominence given to the ‘chromatic’ note Ν becomes very significant: the chromatic genus was in fact felt to be ‘most pleasant and also mournful’ (ἥδιστόν τε καὶ γοερόν, Aristid. Quint. Mus. 92.26). Ν is emphatically alternated with Υ, forming an interval of about a major third, which ancient Greek theorists regarded as a dissonance. This dissonant effect would be magnified in the case of a ‘soft chromatic’ colouring of the chromatic note Ν (G^b₃₊₃₁), producing a distinctly expressive interval of about ~366 cents.¹⁸

In line 4 of DAGM 5.1 (Figure 2A), the chromatic note Ν is possibly followed by Dorian mésē Π F₃, but both readings are uncertain. In contrast, Ν is elsewhere alternated with Dorian paramésē Ϻ G₃, the other central ‘fixed note’ of the Dorian harmonía alongside mésē (c–f–g–c’),¹⁹ see e.g. Fragment 6.42 and possibly also Fragment 6.41 Col. ii (Figures 2B–C).

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New transcription of DAGM 5.1. Doubtful readings are marked by a dot underneath the relative sign

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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New transcription of DAGM 6.42

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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New transcription of DAGM 6.41 Col. ii. Doubtful readings are marked by a dot underneath the relative sign

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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As mentioned above, auletes could easily produce different chromatic ‘colourings’ of most notes by subtle changes in fingering or embouchure. Professional kithara players, in contrast, devised a special key (stróbilos) that allowed them to physically ‘bend’ the tuning of one of the central fixed notes of the Dorian harmonía, either Π F₃ or Ϻ G₃.

The insistent alternation of Ϻ and Ν in these fragments suggests that the ‘bending’ was applied to Dorian paramésē Ϻ G₃. This suggestion is supported by the charge that Lady Music levels against Timotheus in Pherecrates’ Chiron, namely that Timotheus ‘loosened’ harmonía and tore her apart.²⁰

As shown in Lynch 2018a, such a ‘loosening’ of Dorian paramésē G₃ turns the Dorian harmonía into the lamenting mode par excellence, the Mixolydian (Figure 3). This is again consistent with ancient evidence about tragic music: as Aristoxenus reports, tragedians ‘took the Mixolydian harmonía and joined it together (συζεῦξαι) with the Dorian, because the latter produces magnificence and dignity, and the former extreme passion’ (Aristox. fr. 81 Wehrli ap. [Plut.] Mus. 1136d).

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Modulation from Dorian to Mixolydian by bending Dorian paramésē G₃ to G^b₃. Tonic diatonic and chromatic divisions exempli gratia

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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In the fundamentally diatonic context of lyre music, such a modulation from Dorian to Mixolydian could in principle be notated with signs belonging to the Dorian/Hyperdorian tónoi (Figure 3), but these notation keys are not entirely appropriate for the tragic music recorded in the Ashmolean fragments. First, these tónoi feature the diatonic versions of the notes E^b₃ (Τ) and B^b₃ (Η), which play a minor role in the Ashmolean fragments (Figure 1): Η is entirely absent from these pieces, and Τ appears only in chromatic settings, corresponding to E^b₃₊₃₇ in a soft chromatic tuning shade.²¹ Furthermore, these notation keys do not include Υ (soft chromatic E^b_3–29), the third most recurrent note in the Ashmolean fragments. In other words, none of these keys joins Υ and Ν in the same scale whereas the minor third Υ Ν or Ν Υ features prominently in the melodies transcribed in Figure 2A and 2C, suggesting that these notes belonged to the same tuning.

According to Pöhlmann and West, these noteworthy discrepancies are “symptomatic of the inadequacy of handbook theory to accommodate the modal variety of actual music in the late Classical period” (Pöhlmann and West 2001, 25). This is indeed the case but we can bridge the gap between ancient theory and practice thanks to the surviving evidence about the Classical harmoníai preserved by Aristides Quintilianus. His transcription of the Mixolydian mode is especially noteworthy, in that it features a crowd of small intervals at the bottom of the scale followed by large undivided tritone at the top (see Appendix 2). As we read in the pseudo-Plutarchan De musica, the odd structure of this mode posed substantial challenges to Classical musicians, who struggled to produce a theoretically cogent account of its inner organisation based on tetrachords:²²

ἐν δὲ τοῖς Ἱστορικοῖς †τοῖς Ἁρμονικοῖς Πυθοκλείδην φησὶ τὸν αὐλητὴν εὑρετὴν αὐτῆς γεγονέναι, αὖθις δὲ Λαμπροκλέα τὸν Ἀθηναῖον, συνιδόντα ὅτι οὐκ ἐνταῦθα ἔχει τὴν διάζευξιν ὅπου σχεδὸν ἅπαντες ᾤοντο, ἀλλ᾽ ἐπὶ τὸ ὀξύ, τοιοῦτον αὐτῆς ἀπεργάσασθαι τὸ σχῆμα οἷον τὸ ἀπὸ παραμέσης ἐπὶ ὑπάτην ὑπατῶν.

[Plut.] Mus. 1136d7–e2

In their historical works, the harmonikoí say that the aulete Pythocleides invented it [scil. the Mixolydian mode] but then again Lamprocles the Athenian, realising that this harmonía did not have its disjunction where almost everyone supposed it to be, but that it actually stood at the top of the scale, gave it a form such as the one that runs from paramésē to hypátē hypatôn.

Figure 4 illustrates this problem more clearly. ‘Almost everyone’ mistakenly identified the disjunction of the Mixolydian mode with the interval e^b–f, which is roughly midway through the scale and is close to two groups of ‘packed notes’ (pykná) that typically occurred at the bottom of each tetrachord. But this naturalistic interpretation does not organise the notes of the Mixolydian mode into regular tetrachords spanning a fourth, and therefore posed a significant obstacle to the development of systematic modulations between the harmoníai. This problem was eventually solved by the 5th-century aulete Lamprocles, who first identified the functionally correct mésē of the Mixolydian mode with a silent note B^b – a note that falls within the large undivided tritone at the top of the scale and produces the standard form of the Mixolydian octave: St T T St T T T in diatonic (Figure 3) or qq D qq D T in enharmonic (Figure 4, number 2). This is the ‘form’ of the octave mentioned at the end of the passage quoted above.

