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Unlocking the Riddles of Classical Greek Melodies I: Dorian Keys to the Harmonic Revolution of the New Music and the Hellenistic Musical Documents

In: Greek and Roman Musical Studies
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Tosca A.C. Lynch Faculty of Classics, University of Oxford Oxford UK

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Abstract

Bringing together evidence preserved by Aristoxenus, Aristides Quintilianus, Ptolemy, Porphyry and the Greek musical handbooks in a unified framework, this article and its sequels show how the reconstruction of the Classical modulation system offered in Lynch 2018 is confirmed by the melodies recorded in the Greek musical documents. Taken jointly, these articles offer the first comprehensive account of the use of notation tónoi in the ancient Greek musical documents that is fully consistent with the extant technical evidence on Greek harmonic theory and with literary testimonies about the harmonic innovations introduced by the New Musicians. The present article focuses on the Classical/Hellenistic harmonic system, whereas its Imperial counterpart will be discussed in Lynch forthcoming 1 and 2. These theoretical analyses are based upon a newly developed database (dDAGM) that collects all the musical notes attested in the standard edition of the Greek musical fragments (DAGM), comprising over 3,500 notes.

Abstract

Bringing together evidence preserved by Aristoxenus, Aristides Quintilianus, Ptolemy, Porphyry and the Greek musical handbooks in a unified framework, this article and its sequels show how the reconstruction of the Classical modulation system offered in Lynch 2018 is confirmed by the melodies recorded in the Greek musical documents. Taken jointly, these articles offer the first comprehensive account of the use of notation tónoi in the ancient Greek musical documents that is fully consistent with the extant technical evidence on Greek harmonic theory and with literary testimonies about the harmonic innovations introduced by the New Musicians. The present article focuses on the Classical/Hellenistic harmonic system, whereas its Imperial counterpart will be discussed in Lynch forthcoming 1 and 2. These theoretical analyses are based upon a newly developed database (dDAGM) that collects all the musical notes attested in the standard edition of the Greek musical fragments (DAGM), comprising over 3,500 notes.

In grateful memory of Andrew Barker:

κοινὰ γὰρ τὰ τῶν φίλων

In Graeco-Roman antiquity, the science of harmonics and its practical underpinnings were often portrayed as arcane and even ridiculous branches of theoretical inquiry. Plato, for instance, famously made fun of empirical harmonicists who ‘vex and torture strings’ and ‘prefer their ears to their minds’, ‘pricking them up as if trying to catch a voice from next door’ while quarrelling about the existence of tiny and seemingly immaterial musical intervals (Resp. 7.531a–b). On a more serious note, the Roman polymath Vitruvius lamented that ‘harmonics is an obscure and difficult area of musical literature, especially for people who are not familiar with the Greek language’.1 The quest to solve the riddles posed by ancient Greek harmonics triggered contrasting emotions in modern scholars too, ranging from puzzlement to elation and even the despair of sleepless nights: ‘I had to turn completely around more than twice before I could arrive at the truth’, wrote Girolamo Mei to his mentor in 1562, shortly before discovering the first Greek musical scores found in modern times;2 ‘I swear to you that I have passed more than ten nights without sleeping because of these trifles’ (Palisca 1977, 181).

This article and its sequels offer new solutions to key puzzles concerning ancient Greek musical scores, their relationship to Classical harmonic theory and instrumental practice, and their developments in Late Classical and Imperial times. Bringing together evidence offered by Aristoxenus, Aristides Quintilianus, Ptolemy, Porphyry and the musical handbooks in a unified framework, these articles set out, for the first time, a comprehensive and fully consistent account of the use of notation keys (tónoi) in the Greek musical documents and their harmonic significance. The present article and Lynch 2022 look at the Classical harmonic system and the Hellenistic musical documents, whereas Lynch forthcoming 1 and 2 will discuss the Imperial metamorphosis of the Classical harmonic system and its practical implications.

The opening section of this article looks at different ways of conceptualising musical modes (harmoníai) and notation keys (tónoi) that reflect the contrasting frames of mind characteristic of performers of the two main families of instruments of the Greek world: lyres and kitharai on the one hand, auloi on the other. In this context, we shall identify an important shift in the designations of the traditional Lydian harmoníai and the corresponding notation tónoi – a linguistic shift that reflects a deeper process of systematisation and reorganisation of the harmonic system that went hand in hand with the development of professional notation keys.

The focus subsequently moves to the evidence about Classical modulation practice that is offered by the Hellenistic musical documents.3 This section shows that the harmonic system reconstructed in Lynch 2018 is confirmed by the practical use of notation tónoi and the overall distribution of notes recorded in these scores. This comprehensive investigation of the varying distribution of notes and the relative use of tónoi attested in the Classical and Hellenistic musical fragments is based upon a newly developed database (dDAGM, Lynch 2021) that collects all the musical notes attested in the standard edition of the Greek musical documents (DAGM), for a total of over 3,500 notes.4 This new tool makes it possible to analyse the standard record of ancient Greek musical scores on the basis of criteria that include, but are not limited to, the following: Hellenistic vs Imperial documents, instrumental vs vocal notes, and their harmonic organisation into groups of related Dorian, Phrygian and Lydian tónoi. An enhanced version of dDAGM will be developed and made available in the future in order to facilitate further research, in keeping with the principles of open science and scholarship.

The interpretative usefulness of this reconstruction of the Classical harmonic system shall be illustrated in Lynch 2022, which offers a close analysis of musical compositions that illustrate aspects of the chromatic style and intricate modulations developed by the New Musicians in the late 5th century BC: the tragic melodies recorded in the Ashmolean Papyri (DAGM 5–6) and Athenaeus’ Paean (DAGM 20).5

1 ‘What’s in a Name?’ The Ancient Harmoníai Preserved by Aristides Quintilianus and the Changing Designations of the Lydian Scales

In Book 1 of his treatise on music, Aristides Quintilianus offers not only a theoretical account of the harmoníai used by ‘the very ancients’6 as distinctive sequences of tones and semitones but also a transcription of these modes into melodic and instrumental notation. As recently noted by Andrew Barker, this account “almost certainly came originally from the pre‐Aristoxenian harmonikoi”.7 In 2010, Hagel has lucidly argued that we can set the Dorian, Phrygian and Tense Lydian modes recorded by Aristides back to their original Classical registers by aligning their top notes,8 as aulos players would have naturally done when combining different scales on the two pipes of their modulating instruments. Lynch 20189 showed that this effectively means that the distinctive interval sequences proper to the ancient harmoníai were set to the pitch of the corresponding notation keys (tónoi), defined by the position of their own ‘intermediate note’ (mésē).