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Two contrasting analyses of the Mixolydian mode: the archaic ‘naturalistic’ interpretation ascribed to Pythocleides and the cogent, but abstract, analysis developed by Lamprocles

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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Making a significant leap of abstraction, Lamprocles succeeded in creating a theoretically grounded account of the structure of the Mixolydian mode, moving beyond the immediate sounds featured in this scale and identifying its key reference point with a silent note b^b – a note that was rarely, if ever, heard in performance.²³

Lamprocles’ identification of Mixolydian mésē with the silent note b^b made it possible to identify this mode with the Hyperdorian notation tónos, but his clever analysis had a major shortcoming too. His well-formed Mixolydian octave could not account for the note e^b, a note that was so characteristic for the traditional Mixolydian mode to be mistakenly identified as its defining mésē by Lamprocles’ predecessors. This characteristic note now had to be regarded as an ‘exharmonic’ addition to the basic Mixolydian octave: an extra ‘diatonic’ note added alongside a full pyknón²⁴ and set approximately a tone below Dorian mésē f.

Thanks to Ptolemy’s account of the fine tuning of many traditional modes played on kithárai, however, we know that this characteristic Mixolydian tone e^b-f differed from standard disjunctive tones in a very practical sense too: it was a so-called septimal tone (8:7, ~231 cents),²⁵ an interval that was very common in Greek musical performances but is slightly larger than the standard tones that separated mésē from paramésē (9:8, ~204 cents).²⁶

Hence, the characteristic Mixolydian note e^b was flattened by about a sixth of a tone, in comparison to the standard Dorian diatonic model. And this is precisely where we find the seemingly ‘exharmonic’ notation sign Υ in the Ashmolean Papyri. As shown in Figure 5, Υ was borrowed from the adjacent Hypodorian tónos to notate a sound that otherwise could not have been identified unambiguously by basic Dorian signs, given that the ‘diatonic’ sign Τ could indicate a wide range of pitches in this context. In contrast, the Hypodorian note Υ in its soft chromatic version E^b_3–29 or, even more precisely, in its ‘Archytan’ diatonic variant²⁷ E^b_3–33 produced the large septimal tone required by the Mixolydian mode (Figure 5).²⁸

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Modulation from Dorian to Mixolydian by bending Dorian paramésē G to G^b. Kithára tunings at the top, corresponding Dorian notation tónoi at the bottom (cf. n. 28 on the chromatic shades used in these transcriptions)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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The resulting tuning integrates the typically Mixolydian, if seemingly ‘exharmonic’ note Υ into the framework of the Dorian tónos, joining together the two ‘odd’ notes that feature so prominently in many tragic melodies preserved in the Ashmolean papyri: Ν and Υ.²⁹ As shown in Figure 2A, the distinctly expressive interval produced by these notes was employed to imitate the lamenting cadence of typically tragic expressions such as ἰώ(ι) μοι and ἰὼ πόποι – a self-consciously mimetic strategy that exploited the emotional impact of special musical intervals to amplify the natural accents of these words.³⁰

Coupled with Dorian mésē Π, Hypodorian Υ produces the characteristic septimal tone E^b_-33–F_-2 (~231 cents, 8:7) that Lamprocles’ predecessors had mistakenly identified as the ‘disjunction’ of the archaic Mixolydian mode because of its modal prominence. The widespread use of such ‘septimal’ intervals is forcefully critiqued by Aristoxenus in a passage that, ironically, confirms the central role they actually played in late Classical music: unlike Aristoxenus’ neat theoretical models,³¹ the ‘irrational’ if expressive intervals favoured by contemporary musicians could not be tuned by means of perfect fourths and fifths but comprised ‘three, five or seven dieses’.³² In keeping with this, the septimal tone Υ E^b_3–33 – Π F_3–2 is heavily emphasised in several melodies recorded in the Ashmolean fragments, including those transcribed in Figure 6A and B.

Alongside the defining tone Υ E^b_3–33 – Π F_3–2, the fragments transcribed in Figure 6A and B include the note Τ which has two possible functions in the modulation system detailed in Figure 5. On the one hand, Τ appears in conjunction with Υ in the Hypodorian enharmonic/chromatic pyknón ФΥΤ: in a soft chromatic setting, Τ would correspond to about E^b₃₊₃₇. This chromatic note seems to have been employed especially in Phrygian contexts, as is suggested by e.g. Figure 6A Col. ii 4–5: here Dorian mésē Π F₃ is avoided, in keeping with the evidence offered by Aristides’ Phrygian harmonía, and Τ E^b₃₊₃₇ is insistently alternated with Phrygian mésē Ϻ G₃₊₂, producing a distinctive interval of about 365 cents. This ‘grave third’ is remarkably close to the interval spanning seven dieses that was berated by Aristoxenus³³ and appears alongside so-called ‘blue thirds’ (~267 cents) in the Phrygian setting of Athenaeus’ Paean (see §2 below). ‘Blue’ thirds were called ekbolḗ in Greek musical theory – an interval that was closely associated with archaic aulos playing and with the characterisation of different harmoníai.³⁴

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New transcription of DAGM 6.13. Doubtful readings are marked by a dot underneath the relative note sign

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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New transcription of DAGM 6.15. Doubtful readings are marked by a dot underneath the relative note sign

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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In this context we also find the only sound reading of Phrygian Θ B^b_3–27 attested in the Ashmolean fragments³⁵ whereas the distinctively Dorian chromatic note Ν is avoided, once again suggesting that Τ is likely to have been rendered as a Phrygian chromatic note in this auletic context.

Τ could alternatively indicate the ‘diatonic’ note (diátonos) of the Dorian tetrachord C₃–F₃ (ΩΨΤΠ, Figure 5). In a tonic diatonic setting, Τ would be slightly lower in pitch than its chromatic counterpart and would correspond to E^b₃, producing a full 9:8 tone with Dorian mésē Π F₃; in a ‘soft’ chromatic setting, Τ would be a septimal tone (8:7) lower than Dorian mésē Π F_3–2, i.e. E^b_3–33 – effectively corresponding to Phrygian Υ (Figure 5).

As mentioned above, auletes could easily produce such variations in tuning shade, whereas kithara players had to choose one of these diatonic options when tuning their instruments in advance of a performance. As shown in Figure 7,³⁶ both diatonic alternatives are included in the traditional Dorian kithara tunings recorded by Ptolemy (Harm. 80.11–18)³⁷ and these traditional tunings are perfectly compatible with the modes reconstructed in Figure 5. Just like the lower tetrachord of the Dorian ‘Archytan’ harmonía reconstructed in Figure 5, the lower tetrachord (c–f) of the first Dorian tuning recorded by Ptolemy conforms to Archytas’ diatonic division (28:27, 8:7, 9:8), the most common diatonic shade throughout antiquity.³⁸

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Ptolemy’s Dorian kithara tunings (Lýdia and Parhypátai), set in the Classical central octave C₃–C₄ (cf. n. 36)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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In contrast, the lower tetrachord (c–f) of the second Dorian tuning described by Ptolemy features a ‘soft diatonic’ division, which comprises a septimal chromatic semitone at the bottom of the scale (~84 cents) and a septimal tone at the top, E^b_3–33–F_3–2 (~231 cents). This second tuning therefore made it possible to reproduce the characteristically Mixolydian note E^b_3–33 on stringed instruments too – an ‘exharmonic’ diatonic note that could be unambiguously notated as Υ. The soft diatonic variant of the note D^b_3–16 could instead be notated by the same sign Ψ that indicated its tonic diatonic counterpart in the first tuning (D^b_3–37), because the difference between these two notes is still within the 22-cent indifference range indicated by Ptolemy.³⁹ To play the full Mixolydian harmonía, such an instrument would have also needed a ‘tuning key’ to ‘bend’ the pitch of Ϻ G₃ to Ν G^b₃₊₃₁, i.e. about one third tone (see Figure 8). This sequence is attested, for instance, in DAGM 6.41 (Figure 2C).

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Modulation from Dorian to Mixolydian on a professional kithára, based on Ptolemy’s tunings and the relative notation signs

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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All in all, the swift alternations between the soft chromatic and diatonic scales attested in the Ashmolean fragments, coupled with ‘bendings’ and frequent modulations, give us a taste of the New Musicians’ fondness for mixing different harmonic genera as well as different harmoníai in the same piece – much-discussed and distinctive features of their experimental style.⁴⁰

2 Athenaeus’ Delphic Paean (DAGM 20)

In spite of its 2nd century dating, the sophisticated musical style of Athenaeus’ Paean has long been identified as reflecting some defining features of the New Music: its ‘scintillating melodies’ (aióla mélea, Col. 1 14) stretch over a wide compass and include many different notes, frequently shifting between diatonic and chromatic genera as well as conjunct and disjunct tónoi.

The free astrophic form of this piece enabled the composer to exploit fully these elaborate melodic means to “enhance the expressive value of the words”.⁴¹ As we shall see, Athenaeus’ Paean offers many fine examples of musical mimesis and word painting in action, including direct references to the rich instrumental accompaniment of this choral song which exceptionally featured both a ‘clear-braying pipe’ (λιγὺ … λωτὸς βρέμων) and a ‘sweet-voiced golden kithara’ (χρυσέα δ᾽ ἁδύθρους κίθαρις).⁴²

The rhythm of this piece is, in contrast, very simple, and is fittingly based on metrical paeons. This combination of elaborate melodies and simple rhythms was a defining trait of the experimental music valued by late Classical audiences, and the polar opposite of the blend of melodic simplicity and rhythmical variety that characterised traditional Greek music:

πάλιν δ᾽ αὖ εἴ τις καὶ περὶ τῆς ποικιλίας ὀρθῶς τε καὶ ἐμπείρως ἐπισκοποίη, τὰ τότε καὶ τὰ νῦν συγκρίνων, εὕροι ἂν ἐν χρήσει οὖσαν καὶ τότε τὴν ποικιλίαν. τῇ γὰρ περὶ τὰς ῥυθμοποιίας ποικιλίᾳ οὔσῃ ποικιλωτέρᾳ ἐχρήσαντο οἱ παλαιοί· ἐτίμων γοῦν τὴν ῥυθμικὴν ποικιλίαν, καὶ τὰ περὶ τὰς κρουσματικὰς δὲ διαλέκτους τότε ποικιλώτερα ἦν· οἱ μὲν γὰρ νῦν φιλομελεῖς, οἱ δὲ τότε φιλόρρυθμοι. δῆλον οὖν ὅτι οἱ παλαιοὶ οὐ δι᾽ ἄγνοιαν, ἀλλὰ διὰ προαίρεσιν ἀπείχοντο τῶν κεκλασμένων μελῶν.

[Plut.] Mus. 1138b4–c1

But, once again, if you looked at the subject of variety from a correct and informed perspective, comparing the pieces composed back then with those of today, you would find that variety (poikilía) was in use in the old days too. With regard to the kind of variety that concerns ‘rhythm compositions’ (rhythmopoiías), in fact, the ancients employed a rhythmical style that was more varied: they surely held rhythmical variety in high esteem, and the patterns that informed instrumental idioms were more varied back then too. For nowadays people are ‘lovers of melody’, whereas back then they were ‘lovers of rhythm’. So it is clear that the ancients did not abstain from ‘sprained’ melodies out of ignorance, but by choice.

In addition to highlighting a growing fondness for melodic variety at the expense of rhythmical complexity, the closing lines of this passage emphasise the centrality of ‘sprained’ melodies in late Classical, melody-focussed music. As we read in a scholium, the term ‘sprained’ (keklasména) indicated melodies that featured ‘bends’ (kampaí) such as those introduced by Phrynis and enthusiastically embraced by Timotheus, which ‘sprained’ the central joints of harmonía and developed new paths for seamless modulations between the traditional harmoníai.⁴³

The distribution of the notes attested in Athenaeus’ Paean shows clearly that the harmonic organisation of this piece is centred on the Phrygian key:⁴⁴ the most frequent note is Phrygian mésē Ϻ G₃, whereas Dorian mésē Π F₃ is avoided completely (Figure 9).⁴⁵

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Distribution of notes in Athenaeus’ Paean (DAGM 20) with the relative notation tónoi (modern equivalents of notes employed in full pykná correspond to the soft chromatic genus exempli gratia, with the exception of ‘tense’ chromatic Κ – see discussion below). The Phrygian tónos, by contrast, features only diatonic notes in its pykná, which are rendered in accordance with the basic Archytan diatonic shade

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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A prominent role is also played by C₄ in conjunction with D₄, clearly marking their function as Hyperphrygian mésē Г and paramésē Ʊ respectively.⁴⁶ This modulation mirrors Philoxenus’ harmonic innovations, as his ‘hyperbolic’ Locrian music was at home in the high-pitched ‘hyperbolic’ region above the upper boundary of the Dorian octave (Г C₄).⁴⁷ Phrygian Θ B^b_3–31 is also very frequent in this piece, in contrast with its almost complete absence in the Dorian Ashmolean Papyri (Figure 1). Together with Phrygian mésē Ϻ G₃₊₂, Θ B^b_3–31 produces a distinctly plaintive interval of about 267 cents – a septimal minor third (7:6)⁴⁸ in Just Intonation. This interval is still employed for expressive purposes in contemporary Jazz and Blues, where it is known as ‘blue third’,⁴⁹ and is remarkably close to the five quarter-tone interval (~250 cents) called ekbolḗ in Greek musical theory.⁵⁰

Figure 10A displays the notation keys (tónoi) as well as the practical tunings (harmoníai) employed in Athenaeus’ Paean. The fine tuning of these harmoníai follows the corresponding kitharodic models described by Ptolemy (Harm. 80.11–18, see Figure 10B). These charts will be the basis for our subsequent analysis of the modulations that take place in different sections of this piece and their mimetic implications. The interplay of keys and tunings displayed in Figure 10A will also shed light on Athenaeus’ use of different notation signs to represent the most distinctive features of the Mixolydian harmonía in order to integrate it into the overarching Phrygian setting of this piece (as opposed to the essentially Dorian setting of the Ashmolean Papyri).