To restore the ancient harmoníai to their Classical pitch we must therefore set the structural ‘intermediate note’ (mésē) of each mode – the note that was the reference point for ancient scales,10 just as the tonic is the reference point for modern Western keys – to the ‘intermediate note’ (mésē) of the corresponding notation key. For instance, the structural mésē of Aristides’ transcription of the Dorian harmonía must be set to the mésē of the Dorian tónos (Π Ͻ, modern F3), the structural mésē of the Phrygian harmonía must be set to the mésē of the Phrygian tónos (Ϻ 𝈳, modern G3) and so on.11 If we apply these principles to all the modes recorded by Aristides, we can reconstruct the enharmonic, aulos-based version of the Classical harmoníai ‘that the divine Plato too mentioned in the Republic’ (Figure 1). The common top note shared by most of these scales happens to be Dorian nḗtē C4 (Ν in instrumental notation).12

Figure 1
Figure 1

Aristides’ aulos-based harmoníai restored to their Classical registers (mésai are marked in bold and underlined, ≠ signs indicate quarter-tone intervals; on the ‘silent’ mésē of the Mixolydian mode, see Lynch 2022)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

As we shall see in a moment, the relationships between the ‘intermediate notes’ of this motley set of archaic scales are identical to those that shape the core modulation system that is crystallised by the notation keys (tónoi) employed in the Greek musical documents (Figure 4 below). But there are a few seeming incongruities between these two systems that are worth mentioning as they reveal key turning points in the development of ancient harmonic theory and have significant implications for the practical use of different keys in Greek scores.

The list of harmoníai reported by Aristides starts from the simple Lydian mode (Lydistí), followed by Dorian, Phrygian, Iastian, Mixolydian (Mixolydistí) and Tense Lydian (Syntonolydistí). In keeping with Plato and Aristotle, Aristides’ source used the simple traditional term Lydistí to identify one of the ‘relaxed’, low-pitched and ‘festive’ modes. In contrast, Plato, Aristotle as well as Aristides qualify the other two traditional Lydian modes as ‘Mixed’ Lydian (Mixolydistí) and ‘Tense’ Lydian (Syntonolydistí) – two high-pitched modes that were characteristically plaintive and lamenting.13 In a handful of later sources, the simple and festive Lydian harmonía eventually acquired a qualification, and this terminological change is linked to Damon’s harmonic innovations.

According to Aristoxenus, Damon was the first who ‘discovered’ how to integrate this simple Lydian mode into the general modulation system,14 and on this occasion baptised it ‘loose’ Lydian (τὴν Ἐπανειμένην Λυδιστί).15 Damon’s novel characterisation of the simple Lydian harmonía as ‘loose’ is significantly expressed by an adjective that is set next to the traditional term Lydistí as a separate word: in other words, Damon called his new analysis of the traditional Lydian mode Epaneiménēn Lydistí, and not *Epaneimenolydistí or *Aneimenolydistí. Conversely, the two Lydian modes that were traditionally qualified as ‘tense’ or ‘mixed’ variants of the basic Lydian harmonía incorporate the adjectives into their time-honoured names (Syntonolydistí and Mixolydistí), reflecting their long history alongside the simple Lydian mode (Lydistí).

This distinction is coupled with another seemingly odd disagreement between the terminology employed to describe the traditional Lydian harmoníai on the one hand, and their counterparts in the formalised system of notation keys (tónoi) on the other. Rather surprisingly, the traditional mode that was simply known as Lydian (Lydistí) does not correspond to the notation key called Lydian (Lýdios tónos), as one might have reasonably expected, but is assigned to the key that was later called Hypolydian (mésē С С = E3). Conversely, the high-pitched mode that was traditionally known as ‘Tense Lydian’ (Syntonolydistí) corresponds to the notation key that came to be called Lydian without further qualifications (mésē Ι 𝈶 = A3).

But this change in terminology did not affect the practical nature and aesthetic character of these tunings: as shown in Figure 2, the ‘Tense Lydian’ mode Syntonolydistí remained higher in pitch than the simple Lydian mode Lydistí even when they came to be notated respectively by the Lydian and Hypolydian keys (tónoi).16

Figure 2
Figure 2

Shifts in terminology between traditional modes (harmoníai) and formalised notation keys (tónoi): the simple Lydian harmonía corresponds to the Hypolydian tónos and the Tense Lydian harmonía to the Lydian tónos (enharmonic forms exempli gratia)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

This odd-looking discrepancy is simply a reflection of the different nature and separate evolution of the two types of terminology we are looking at: the traditional names of the harmoníai versus the new technical labels coined by professional musicians who developed the system of notation tónoi. The need to alter the traditional names of the modes arose from a very practical problem faced by professional musicians, namely identifying a single set of terms that would allow them to label notation keys on the basis of simple, uniform and consistent principles.

2 Classical harmoníai and Notation Keys (tónoi): From Sliding Aulos Scales to Octave Lyre ‘Forms’

The new system of notation keys (tónoi) offered a different theoretical organisation of the harmoníai that moved beyond two conflicting but equally established conceptions of these traditional scales: aulos-based definitions of the modes as sliding scales aligned to a common top note (Dorian nḗtē C4, Figure 1) and lyre-based definitions of the modes as different ‘forms’ or ‘shapes’ (eídē) of a fixed octave range (C3–C4, Figure 3A).17 Auletes intuitively conceived the modes as different ‘alignments’ of notes and intervals on the two pipes of their instruments, just as they gradually aligned the two pipes in order to tune their instruments before a performance.18 Similarly, the lyre-based conception of the modes as cyclic arrangements of tones and semitone within a fixed octave range stems from the basic pre-requisite of all lyre performances: tuning these instruments. The diatonic ‘forms’, or species, of the octave were in fact a ‘natural’ by-product of the practice of tuning lyres and kitharai ‘by consonances’ (dià symphōnías) – that is to say, by a series of interlocking fourths and fifths.19

Figure 3A
Figure 3A

Lyre-based diatonic harmoníai as ‘Forms’ of the Octave (eídē dià pasôn), mésai marked in bold (cf. Cleonid. 197.7–199.3, Aristid. Quint. Mus. 15.8–15, Gaud. Harm. 346.10–347.10, Ptol. Harm. 60.1–63.14)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

The system of notation keys (tónoi) builds a bridge between the traditional auletic and lyre systems. This unified approach is based on a single model: the lyre-based form of the Dorian octave, which comprises two tetrachords separated by a tone set above the central note mésē (f–g, Figure 3B).

Figure 3B
Figure 3B

The basic model for all notation keys (tónoi): the diatonic ‘form’ of the Dorian octave

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

In the new system of notation tónoi, this fixed lyre octave template was shifted up and down in pitch, just like aulos tunings, thereby identifying different sets of notes and intervals that were distinctive of each traditional mode. These notation keys (tónoi) were organised in five groups – Dorian, Phrygian, Lydian, Iastian and Aeolian – each of which comprised a basic key (e.g. Dorian), its Hypo-variant set a fourth below the basic scale (e.g. Hypodorian) and its Hyper- variant a fourth above it (e.g. Hyperdorian).

Figure 4 represents the Classical core of the notation system – the Dorian, Phrygian and Lydian keys, along with their Hypo- and Hyper- counterparts. As testified by Dionysius of Halicarnassus and other technical sources, these are the keys that underlie the innovative modulation system developed by the New Musicians in the late 5th century BC, who ‘used to switch between modes, employing Dorian ones as well as Phrygian ones and Lydian ones in the same song’.20 As shown in Figure 4, the seven traditional harmoníai could indeed be accounted for by the simple triad of Dorian, Phrygian and Lydian keys (corresponding to the Dorian, Phrygian and Tense Lydian harmoníai) along with their hypo-keys (Hypodorian, Hypophrygian and Hypolydian, corresponding to the Locrian, Iastian and Lydian harmoníai) and a single hyper-key: the Hyperdorian, which embodied the lower variety of the traditional Mixolydian mode.21

Figure 4
Figure 4

The modulation system of the New Music: Dorian, Phrygian and Lydian notation tónoi (central octaves, diatonic variety exempli gratia), the corresponding traditional harmoníai (on the Locrian mode, cf. n. 26 below) and the overall range of the male voice (=the whole Dorian notation tónos, or the Dorian Perfect System)

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

The New Musicians also varied the inner divisions of the tetrachords, ‘making them sometimes enharmonic, sometimes chromatic and sometimes diatonic’.22 For the sake of simplicity, Figure 4 represents the relevant notation keys in their diatonic variety, the ‘first and oldest’ and ‘most natural’ (physikōteron) of the three genera, and the basic framework of reference that underlies the other two.23

The reason why professional musicians decided to alter the traditional names of the Lydian harmoníai when they created the new system of notation tónoi becomes apparent in Figure 4: they had to do so in order to create a systematic correspondence between key names and their relative position in each triad. As shown in the left-hand column of Figure 4, keeping the traditional designations of the Lydian harmoníai would have introduced an anomaly into the system, as the basic Lydian harmonía is the lowest scale in the Lydian triad of notation keys (tónoi), and not the intermediate one as in the Dorian and Phrygian triads.24

In similar vein, the traditional Tense Lydian harmonía corresponds to the intermediate key of the Lydian triad and not to the highest, as the name would have suggested. To fix this anomaly, the ‘new’ musicians and theorists changed the name of the notation keys that corresponded to the traditional Lydian and Tense Lydian harmoníai into Hypolydian tónos and Lydian tónos respectively, a change that produced systematic links between the relative pitch of these notation keys and their names: basic keys in the middle, Hypo-keys a fourth lower than the basic key and Hyper-keys a fourth higher.

They also introduced a new Hyperlydian tónos25 – a notation key based on mésē D4 that does not have a counterpart in the realm of traditional harmoníai and is therefore absent from the list of tónoi attributed to Aristoxenus.26 This addition was however essential in order to create a fully modulating version of the Tense Lydian mode.

As shown by Aristides Quintilianus (18.24f.), the top note of the Tense Lydian mode was set ‘three semitones’ above its central note, and therefore coincided with the fixed upper boundary of the Dorian octave C4 (Ν in instrumental notation, corresponding to Nḗtē). But this Dorian notation sign was not included in the Lydian notation tónos. In the Lydian tónos, the diatonic note C4 was notated as 𝈈, a sign that represented the lower movable note of the tetrachord B3–E4 and was therefore variable in pitch (Figure 5). The most common diatonic shade employed by Classical musicians was Archytas’ diatonic,27 which features a narrow interval of ~63 cents (28:27) instead of a full semitone at the bottom of the tetrachord. Such an interval would have been significantly flatter than the upper boundary of the central Dorian octave (Ν C4) that represented the common point of reference for Classical tunings, making systematic modulations impossible.

Figure 5
Figure 5

Diatonic shades and their implications for the Lydian notation keys

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Hence the New Musicians introduced a new Hyperlydian notation key, which included the Dorian fixed note C4 Г Ν as well as the other notes required by the Tense Lydian mode, allowing them to offer a fully consistent, Dorian-based account of the core modulation system Dorian-Phrygian-Lydian (Figure 6).

Figure 6
Figure 6

Mapping the Lydian modes onto the Dorian octave system and the addition of the new Hyperlydian key

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Instrumental notation bears clear traces of the gradual expansion of the core Dorian octave towards the ‘hyperbolic’ tetrachord introduced by the New Musicians. The basic instrumental sign Ν (C4) predictably identifies the ‘basic’ Dorian nḗtē, whereas its first inversion 𝈼 (D4) corresponds to the first expansion of the Dorian octave: Philoxenus’ addition of the extra string D4, which represented Phrygian nḗtē and allowed him to reproduce on his many-stringed kithara the Hyperphrygian key/Locrian mode, centred on mésē C4paramésē D4. Likewise, the second inversion of the nḗtē sign 𝈿 (E4) stands for Lydian nḗtē, once again the necessary prerequisite for the introduction of a new Hyperlydian key based on mésē D4paramésē E4.

This new Hyperlydian tónos was also the highest key that could theoretically be included in the Dorian ‘hyperbolic’ tetrachord (C4–F4) within the Classical core of the Greek notation system.28 The defining tone mésē – paramésē of any hypothetical keys higher than the Hyperlydian (e.g. *E4–F4#) would have fallen above the top Dorian note F4, the highest boundary of the Dorian Perfect System and of the male vocal range identified by Aristides Quintilianus (see §3).29 In keeping with this principle, the Greek notation system does not include any notation keys higher than the Hyperlydian (mésē D4).

3 A Dorian Key for Dorian Gates: The Dorian Perfect System and the Role of ‘Intermediate Notes’

Figure 4 shows that the overall range covered by the central octaves of the Classical tónoi – the keys that correspond to the modulation system developed by the New Musicians – is practically identical to the Dorian tónos. This correspondence is consistent with the paradigmatic role played by the Dorian octave species in Greek harmonic theory,30 and fully substantiates Aristides Quintilianus’ testimony concerning the unique status of the Dorian tónos in ancient musical practice as the only key to be employed in its entirety in (male) vocal music.