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Notation keys and tunings employed in Athenaeus’ Paean (DAGM 20); Aristides Quintilianus’ aulos-based harmoníai (Mixolydian and Phrygian; see also Appendix 2)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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Ptolemy’s kitharodic tunings set in the Classical central octave C₃–C₄ (cf. n. 36)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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The fundamentally Phrygian character of this piece is clearly established in its opening section, transcribed in Figure 11A. Regular noteheads reflect the pitch of the Greek notes written underneath them (or their repetition over subsequent syllables) whereas x-shaped noteheads indicate supplements, which are offered as mere suggestions that may help us imagine the general flow of the song.

In keeping with theoretical evidence, this opening section centres around Phrygian mésē Ϻ G₃, which is clearly identified as such by the frequent appearance of paramésē Ι A₃.⁵¹ The ‘middle’ tetrachord Ф D₃ – Ϻ G₃ consistently skips the ‘diatonic’ step that would correspond to Dorian mésē F₃, producing an undivided enharmonic pattern (St+Ditone) that gives an archaic flavour to this section.⁵² In the opening lines of the Paean, the disjunct tetrachord Ι A₃ – Ʊ D₄ also features this archaic enharmonic division but shifts to a fully diatonic scale with the appearance of the note Г C₄ (Figure 11A, line 6).

Up to this point, the melody mainly moved within the central Phrygian octave Ф D₃ – Ʊ D₄, with only brief but significant excursions to the upper and lower tetrachords. The appearance of the high-pitched note 𝈘 E^b_4–33 (Figure 11A, line 4) in fact marks the apex of a melodic line that seems designed to imitate the content of the lyrics. As Martin West put it, “it is no accident that this high passage introduces mention of Parnassus with its twin peaks, and that it has two peaks itself” (West 1994, 289). The first peak coincides with the beginning of the word that indicates the very ‘top’ of the mountain (-kórymb-) and corresponds to the highest note of this musical phrase (𝈘 E^b_4–33), whereas the second peak is slightly lower (Ʊ D₄) and coincides with the name of this two- peaked mountain (Parnassíd-).⁵³ The opposite excursion to the lower tetrachord with the note 𝈓 B^b_2–31 (Figure 11A, line 4) is equally significant: this note is an octave lower than the typically Phrygian note Θ B^b_3–31 that is highlighted at the start of the following phrase, which starts from this solid Phrygian anchor and rises up to Parnassus.

The appearance of Г C₄ in line 6 marks the beginning of a more systematic upward shift in the tonal centre of the melody, which strongly emphasises the tone Г C₄ – Ʊ D₄ but also echoes the high-pitched note 𝈘 E^b_4–33 (Figure 11A, line 6). This high plateau foreshadows the modulation to the Hyperphrygian key that will take place in full in Section 2. For the moment, however, Athenaeus limits himself to introducing the note Λ A^b_3–18 in line 7, which belongs to the Hyperphrygian key but effectively produces the undivided enharmonic tetrachord G₃ A^b_3–18 C₄ (Ϻ Λ Г) that was characteristic of the Dorian harmonía.⁵⁴ Nevertheless, in the absence of Dorian mésē Π F_3, this transition could not be perceived as a full Dorian modulation but rather offered a foretaste of the motley character of the Hyperphrygian tuning Tropiká that will dominate the intricate chromatic sequences featured in Section 2. This hint may have been emphasised by the odd microtonal character of this tuning (tense chromatic Λ A^b_3–18 vs tonic diatonic Λ A^b_3–35 or ditonic diatonic Λ A^b_3–8). This fleeting transition ends in line 8, where Ϻ G₃ is re-established as Phrygian mésē in conjunction with paramésē Ι A₃ just before drawing this section to a close on Phrygian hypátē mésōn Ф D₃.

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Athenaeus’ Paean (DAGM 20), Section 1

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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The relatively traditional nature of the tunings employed in this opening section is coupled with a generous use of melismas,⁵⁵ a distinctive feature of experimental Late Classical songs that was often caricatured by comic poets. Aristophanes, for instance, famously mocked Euripides’ fondness for ‘wiiiiiiiiinding’ melodies⁵⁶ and melismas are indeed employed in the choral song preserved in the Orestes papyrus (DAGM 3), albeit more sparingly than Aristophanes’ parodic exaggeration would suggest. Athenaeus too deploys melismas strategically to highlight key elements of the text, enhancing their expressive power.⁵⁷ So, in lines 1–2, we hear of the Mount ‘Helicooon’ (Ἑλικ]ωῶνα) that is protected by the daughters of Zeus the ‘loud-booooming’ (ἐ[ρι]βρόμουου), whilst their brother ‘Phoeeebus’ (Φοιοῖβον) and the ‘very gloriooous Deelphiaaan’ ([ἀ]γακλυταιεῖς Δεελφίσιιν) maidens enter into the picture in line 3 and 6 respectively.⁵⁸ Key features of this natural and sacred environment are also brought to the fore by means of melismas and unusual spellings, which highlight the ‘weell-waaatered’ (ἐουύδρου) Castalian spring and the Delphic ‘foooreland’ ([πρ]ωῶνα) upon which Apollo’s ‘saanctuuary’ (μααντειεῖον) was built.

Section 2 (Figure 11B) is centred on the high Hyperphrygian register and fully exploits the chromatic potential of the Locrian tuning reshaped by Philoxenus, which centres on mésē Г C₄.⁵⁹ This scale significantly corresponds to Ptolemy’s Tropiká/Trópoi (‘turning’), which is the only kitharodic tuning recorded by Ptolemy that features a chromatic tetrachord (Figure 10B).