τούτων δὲ οἱ μὲν μελῳδοῦνται διόλου, οἱ δὲ οὐχί. ὁ μὲν οὖν δώριος σύμπας μελῳδεῖται διὰ τὸ μέχρι τῶν ⟨ιβ⟩ τόνων τὴν φωνὴν ἡμῖν ὑπηρετεῖσθαι καὶ διὰ τὸ μέσον αὐτοῦ τὸν προσλαμβανόμενον τοῦ διὰ πασῶν εἶναι ὑποδωρίου· τῶν δὲ λοιπῶν οἱ μὲν βαρύτεροι τοῦ δωρίου μέχρι τοῦ συμφωνοῦντος φθόγγου ⟨τῷ Δωρίῳ προσλαμβανομένῳ, οἱ δ᾽ ὁξύτεροι μέχρι τοῦ συμφωνοῦντος φθόγγου⟩31 τῇ νήτῃ τῶν ὑπερβολαίων. οὕτως οὖν καὶ τὰς ᾠδὰς ἢ τὰ κῶλα τοῖς τρόποις συστησόμεθα κτλ.

Aristid. Quint. Mus. 21.12–19

Some of these keys are employed throughout in melodic compositions, but others certainly not. The Dorian key is in fact used in its entirety in melodic compositions, because our voice stretches up to twelve tones and because its ‘additional note’ (proslambanómenon)32 falls in the middle of the Hypodorian octave. Out of the remaining keys, however, the ones that are lower than the Dorian are employed as far down as the note that is in unison with Dorian proslambanómenos, whereas keys that are higher than the Dorian are employed up to the note that corresponds to the highest note of the ‘hyperbolic’ tetrachord (nḗtē hyperbolaíōn). That is also how we can match songs or instrumental pieces to their modes (trópoi).

Aristides points out that the Dorian tónos constituted an overarching and stable framework within which the other keys and the related modal patterns (trópoi) were organised and identified. In more poetic terms, the fixed notes of the Dorian key – the defining boundaries of the so-called ‘Greater’ (μεῖζον) Perfect System (σύστημα τέλειον, Cleon. 200.10–201.7 Jan) – were the main gates leading into the world of harmonía.

In keeping with this, the upper and lower limits of the Dorian tónos defined the overall boundaries of male vocal music, a two-octave range that spans from Dorian proslambanómenos (F2, or simply F) to Dorian nḗtē hyperbolaíōn (F4, or simply f’).33 Only two notes in the key system set out in Figure 4 fall above the upper limit of the Dorian ‘hyperbolic’ tetrachord (f’) and none goes below its lower limit (F): in other words, the core keys of the Classical modulation system are largely contained within the limits of the Dorian Perfect System.

Vocal melodies set in notation keys whose mésē is higher than the Dorian – i.e. the Phrygian, Lydian, Hyperdorian, Hyperphrygian and Hyperlydian tónoi – featured only notes that fell below the limit of Dorian nḗtē hyperbolaíōn, f’: in more practical terms, they avoided the notes g’ and a’, which go beyond the upper Dorian limit f’, even though they theoretically belong to the central octaves of the Hyperphyrgian and Hyperlydian key.34 Conversely, vocal melodies set in keys whose mésē is lower than the Dorian – i.e. the Hypodorian, Hypophrygian and Hypolydian tónoi – used only a few notes that belong to their lowest hypatôn tetrachord, effectively adding only the note F#2 to the network of sounds created by the core system displayed in Figure 4.35

This clear agreement between Aristides’ theoretical testimony and the practical evidence offered by the system of Classical notation tónoi suggests that most of the notes attested in the Hellenistic musical fragments should fall in the two-octave range of the Dorian tónos. This is indeed the case: 100% of the notes attested in the Hellenistic musical documents do in fact fall into the range of the Dorian tónos F2–F4 and 89% into the central Dorian octave C3–C4, i.e. the basic octave range employed in lyre tunings.36 The lowest note recorded in these documents is instrumental 𝈥 (F#2), a semitone higher than Dorian proslambanómenos F2, whereas the highest one is vocal 𝈜 (F4),37 i.e. the top note of the Dorian ‘hyperbolic’ tetrachord (nḗtē hyperbolaíōn) that Aristides identified as the ideal upper limit of male vocal music.

This general rule holds true also for Imperial and Late antique documents, in spite of the small shift of the central point of reference of the Imperial harmonic system that will be discussed in Lynch forthcoming 1: 99% of the notes attested in the Imperial musical documents fall within the Dorian tónos, 0.66% above Dorian nḗtē hyperbolaíōn F4,38 and 0.33% below Dorian proslambanómenos F2.39

As shown above, the modulation system developed by the New Musicians in late Classical times was based upon the Dorian, Phrygian and Lydian keys.40 The invention of this modulation practice is ascribed to Pronomus of Thebes, a virtuoso aulos player active around the end of the fifth century BC who rose to fame as the first performer who could modulate seamlessly between Dorian, Phrygian and Lydian harmoníai on the same instrument.41

This theoretical and practical background strongly suggests that the distinctive ‘intermediate notes’ (mésai) of the Dorian, Phrygian and Lydian modes (harmoníai) should play a prominent role in the Hellenistic musical documents set in the respective notation keys (tónoi). This is indeed the case and the distribution of notes within Dorian, Phrygian and Lydian groups of tónoi42 is fully consistent with the evidence offered by theoretical sources.

The note that corresponds to Dorian mésē F3 (Π) is the most frequent in musical pieces notated in Dorian keys, and 99.5% of Dorian notes fall within the central Dorian octave C3–C4 (Figure 7).43 The relationship between Dorian keys and the relative harmoníai will be illustrated in Lynch 2022 on the basis of the practical evidence of the Ashmolean Papyri (DAGM 5–6).

Figure 7
Figure 7

Distribution of Dorian vocal notes and the relative notation tónoi

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Likewise, the note that corresponds to Phrygian mésē G3 (Ϻ) is the most frequent in musical pieces notated in Phrygian keys, and 89% of Phrygian notes fall within the central Phrygian octave D3–D4 (Figure 8). The relationship between Phrygian keys and the relative harmoníai will be discussed in Lynch 2022, taking Athenaeus’ Paean (DAGM 20) as a case study.

Figure 8
Figure 8

Distribution of Phrygian vocal notes and the relative notation tónoi

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Lydian music offers an interesting variation on this pattern that is consistent with the double denomination of the traditional Lydian harmoníai discussed in §1 above. The note that is most frequent in Lydian music written in vocal notation corresponds to the mésē of the traditional Lydian harmonía (Lydistí), E3 (С), and 96.5% of Lydian vocal notes fall within the simple Lydian octave B2–B3 (Figure 9),44 which came to be re-labelled as Hypolydian tónos in the technically-minded system of notation keys. A striking 98.6% of these notes fall within the compass of Aristides Quintilianus’ Lydian harmonía (Lydistí), dispelling any doubts concerning its authenticity.45

Figure 9
Figure 9

Distribution of Lydian vocal notes, the relative notation tónoi and Aristides Quintilianus’ Lydistí

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

This characteristic link between vocal music and the traditionally lower-pitched, sympotic Lydian harmonía is confirmed by Aristotle, who includes the simple Lydistí amongst the modes that ought to be taught to children alongside the Dorian with a view to the needs of old age, when singers are no longer capable of sustaining the strain of ‘tense’, high-pitched notes.46

ἔστι δὲ καὶ ταῦτα ὡρισμένα ταῖς ἡλικίαις, οἷον τοῖς ἀπειρηκόσι διὰ χρόνον οὐ ῥᾴδιον ᾄδειν τὰς συντόνους ἁρμονίας, ἀλλὰ τὰς ἀνειμένας ἡ φύσις ὑποβάλλει τοῖς τηλικούτοις. […] ὥστε καὶ πρὸς τὴν ἐσομένην ἡλικίαν, τὴν τῶν πρεσβυτέρων, δεῖ καὶ τῶν τοιούτων ἁρμονιῶν ἅπτεσθαι καὶ τῶν μελῶν τῶν τοιούτων, ἔτι δ᾽ εἴ τίς ἐστι τοιαύτη τῶν ἁρμονιῶν ἣ πρέπει τῇ τῶν παίδων ἡλικίᾳ διὰ τὸ δύνασθαι κόσμον τ᾽ ἔχειν ἅμα καὶ παιδείαν, οἷον ἡ λυδιστὶ φαίνεται πεπονθέναι μάλιστα τῶν ἁρμονιῶν.

Arist. Pol. 8.1342b20–33

Singing ‘tense’ modes is difficult for those who have become feeble through the lapse of time, but nature suggests ‘relaxed’ modes to people of this age […]. So it is with a view to this coming stage of life, that of older people, that these kinds of modes and such sorts of melodies should be taken up too – if there even exists such a tuning among the modes that is appropriate for children of this age because it is able to join order (kósmos) with education:47 this is how the Lydian (Lydistí) seems to be shaped most of all the modes.

In contrast, the note that is most frequent in Hellenistic music written in Lydian instrumental notation – i.e. the kind of notation that was most closely related to professional musical practice – corresponds to the mésē of the Lydian notation tónos, A3 𝈶. As we have seen earlier, professional musicians assigned this tónos to the traditional Tense Lydian harmonía (Syntonolydistí). In keeping with this, 90.5% of Lydian instrumental notes fall in the respective octave E3–E4 (Figure 10).

Figure 10
Figure 10

Distribution of Lydian instrumental notes, the relative notation tónoi and harmoníai

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

But this matter is complicated by the fact that the bulk of Hellenistic music written in Lydian instrumental notation in fact records a vocal piece written by a professional kitharode, Limenius’ Paean (DAGM 21), which represents 89.6% of the total.48 This elaborate composition raises important questions about the relationship between Limenius’ professional status and his notational and stylistic choices. His Paean is in fact a specimen of ‘a sophisticated style of composition practised by and for professional artists of the high Hellenistic age’ (West 1994, 288) who inherited the innovations introduced by the New Musicians, including daring combinations of modes, harmonic genera and instruments that traditionally belonged to different genres.49

Such a background may explain why the note B3 is the second most frequent in this subset – a note that is markedly absent in the traditionally auletic Tense Lydian harmonía,50 irrespective of any variations in genus. On the other hand, both A3 and B3 were included in the structure of another traditional harmonía, the diatonic variety of the simple Lydian harmonía that was at home on stringed instruments such as Limenius’ kithara; in keeping with this, Ptolemy tells us that the kitharodic tuning called Lýdia had a ‘modulating character’ (metabolikós êthos).51 As shown in Figure 10, this tuning falls within the central octave of the Hypolydian tónos B2–B3, an octave that is marked very strongly in the melodies recorded in Limenius’ Paean. Such octave leaps are for instance employed in cadences that mark the beginning and the end of various sections of this piece and highlight their basic range,52 while the Tense Lydian octave E3–E4 is notably absent.

This clear melodic idiom, coupled with the fact that ‘hyperbolic’ notes53 are clustered in 8 out of 40 surviving lines of this Paean (20%),54 strongly suggests that the basic range of reference for Lydian music was the simple Lydian octave, B2–B3. In keeping with this, 91.74% of Lydian notes written in instrumental notation fall within the range covered by Aristides’ auletic Lydian (Lydistí) plus Ptolemy’s kitharodic Lýdia. The figure increases to 92.3% if we take into account also Aristides’ Tense Lydian mode (Syntonolydistí); these harmoníai are reproduced at the bottom of Figure 10.

This principle applies also to Lydian vocal notes (Figure 9): as pointed out above, 98.6% of Lydian vocal notes fall within the range of Aristides’ Lydistí, and this figure rises to 100% with the addition of Aristides’ Tense Lydian mode and Ptolemy’s Lýdia.55

Given that the three groups of Dorian, Phrygian and Lydian tónoi differ in magnitude,56 we cannot rely on the absolute number of occurrences of each mésē in order to gain a sense of their modal prominence but we must look at percentages. And the percentages are unmistakable: Dorian mésē F3 Π accounts for 22.5% of Dorian notes, Phrygian mésē G3 Ϻ for 19.1% of Phrygian notes, Lydian/Lydistí mésē E3 С for 20.8% of Lydian vocal notes, and Tense Lydian/Syntonolydistí mésē A3 Ι (=instrumental 𝈶) for 18.3% of Lydian instrumental notes.

In other words, the relative mésē of the basic Dorian, Phrygian and Lydian modes effectively represented about one in five notes (an average of 20.2%) employed in pieces set in the relative triad of keys (e.g. basic Dorian with Hypodorian and Hyperdorian). The marked melodic prominence of the relative mésai of these keys is perfectly consistent with theoretical evidence on modulating harmonic systems57 and is eloquently described in a passage from the Pseudo Aristotelian Problems, which points out the connection between the structural function of ‘intermediate’ notes and their aesthetic role as a ‘bond’ that holds a musical piece together:

… πάντα γὰρ τὰ χρηστὰ μέλη πολλάκις τῇ μέσῃ χρῆται, καὶ πάντες οἱ ἀγαθοὶ ποιηταὶ πυκνὰ πρὸς τὴν μέσην ἀπαντῶσι, κἂν ἀπέλθωσι, ταχὺ ἐπανέρχονται, πρὸς δὲ ἄλλην οὕτως οὐδεμίαν. καθάπερ ἐκ τῶν λόγων ἐνίων ἐξαιρεθέντων συνδέσμων οὐκ ἔστιν ὁ λόγος Ἑλληνικός, οἷον τὸ τέ καὶ τὸ καί, ἔνιοι δὲ οὐθὲν λυποῦσι διὰ τὸ τοῖς μὲν ἀναγκαῖον εἶναι χρῆσθαι πολλάκις, εἰ ἔσται λόγος, τοῖς δὲ μή, οὕτω καὶ τῶν φθόγγων ἡ μέση ὥσπερ σύνδεσμός ἐστι, καὶ μάλιστα τῶν καλῶν, διὰ τὸ πλειστάκις ἐνυπάρχειν τὸν φθόγγον αὐτῆς.