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Athenaeus’ Paean (DAGM 20), Section 2

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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The dominant role of Hyperphrygian mésē Г C₄ is clearly established in the first line of Section 2 and is closely followed by the most distinctive note of this chromatic tuning, Κ, and by the other two notes of the same pyknón (Λ and Ϻ). As shown in Figure 10B, the evidence of Ptolemy’s harmogaí offers a straightforward explanation for the alternation between Ι and Κ in this highly chromatic section of Athenaeus’ Paean: in this context, Ι and Κ indicate notes that are actually different in pitch, and not merely theoretical distinctions.⁶⁰ It would have been impossible to notate the ‘irregular’ pitch of the defining chromatic note of Ptolemy’s Tropiká, A₃₊₃₃, by means of basic Phrygian signs, given this note falls squarely in between Ι A₃ and Θ B^b_3–31 (cf. Figure 10A). In keeping with its odd chromatic status, vocal Κ is attested only 16 times in Hellenistic scores⁶¹ and is completely absent in its instrumental variant, suggesting that these nuances were primarily expressed by vocal means.⁶² It is also interesting to note that, just as Aristides’ transcription of the Mixolydian mode attempted to capture the ‘irregular’ shape of this mode by adding what looks like an extra ‘diatonic’ note to its lower tetrachord, Aristides’ transcription of the Phrygian harmonía includes an additional enharmonic/chromatic note in its higher diatonic tetrachord – a note which corresponds precisely to the ‘irregular’ tense chromatic note Κ (cf. bottom of Figure 10A).⁶³

In the second line of Section 2, we encounter the first instance of the melodic ‘spraining’ mentioned by Pseudo-Plutarch: the bending (kampḗ) of Phrygian mésē Ϻ G₃ to the ‘alien’⁶⁴ chromatic note Ο F#₃, which paves the way for the modulation to the Mixolydian harmonía that will take place in full in the following line. The need to integrate the Mixolydian mode within the basic Phrygian setting of this paean also explains why Athenaeus chose the sign Ο to identify this chromatic ‘bending’ instead of Ν, which was employed for this purpose in the Dorian setting of the Ashmolean Papyri. As shown in Figure 8, Dorian mésē Π F₃ acted as the common reference point that joined the Mixolydian mode with the other tunings employed in the Ashmolean Papyri.

Given that Dorian mésē Π is wholly absent from Athenaeus’ Paean, it was necessary to align the Mixolydian mode with the other ‘fixed’ note of the central octave, Ϻ G₃, i.e. Phrygian mésē.⁶⁵ This could be easily achieved by means of a tonic chromatic division of the central tetrachord of the Mixolydian mode, which makes the second step of the pyknón (Ν) effectively identical in pitch to Phrygian mésē Ϻ G₃ (Figure 10A). Thanks to this slight change in tuning shade, the chromatic note Ο F#₃ forms a full tritone with the top note Г C₄, a shrill interval that replaced the classic augmented fourth created by Ν G^b₊₃₁ in the Ashmolean fragments (25:18, ~568.7 cents) as the hallmark of archaic Mixolydian music (Figure 4).⁶⁶

This characteristically Mixolydian tritone Г C₄ – Ο F#₃ does in fact appear at the end of line 3 of this section. This high-pitched, descending tritone is also combined with a melisma that, coupled with the subsequent ‘bending’ of chromatic Ο F#₃ to Phrygian mésē Ϻ G₃, draws attention to the ‘altaaaars’ (βωμοι-οῖσιν) first mentioned here. The opening words of this noun phrase further highlight the sacred status of these altars (ἁγίοις δὲ βωμοι-οῖσιν) and are aptly marked by another melodic trope that underscores the interplay between the Mixolydian mode and Tropiká, namely ГΒГ.⁶⁷ Β corresponds to D^b_4–15 in the soft diatonic variety of the relative tuning described by Ptolemy (Figure 10B, line 2), making it almost identical to a hemiolic chromatic rendering of the corresponding note in Aristides Quintilianus’ Mixolydian harmonía (D^b_4–25, Figure 10A–a negligible difference of 10 cents).⁶⁸

In keeping with Aristides’ testimony,⁶⁹ the diatonic note Β D^b_4–15 that follows Г C₄ in the vocal setting of Athenaeus’ Paean is transposed an octave lower in the auletic variety of the Mixolydian harmonía, reflecting a theoretical and practical conceptualisation of the harmoníai as cyclic re-arrangements of interval series within an octave that Aristoxenus attributes to Eratocles and his followers.⁷⁰

From a more practical point of view, this potential divergence between notes employed in vocal melodies and those favoured in their aulos accompaniment is not so strange as it might seem at first sight. As we read in a passage of the pseudo-Plutarchan De musica, this sort of heterophony was a recognised and indeed essential feature of other kinds of aulos-accompanied songs, where the avoidance of specific notes in the melody, combined with their use on auloi, played a central role in creating the particular ‘character’ (êthos) of different traditional songs.⁷¹

In line 4 (Figure 11B), the melody shifts back to the chromatic tuning Tropiká via the common note Г C₄ and features a winding sequence of microtones that pivots on Ϻ G₃ and underscores Hephaestus’ ‘burning the thighs of young bulls’, stopping emphatically on the chromatic note Ο F#_3. A brief modulation back to the Phrygian mode occurs in the middle of line 5, in correspondence with a rapidly ascending melodic phrase that neatly illustrates a cloud of ‘Arabian smoke’ rising towards Olympus. The verb anakídnatai (‘spreads up’) is highlighted by an ascending and descending melodic phrase that audibly depicts the cloud’s motion, a trope that puts a strong emphasis on the chromatic note Ο F#₃ and significantly paves the way for a subsequent modulation from Phrygian to Mixolydian via the common note Υ E^b_3–33. In keeping with the evidence offered by the Ashmolean Papyri, Athenaeus employs the Phrygian sign Υ not only in its original Phrygian context but also in connection with the Mixolydian mode, where it indicates the extra ‘diatonic’ note E^b_3–33 featured in this harmonía, a septimal tone lower than Dorian Π F_3–2 (cf. Figure 10A and Figure 5 above).

The ascending-descending chromatic phrase that highlights the verb anakídnatai echoes the closing of the previous melodic phrase (mêra thaúrōn) and at the same time foreshadows the central role played by Ο F#₃ in the intricate sequence of microtones featured in lines 6–7: a vivid illustration of the ‘scintillatiing melodies’ (aeióloiois mélesin) that the ‘clear-braying pipe weaves into the singing’.

This self-referential comment on the ‘shimmering’ character of the melody and its interweaving of different harmonic ‘strands’ significantly accompanies the most complex, heavily chromatic passage of the whole piece – a passage that pushes the Classical harmonic system to its limits and at one point even attempts to step beyond them, hinting at the Imperial metamorphosis of the harmonic system that will be discussed in Lynch forthcoming 1.