[Arist.] Prob. 19.20

… For all effective melodies use mésē a lot, and all good composers come upon it often (pykná); and when they get away from mésē, they come back to it quickly, whereas they do not behave in this way with any other note. Just as a Greek sentence would not exist if some of the conjunctions, such as and kaí, were taken away whilst others would not be missed in the slightest – because the former must necessarily be used often to produce a sentence whereas the latter not so much – likewise mésē is, as it were, a conjunction (sýndesmos) among notes, and especially between beautiful ones, because notes very often originate in mésē.58

The shift between the melodic prominence of ‘tense’ and ‘relaxed’ mésai in the Lydian keys is mirrored by another noteworthy difference between the distribution of notes in these keys. Lydian music written in instrumental notation covers a much wider range than all other groups, and therefore requires several tónoi (Figure 10): the lowest note F#2 points to Hypolydian, but the highest attested note F4 lies beyond the upper boundary of this key (E4) and belongs to the Lydian hyperbolaíōn/Hyperlydian diezeugménōn tetrachord. This wide melodic range is nevertheless enclosed within the overall boundaries of the Dorian tónos, the general framework of reference for the modulation system as a whole: the lowest note attested in Lydian fragments (F#2) is a semitone higher than the lowest note of the Dorian tónos (proslambanómenos F2) and the top note F4 coincides with the upper boundary of the Dorian tónos (nḗtē hyperbolaíōn).

The wide range of Lydian music written in instrumental notation, its melodic emphasis on the higher end of the traditional modes and their expansion by means of the addition of the ‘hyperbolic’ high-pitched tetrachord reflect the fact that the system of notation tónoi was developed by professional musicians, who carefully trained their voices to produce high-pitched notes that were out of reach for amateur singers.59 In keeping with this, the centrality granted to the Lydian key in the system of notation tónoi – a centrality that is a direct consequence of the change in professional nomenclature discussed in §1 above – goes hand in hand with the New Musicians’ interest in instrumental modulations and the key role they played in their experimental, free-form compositions.60

In part II of this study (Lynch 2022) we shall see how the revolutionary – and, to conservative ears, jarring – combinations of modes, harmonic genera and instruments championed by the New Musicians shed light on the highly modulating Dorian melodies recorded in the Ashmolean Papyri (DAGM 5–6) and the equally complex Phrygian music of Athenaeus’ Paean (DAGM 21). These analyses will also identify the practical implications of their insistent use of ‘exharmonic’ and chromatic notes, mercilessly parodied by comic poets such as Aristophanes and Pherecrates.

Bibliography

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Appendix 1: Aristoxenus’ ‘Diagram of Many trópoi’ and the System of 13 tónoi (diatonic forms exempli gratia)

IMG000012

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Adrastus reports that Aristoxenus’ ‘diagram of many trópoi’ (polýtropon) had a ‘magnitude of two octaves and a fourth’ (Adrastus ap. Theon Math. Plat. 64.1–4). Cleonides (203.5–204.8 Jan) and Aristides Quintilianus (Mus. 20.9–21.1) list the 13 tónoi included in the Aristoxenian system, and the relative pitch of their mésai. Barker 1989, 220 n. 50, suggests that the basic model of the Dorian tónos used by Aristoxenus spanned an octave and a fourth – i.e. it included the central octave C3–C4 and the hyperbolic tetrachord C4–F4 inaugurated by Philoxenus. Aristoxenus’ Dorian template was therefore narrower than the two-octave model used in the 15-tónoi notation system, and did not include the hypatôn tetrachord G2–C3 (cf. [Plut.] Mus. 1137d) as well as the ‘additional tone’ at the bottom of the scale (proslambanómenos, F2–G2).

Aristoxenus’ Dorian template was shifted to the different mésai of the 13 keys featured in his system, covering a range that starts from the lower boundary of the Hypodorian central octave (G2) and goes up to the higher boundary of the Hypermixolydian tónos (C5). In other words, this diagram covers the range of two octaves and a fourth described by Adrastus.

Aristoxenus’ Hypermixolydian tónos (mésē C4) corresponds to the key that is called Hyperphrygian in the system of 15 notation tónoi (cf. Appendix 2).

Appendix 2: Dorian, Phrygian and Lydian Diatonic Notation tónoi in Full and Their Relationship to the Dorian Range

IMG000013

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Appendix 3: Notes Attested in Hellenistic Documents (dDAGM)

IMG000014

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

Appendix 4: Notes Attested in Imperial Documents (dDAGM)

IMG000015

Citation: Greek and Roman Musical Studies 10, 2 (2022) ; 10.1163/22129758-bja10046

1

Vitr. 5.4.1 harmonia autem est musica litteratura obscura et difficilis, maxime quidem quibus graecae litterae non sunt notae.

2

In a letter sent to Galilei in 1579, Mei dates his discovery of Mesomedes’ hymns to ‘fifteen or sixteen years ago’ (Palisca 1954, 15), i.e. around 1563/4.

3

I.e. DAGM 3–16 and 19–22. On DAGM 17–18, see n. 38 below.

4

References to the musical documents collected in the standard edition will follow the usual format (DAGM followed by the document number). In contrast, I shall refer to the editors’ comments on the documents and their features as Pöhlmann and West 2001, followed by the relevant page numbers. The database collects all the notes that Pöhlmann and West identified as belonging to melodies, and therefore omits a few ‘nonsense syllables’ that represent the sound of a trumpet call played by an Amazon depicted on a black-figure epínētron (DAGM 1; cf. Martinelli 2020, 103f.) and seven uncertain notes recorded in DAGM 7.3, lines 1–4, which do not belong to a melody but ‘to some sort of table of notes’ whose purpose is unclear (Pöhlmann and West 2001, 40). On the possible meaning of this sequence of notes, see West 1992, 3f.

5

Pöhlmann 2018.

6

οἱ πάνυ παλαιότατοι, Aristid. Quint. Mus. 18.5f.

7

Barker 2020, 260.

8

Hagel 2010, 16–44; 366–96.

9

Lynch 2018, 295f.

10

Mésē is by definition the note that lies ‘below the disjunctive tone’ that separates the two central tetrachords of the central octave of each tónos (Cleonides 201.18–20 Jan). The crucial role played by the note mésē in ancient musical theory is reflected by its technical characterisation as ‘origin’ (archḗ, [Arist.] Prob. 19.44) or ‘leader’ (hēgemṓn, e.g. [Arist.] Prob. 19.33, 19.36, Aristox. ap. [Plut.] Mus. 1135a, D. Chrys. 68.7).

11

On this principle, see Ptol. Harm. 64.16–65.19 and Anon. Bell. §62, with Lynch 2018. The Iastian mode is based on Hypophrygian mésē D3, cf. n. 21 below.

12

Only the two ‘relaxed’ modes do not share this common top note, even though the presence of the corresponding hole is implied by the use of a single quarter-tone at the top of the Lydian mode. Thanks are due to Stefan Hagel for providing the Greek musical notation fonts used in this article and in dDAGM.

13

Pl. Resp. 3.398d11–399a4, esp. 398e10 (Ἰαστί, ἦ δ᾽ ὅς, καὶ λυδιστὶ αὖ τινες χαλαραὶ καλοῦνται, cf. Lach. 188d); Arist. Pol. 8.1342b12–34. See also Poll. 4.78, where the simple Lydian harmonía is contrasted with the Tense Lydian: καὶ ἁρμονία μὲν αὐλητικὴ δωριστὶ καὶ φρυγιστὶ καὶ λύδιος καὶ ἰωνικὴ καὶ σύντονος λυδιστί, ἣν Ἄνθιππος προσεξεῦρεν. Plato’s traditional division of the harmoníai into ‘tense’, ‘relaxed’ and ‘intermediate’ modes is mirrored by Ptolemy’s discussion of the corresponding tónoi: Ptol. Harm. 99.11–25 Düring. The Tense Lydian and Mixolydian modes were perceived as being higher in pitch because their intermediate notes (mésai) are higher than the mésai characteristic of other modes.

14

Cf. Lynch 2018, 312: Damon aligned the traditional Lydian harmonía with the Tense Lydian, setting the mésē of the former a perfect fourth lower than the mésē of the latter (Lydian, mésē e; Tense Lydian, mésē a). The two diatonic, lyre-based versions of these tunings therefore differed only in one note, f#: Tense Lydian harmonía c d e f g a b c’, (Loose/Simple) Lydian harmonía c d e f# g a b c’. This ‘new’ note f# (Ο Κ) was called chrōmatikḗ, a ‘colouring’ of the basic diatonic system. This mindset reflected the basic procedure followed in tuning this mode on a stringed instrument: after setting the basic harmonía structure (c–f–g–c’), the other notes can be tuned by interlocking fourths and fifths, ending on the ‘chromatic note’ f# (g–d; d–a; a–e; e–b; b–f#). On a seven-stringed instrument, this f# could be obtained by altering the pitch of one of the two ‘intermediate’ strings of the basic harmonía tuning, f or g.

15

Aristox. ap. [Plut.] Mus. 1136e.

16

Aristides Quintilianus (18.24f.) points out that the top note of ‘what is called Tense Lydian’ was ‘three semitones’ higher than its central note, a fact that had significant implications for the creation of a fully modulating system and ultimately required the addition of an Hyperlydian notation sign C4 Г Ν: see §2 below.

17

See full discussion in Lynch 2018.

18

A practical demonstration of this tuning technique is offered by Barnaby Brown in the following video: https://youtu.be/nkT-qbpqAGY.

19

See e.g. Aristox. Harm. 68.10–70.2. Starting from the ‘intermediate note’, a performer could easily tune the other intervals of a given lyre harmonía by fourths and fifths: e.g. f–c’; c’–g; f–bb; etc. On this procedure, its role in lyre playing and harmonic theory, see Franklin 2018 and Lynch 2020, 144–6 (esp. Figure 9).

20

Dion. Hal. Comp. §19, 85.18–86.4 Usener: οἱ δέ γε διθυραμβοποιοὶ καὶ τοὺς τρόπους μετέβαλλον Δωρίους τε καὶ Φρυγίους καὶ Λυδίους ἐν τῷ αὐτῷ ᾄσματι ποιοῦντες, καὶ τὰς μελῳδίας ἐξήλλαττον τότε μὲν ἐναρμονίους ποιοῦντες, τότε δὲ χρωματικάς, τότε δὲ διατόνους, κτλ. Dionysius’ use of plural forms to refer to Dorian, Phrygian and Lydian trópoi is revealing: these three families of scales in fact covered several modes each, just as each group of notation tónoi comprises three keys. On the central importance of modulations between the three basic trópoi, Dorian, Phrygian and Lydian, see also Aristid. Quint. Mus. 23.1f. (εἰσὶ δὲ τῷ γένει τόνοιγδώριος φρύγιος λύδιος) and Ath. 14.637d–e (διένειμεν δὲ τὰς τρεῖς χώρας ταῖς τρισὶν ἁρμονίαις τῇ τε δωριστὶ καὶ φρυγιστὶ καὶ λυδιστὶ). On Pronomus of Thebes, see §3 below. The other traditional harmoníai were also included in the developed system comprising the hypo-/hyper- variants of these three basic keys, cf. Bacch. 303.3–6 Jan: ‘Those who sing the three trópoi, which ones do they sing? / Lydian, Phrygian and Dorian. /And those who sing seven, which ones?/ Mixolydian, Lydian, Phrygian, Dorian, Hypolydian, Hypophrygian, Hypodorian’.

21

Cf. Lynch 2018 and Lynch 2022. On the correspondence of Hypophrygian and Iastian in traditional kithara tunings, cf. Ptol. Harm. 39.14 and 80.16 Düring, with Lynch 2022, Figure 10B; see also Winnington-Ingram 1936, 17, 27, Barker 1984, 283, Barker 1989, 360. It is also worth noting that the single Hyper-scale needed in order to account for the traditional harmoníai – the Hyperdorian/Lower Mixolydian – is described by Ptolemy as the ‘first consonant metabolḗ’ that was introduced by the ancients after the first three basic tónoi, i.e. Dorian, Phrygian and Lydian (Ptol. Harm. 62.18–63.1, quoted and discussed in Lynch 2018, 317f.). The addition of Hypo- and Hyper- keys produce what the Greeks called a ‘conjunct’ system (τὸ συνημμένον σύστημα), where the central octave does not feature a disjunctive tone between mésē and paramésē, but mésē itself acts as a ‘joint’ between the higher tetrachord and the lower one (e.g. c–f; f –bb). The introduction of conjunct systems was strictly linked to the development of the modulation system: ‘It appears that this sort of systēma was added by the ancients alongside the other (parapepoiêsthai) to accommodate a different form of modulation, being treated as ‘modulating’ (metabolikon) by contrast with the other one which is ‘changeless’ (ametabolon)’ (Ptol. Harm. 54.7–9 Düring, Transl. Barker 1989, 328, slightly modified). On the significance of the prefix para- in Ptol. Harm. 51.19f., see Lynch 2018, 314f., which also addresses the significance of the verb paramixolydiázein in connection with harmonic modulations between disjunct and conjunct systems.