This crucial musical phrase opens with the major third Υ E^b_3–33 Ο F#₃, which is akin to the ‘grave’ major third Υ Ν employed in the Ashmolean papyri (see DAGM 5.1 above) and puts the spotlight onto the ‘clear-braying pipe’ (λιγὺ … λωτὸς βρέμων). This interval is followed by several repetitions of the chromatic note Ο F#₃ and a sinuous sequence of microtonal intervals that, in the Hellenistic system, can only be interpreted as a ‘bending’ of chromatic Ο F#₃ back to Ϻ G₃ followed by a step to the note immediately above it, Λ A^b_3–18.⁷² In this context, Ϻ G₃ represents Hyperphrygian hypátē – a modulation confirmed by the subsequent use of the full tense chromatic pyknón ϺΛΚ that was typical of Tropiká.

This theoretical analysis is perfectly within the boundaries of the Classical harmonic system but takes considerable mental gymnastics, especially in the light of the strong emphasis put on the chromatic note Ο F#₃ just before the start of this intricate sequence. Taken at face value, this strategy seems to set apart the chromatic note Ο F#₃ and attempts to establish it as the basic note of a new pyknón – a move that, however, contradicts the intrinsically transient status of chromatic notes in the Hellenistic modulation system. In other words, Ο F#₃ is momentarily turned into a ‘fixed note’, hinting at the metamorphosis of the Hellenistic harmonic system into the Imperial one by evoking a ‘new’ chromatic pyknón F#₃ G₃ A^b₃. This ‘irregular’ Classical triplet will, however, turn into a standard pyknón in the Imperial system, which includes a regular triplet based on Ο F#₃ that belongs to the Hyperiastian key: the ‘Higher’ Mixolydian tónos, which will replace the Lower Mixolydian mode in the Imperial harmonic system.⁷³

As pointed out above, the ‘lower’ variant of the Mixolydian mode that was at home in the Classical and Hellenistic harmonic system was aligned with the Dorian octave (C₃–C₄), and therefore corresponded to the Hyperdorian notation key (Figure 5). In contrast, the Hyperiastian or ‘Higher Mixolydian’ scale aligns its central pyknón to the Hypolydian/Lydistí octave (B₂–B₃, see Appendix 3): that is to say, the octave that will replace the Dorian as the central point of reference for the Imperial harmonic system (Lynch forthcoming 1).

The introduction of the Higher Mixolydian/Hyperiastian key therefore marks the beginning of the transition from the Dorian-based Classical system towards the new Imperial system centred on mésē С E₃, bringing to completion the chromatic revolution initiated by Phrynis’ chromatic bending of the Iastian mode:⁷⁴ what originated as a transient chromatic bending eventually turned into a fixed note in its own right, generating a new formalised pyknón ΟΝ based on chrōmatikḗ Ο F#₃.

Athenaeus’ Paean only hints at this future development, as the ‘irregular’ pyknón F# G A^b is evoked as a sort of temporary ‘expansion’ of the basic Phrygian system – a point that is indicated clearly by Athenaeus’ consistent use of Phrygian notation signs, ‘expanded’ by the Hyperdorian chromatic note Ο F#₃. In keeping with this, the ‘anomalous’ pyknón is only hinted at in correspondence with the words ‘clear-braying pipe’, but the melody immediately reverts back to the core Phrygian/Hyperphrygian system via the note Ϻ G₃. This note is clearly characterised as the basic reference point of the Hyperphrygian chromatic pyknón ϺΛΚ, which is exploited to produce a very effective illustration of the ‘shimmering melodies’ described by the lyrics.

Listeners are then presented with another fleeting transition through the ‘irregular’ pyknón F# G A^b (ΟϺΛ): as the lyrics tell us, this is literally a new harmonic strand that the pipe employs to better ‘weave the song’ (ᾠδὰν κρέκει). This trope is repeated once again at the very end of this section, giving listeners the impression of hearing repeated alternations of two overlapping pykná placed just a semitone apart – an embodiment of the most extreme kind of modulation that could be accounted for by the Aristoxenian system.⁷⁵ Athenaeus only evokes it by moving repeatedly through the notes ΟϺΛ as a de facto, illegitimate pyknón but stops short of developing a full modulation of this sort, which would have required a shift to the Hyperiastian key – a key that is not employed in this piece, or in any other Hellenistic score.⁷⁶

Trying to follow the logic that governs these meandering chromatic lines requires some considerable mental gymnastics, and modern readers may be forgiven for finding this effort to make sense of competing tensions within ancient harmonic systems rather absurd. But we know that this feeling was experienced by many ancient listeners too. Conservative Greek audiences in fact found these intricate sequences of microtones and chromatic bends as bewildering as we do, and their puzzlement was exploited for comic purposes by celebrated poets such as Pherecrates and Aristophanes. The champion of the New Music, Timotheus, was mercilessly mocked as ‘leading deviant anthills’ (ἄγων ἐκτραπέλους μυρμηκιάς, Pherecr. fr. 155.23 K.-A.) and Agathon was similarly parodied as ‘warbling his way through ant tracks’ (Μύρμηκος ἀτραπούς, ἢ τί διαμινυρίζεται; Ar. Th. 100).⁷⁷

Pherecrates’ critique of Timotheus’ ‘deviant’ style includes another revealing detail that sheds light on Athenaeus’ choice to end this section of the paean on the ‘exharmonic’ note Ο F#₃. Pherecrates’ Lady Music laments that Phrynis was the first who introduced these ‘lawbreaking’ chromatic bends but also points out that his ‘mistake’ was only temporary, a passing transition, and the ‘natural’ shape of harmonía was restored before the end of his pieces.⁷⁸ Timotheus, by contrast, turned these chromatic bendings into a structural feature of his modulations to the Mixolydian mode – a change that thoroughly ‘sprained’ the central joints of harmonía, splitting the Dorian core of traditional music into two once and for all.⁷⁹ Unlike Phrynis’ transient ‘error’, Timotheus did not rectify these ‘lawbreaking’ chromatic bendings before the end of his kitharodic strophes,⁸⁰ and this is precisely what happens in Athenaeus’ Paean too: the hymns struck up by ‘the sweet-voiced golden kithara’ culminate in the chromatic note par excellence, Ο F#₃, which brings this heavily chromatic section to a close.

Section 3 opens with an octave jump, a melodic figure that auletes called kompismós⁸¹ and marks out the central Phrygian octave Ф D₃ – Ʊ D₄, re-establishing the primacy of this octave as a key point of reference for the Phrygian tunings employed in the following lines. In contrast with the highly chromatic scales of Section 2, the melody now switches back to the traditional Phrygian harmonía used in the opening section of the piece but emphasises more strongly the high, ‘hyperbolic’ tetrachord inaugurated by the note D₄.⁸²

In keeping with Section 1, this Phrygian tuning combines a diatonic division of its higher tetrachord with an archaic enharmonic division of the lower tetrachord ФΥ Ϻ, which skips the ‘diatonic’ note that coincides with Dorian mésē Π F₃. In line 4, however, Athenaeus introduces an unexpected twist that exploits the expressive potential of the ‘hyperbolic’ Hyperphrygian tuning by using a dissonant interval that he had carefully avoided in Section 1: a plangent descending tritone between Ʊ D₄ and Λ A^b_3–35, which he aptly employs in a melisma on the word ‘mortaaals’ (thnatoioîs).⁸³

The melody then switches back to the basic Phrygian mode, which characterises the remainder of this section (Figure 11C, lines 5–8). But this move is less traditionally minded than it may seem at first sight, given that the lyrics celebrate distinctive elements of Apollo’s cult, both physical (his tripod and sanctuary) and mythical (his slaying of the serpent). Such defining traits of Apollonian worship were traditionally associated with Dorian music and string instruments, whereas the discovery of the Phrygian mode that forms the core of the harmonic system of Athenaeus’ Paean was attributed to a legendary aulos player: the satyr Marsyas, Apollo’s mythical opponent and eventual victim.⁸⁴ A famous passage of Plato’s Laws singles out precisely such combinations of seemingly contradictory musical elements as typical of the musical ‘lawbreaking’ (paranomía) championed by the New Musicians:

μετὰ δὲ ταῦτα, προϊόντος τοῦ χρόνου, ἄρχοντες μὲν τῆς ἀμούσου παρανομίας ποιηταὶ ἐγίγνοντο φύσει μὲν ποιητικοί, ἀγνώμονες δὲ περὶ τὸ δίκαιον τῆς Μούσης καὶ τὸ νόμιμον, βακχεύοντες καὶ μᾶλλον τοῦ δέοντος κατεχόμενοι ὑφ᾽ ἡδονῆς, κεραννύντες δὲ θρήνους τε ὕμνοις καὶ παίωνας διθυράμβοις, καὶ αὐλῳδίας δὴ ταῖς κιθαρῳδίαις μιμούμενοι, καὶ πάντα εἰς πάντα συνάγοντες, μουσικῆς ἄκοντες ὑπ᾽ ἀνοίας καταψευδόμενοι ὡς ὀρθότητα μὲν οὐκ ἔχοι οὐδ’ ἡντινοῦν μουσική.

Plat. Leg. 3.700d2–e2

Then, after some time had gone by, leaders of a museless sort of lawbreaking were born – poets that were naturally gifted, but clueless about what is just and lawful in the realm of the Muse. Possessed by bacchic frenzy, and overcome by pleasure to a greater extent than they should have been, they mixed laments with hymns and paeans with dithyrambs, imitating the melodies of the aulos with their kithara songs, and blending all sorts of things with each other – unwittingly bearing witness against music out of their ignorance, as if music itself did not have any standard of correctness whatsoever.

Athenaeus’ Paean does indeed mix ‘measured’ paeonic metres with complex melodic features characteristic of late Classical dithyrambs, such as modulations between Phrygian and Mixolydian modes and changes in genus (diatonic, chromatic and ‘undivided’ enharmonic), as well as ‘hyperbolic’ notes and ‘twitterings’.⁸⁵ This self-conscious use of harmonic models that belonged to different traditional genres is made clear in Section 2, where Athenaeus refers explicitly to the ways in which the ‘sweet-voiced kithara’ responded ‘with hymns’ (ὕμνοισιν) to the complex and highly chromatic aulos tunes of this ‘dithyrambic’ paean. This effort to emulate the legendary harmonic flexibility of modulating auloi on professional kitharai was the key factor that led to the development of ‘many-stringed’ music – a well-known derogatory label that conservative intellectuals attached to the New Music.⁸⁶

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Athenaeus’ Paean (DAGM 20), Section 3

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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In keeping with this, Athenaeus employs plenty of ‘lawless’ melismas in this section of the song, the first of which highlights the role played by professional ‘artiiists’ (technitōôn) in this challenging performance, whereas the second draws attention to the ‘mortaaals’ (thnatoioîs) that are waiting to receive Apollo’s immortal oracles. The melismas employed in the closing lines of this section also highlight salient details of Apollo’s mythical killing of the Python – a topic that offered plenty of scope for auletes to produce spectacular mimetic effects in their accompaniment, imitating the serpent’s hissing (syrigmós) and gnashing (odontismós) just as they did in solo performances that had long been a central element of the Pythian festival.⁸⁷ So in lines 5–6, we hear of how Apollo ‘seeeized’ (εἱεῖλες) the ‘propheeeetic’ (μαντειεῖον) tripod that the serpent ‘guaaardeeed’ (ἐφρουούρειει), melismas based on the same stretched diphthong ειει that was ridiculed in Aristophanes’ Frogs.⁸⁸ Other interesting melismas occur in the closing line of this section, and illustrate the serpent ‘whiiistling’ (ἱιεὶς) charmless ‘hiiissings’ (syyrígmath’) as it expired.

The final section of the piece (Figure 11D) is heavily damaged and therefore highly fragmentary. It is nevertheless clear that the melody features many clusters of semitones and is set in the ‘hyperbolic’ Phrygian tetrachord, including for the first time the highest note attested in this piece: Ж E^b₄₊₃₇. This combination of chromaticism with a high register suggests a Hyperphrygian setting, akin to the ‘ex-harmonic, hyperbolic and immoral (anosíous)’ notes attributed to Philoxenus.⁸⁹ In keeping with this, the melody featured in the first lines of Section 4, which describe the Gauls crossing ‘impiously’ (aséptōs) into the land, circles around the defining notes of the Locrian/Hyperphrygian tuning: its disjunctive tone C₄–D₄ and the pyknón set above it.

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Athenaeus’ Paean (DAGM 20), Section 4

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10047

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3 Conclusions: Simple Keys for a Complex Riddle

This article and Lynch 2022a examined theoretical as well as practical evidence concerning the Classical Greek harmonic system, its relationship with the traditional harmoníai and their practical use in the Hellenistic musical documents. To begin with, these articles have shown how the Classical Greek harmonic system as a whole was fundamentally rooted in the Dorian tónos: 100% of the notes attested in the Classical/Hellenistic musical documents fall within the range of this notation key (F₂–F₄), which Aristides Quintilianus aptly described as ‘the only tónos used in its entirety by [male] singers’ (Aristid. Quint. Mus. 21.12–19).⁹⁰ In keeping with this, the Dorian ‘form’, or species, of the octave became the basic theoretical model for the late Classical system of notation keys (tónoi), which was developed by professional musicians to produce a consistent map of the traditional harmoníai and their pitch relations, and create written records of modulating music that featured these traditional scales.⁹¹ By means of a suitable combination of several Dorian-shaped notation keys, professional musicians and theorists created a straightforward way to account for the idiosyncratic structures of the traditional modes and their relative relationships – a brilliant achievement that went hand in hand with the use of complex, yet seamless, modulations that became a distinctive trait of the New Music.

These modulations revolved around the Dorian, Phrygian and Lydian notation keys, which gave a systematic organisation to the relative harmoníai. The Dorian harmonía (Dōristí) corresponded to the Dorian notation tónos, whereas the Hyperdorian tónos represented the (lower) Mixolydian mode and the Hypodorian tónos stood for the Locrian mode. Similarly, the Phrygian harmonía (Phrygistí) corresponded to the Phrygian notation tónos and the Hypophrygian key was assigned to the Iastian harmonía. The Hyperphrygian tónos, with its defining mésē falling on the note C₄, effectively reproduced the Hypodorian key an octave higher – a development required by the upward extension of the traditional lyre octave introduced by Philoxenus, who thereby inaugurated the use of the ‘hyperbolic’ Dorian tetrachord C₄–F₄. The Hyperphrygian tónos was therefore identical in structure to the Hypodorian key, and likewise corresponded to the Locrian mode – a seemingly unnecessary duplication that would be much criticised by traditionalists such as Heraclides of Pontus and Ptolemy, who identified the essence of different harmoníai with their distinctive octave ‘forms’.⁹²

In contrast with the straightforward correspondence established between Dorian and Phrygian harmoníai and their like-named notation tónoi, the traditional Lydian harmonía (Lydistí) was not assigned to the Lydian notation tónos but to the Hypolydian key. This surprising shift is, once again, tied to the New Musicians’ need to account for a new scale that they added at the top end of the ‘hyperbolic’ tetrachord: a scale centred on mésē D₄, a fourth higher than the traditional Tense Lydian mode (mésē A₃). Being the highest of the Lydian scales, this new addition was called Hyperlydian⁹³ but this choice had a knock-on effect on the two existing Lydian keys: the mode that was traditionally known as Tense Lydian (Syntonolydistí, mésē A₃) came to correspond to the Lydian notation tónos (mésē A₃), and the simple Lydian mode (Lydistí, mésē E₃) was identified with the Hypolydian notation tónos (mésē E₃ – see Appendix 1). This discrepancy generated considerable confusion for centuries to come and contributed to the breakdown of knowledge transfer that occurred in the early Middle Ages, eventually bringing the Greek musical tradition into oblivion.⁹⁴

As shown in Lynch 2022a, the three Classical groups of Dorian, Phrygian and Lydian keys described in theoretical works are reflected by their practical use in the musical documents. Thanks to the newly-developed database dDAGM, it has been possible to demonstrate that the most frequent notes featured in late Classical and Hellenistic scores set in the Dorian, Phrygian and Lydian tónoi are precisely their relative ‘intermediate notes’ (mésai) – the defining notes of the different modes identified in theoretical sources.

These abstract models have been fleshed out in the present article by looking at selected examples of late Classical and Hellenistic songs: a range of elaborate tragic music set in Dorian keys (Ashmolean Papyri, DAGM 5–6) and Athenaeus’ Paean, set in Phrygian keys (DAGM 20). The extensive specimen of elaborate Lydian music offered by Limenius’ Paean (DAGM 21) has not been discussed in the present article for the sake of space, but shall be included in other publications currently in preparation. For the moment, it is worth noting that Limenius’ Paean does indeed feature the Hyperlydian notation key – that is to say, the key that necessitated the shift in denomination discussed above.

All of these scores have long been recognised as featuring complex modulations and other stylistic traits akin to those first introduced by the New Musicians, including their characteristic use of ‘exharmonic’ notes and chromatic ‘bends’ (kampaí). As we have seen above, the ‘exharmonic’ yet very frequent notes attested in the Ashmolean Papyri (Ν, ~ G^b_3–33) and Athenaeus’ Paean (Ο, F#₃) correspond precisely to the chromatic ‘bends’ predicted in Lynch 2018a–variations in pitch ranging up to a semitone that were most likely produced by the stróbilos mechanism attributed to Phrynis. As shown in Lynch 2018a, this modulating key ‘coloured’ and ‘distorted’ the central pillars of the traditional Dorian harmonía, its defining mésē F₃ or paramésē G₃, turning this solemn mode into its polar opposite: the Mixolydian, the emotional and lamenting mode par excellence.

This harmonic model has been further refined thanks to Ptolemy’s detailed account of the microtonal fine-tuning proper to a variety of Dorian and Phrygian scales that kitharodes employed to accompany their singing. Integrating these microtonal features into the general model reconstructed in Lynch 2018a provided new explanations for seemingly arbitrary notation choices made by Athenaeus and the author of the Ashmolean songs (Sophocles Junior?). Far from being arbitrary, their choices closely reflected a widespread fondness for septimal intervals in late Classical music. These composers therefore used seemingly ‘exharmonic’ notation signs to indicate unambiguously the pitch of the notes required to produce these ‘novel’ intervals. More generally, their choices cast light on the gradual development of a unified harmonic system out of different traditional modes and their idiosyncratic interval sequences.

Following in the footsteps of Timotheus and Euripides, these distinguished composers combined the distinctly expressive intervals produced by chromatic notes with tritones and vocal melismas. These emotionally charged and elaborate means made it possible for them to produce complex melodies that had clear mimetic purposes, such as imitating the lamenting cadences of typically tragic expressions or illustrating the ‘scintillatiing melodies’ (aeióloiois mélesin) performed by professional artists in honour of Apollo at Delphi.

The complex chromatic sequences employed by Athenaeus also hint at the tectonic transformation of the Classical harmonic system that was already in the making, even though Athenaeus stops short of taking the plunge himself. This deep transformation began with the addition of a new, ‘higher’ Mixolydian key which expanded the Classical core of the harmonic system and eventually resulted in a fundamental shift of its tonal centre (cf. Appendix 3). The Imperial metamorphosis of the Classical harmonic system and its lasting traces in the musical scores shall be discussed in Lynch forthcoming 1 and 2.