22

Practical examples of such combinations of different genera are offered in the transcriptions of selected Ashmolean Papyri (DAGM 5–6) and Athenaeus’ Paean (DAGM 20) included in Lynch 2022. See also DAGM 15–16, which interestingly combine Hypolydian chromatic notes in the vocal part with Hypolydian diatonic notes written in instrumental notation that belong to instrumental interludes – see Pöhlmann and West 2001, 55.

23

On the diatonic genus, see Aristox. Harm. 24.20–25.4, Aristid. Quint. Mus. 16.10f., Theon Math. Plat. 56.3–5. The chromatic resulted from an alteration of this basic diatonic model: cf. P. Hib. 1.13.15–22, Adrastus ap. Theon Math. Plat. 55.4–6, Nicom. Ench. 263.7–10 Jan, and Aristid. Quint. Mus. 92.19–26, with Lynch 2018, 310–12. The enharmonic genus was defined on the basis of the diatonic model: see Aristox. ap. [Plut.] Mus. 1134f–1135a on Olympus’ discovery of the enharmonic genus. The enharmonic and chromatic variants of the scales set out in Figure 4 can be identified by substituting the diatonic divisions of the tetrachords (Semitone – Tone – Tone) with a chromatic (Semitone – Semitone – Tone) or an enharmonic one (Quartertone– Quartertone – Ditone; cf. Aristox. ap. [Plut.] Mus. 1143e). As we shall see in Lynch 2022, musicians often altered these basic templates producing different harmonic ‘shades’ (cf. Barker 1989, 12–14). This was especially true for the diatonic genus, which was generally employed in its ‘tonic diatonic’ variety (28:27, 8:7, 9:8; cf. Winnington-Ingram 1932, 198).

24

These correspondences are marked in Figure 4 with solid white boxes, while the Lydian discrepancy is marked with a dashed box and grey gradient.

25

Cf. Varro fr. 282: ‘these signs show that acute accents as a whole are set at a higher level, and grave accents are lower. The same is shown by the musicians’ diagram, where scales are written higher up because of the acuteness of their notes; hence the highest is the Hyperlydian, because it is highest in pitch, and the lowest is the Hypodorian, because no other scale is lower than this one’ (quae notae demonstrant omnem acutam vocem sursum esse et gravem deorsum. Ipsum etiam musicorum docetur diagrammate, in quo tropi pro acumine vocum superiores scribuntur, denique summus hyperlydius, quia acutissimus, infimus hypodorius, quo nullus est gravior).

26

This list of tónoi ascribed to Aristoxenus is reported by Cleonides (203.5–204.8 Jan) and Aristides Quintilianus (Mus. 20.9–21.1) and comprises thirteen tónoi (cf. Appendix 1), as opposed to the fifteen tónoi of the notation system. ‘Newer [composers and theorists] added the Hyperaeolian and the Hyperlydian keys to the other ones, so that each [basic] tónos had a low register, an intermediate register and a high one’ (τούτοις ὑπὸ τῶν νεωτέρων προστέθεινται ὅ τε ὑπεραιόλιος καὶ ὁ ὑπερλύδιος, ὅπως γ᾽ ἂν ἕκαστος βαρύτητά τε ἔχοι καὶ μεσότητα καὶ ὀξύτητα, Aristid. Quint. Mus. 21.1–3). Earlier on, Aristides had pointed out that these ‘newer’ composers and theorists included an extra tone, the ‘tone of disjunction’ (Aristid. Quint. Mus. 20.7–9), when listing the placement of the proslambanómenos of each key (see note 32). This shows that the point of reference for the placement of proslambanómenoi was the Hypodorian tónos, as suggested by Barker 1989, 422 n. 123, interpreting it as an octave species: both Hyperaeolian proslambanómenos (C#3) and Hyperlydian proslambanómenos (D3) do in fact fall within the ‘disjunctive tone’ of the Hypodorian octave species, c–d, but only if this octave species is set in the central Dorian octave range (C3–C4). In keeping with this, the Hypodorian key was the lowest of all (cf. n. 25 and Figure 4) and its mésē was marked as Ω in vocal notation. These points have interesting implications for the relationships between traditional harmoníai and the ‘newer’ system of tónoi, especially given that neither Aristides’ transcription of the ancient harmoníai nor Plato and Aristotle’s discussions of these traditional modes include a Hypodorian ‘mode’. A Hypodorian harmonía is mentioned by Heraclides of Pontus, but he employs this adjective in its pre-systematic meaning that indicates an aulos harmonía set ‘immediately below the Dorian’ (ὑπὸ τὴν Δώριον ἁρμονίαν) and not the notation key set a fourth below the Dorian tónos (cf. Lynch 2018, 320 n. 87, replacing ‘suffix’ with ‘prefix’). The tónos set a fourth below the Dorian is also the only notation key that both Cleonides and Bacchius explicitly associate with a harmonía, namely the Locrian (ἐκαλεῖτο δὲ κοινὸν καὶ λοκριστὶ καὶ ὑποδώριον, Cleon. 198.10–13 and Bacchius 309.7–9). This isolated emphasis on the correspondence of the Hypodorian key with a particular mode is a reflection of its ‘new’ status as an addition to the six traditional harmoníai mentioned by Plato and Aristides: the Locrian kithara tuning was in fact a late Classical addition to the traditional system made by the New Musician Philoxenus (Poll. 4.65 Λοκρική· Φιλοξένου τὸ εὕρημα). Thanks to the introduction of an extra string (D4) that extends the system of kithara tunings beyond its traditional Dorian limit (C4), Philoxenus inaugurated the use of the so-called ‘hyperbolic’ tetrachord on professional kitharai (Lynch 2018, 319–22). Philoxenus’ addition of the note D4 was also the theoretical prerequisite that was needed for the expansion of the tónoi system to fifteen scales: this tone (C4–D4) corresponds to the disjunctive tone that Aristides identified as one that was ‘added’ to the basic system in order to include the Hyperaeolian and Hyperlydian keys (mésai C#4 and D4; proslambanómenoi C#3 and D3).

27

28:27, 8:7, 9:8 (Figure 5). The widespread use of this diatonic shade is confirmed by Ptolemy’s transcription of traditional kithara tunings, discussed in Lynch 2022. Ptolemy called this shade ‘tonic diatonic’, referring to the full 9:8 tone at the top of the tetrachord. Cf. Winnigton-Ingram 1932, 198.

28

I.e. Dorian, Hyperdorian, Hypodorian/Hyperphrygian, Phrygian, Hypophrygian/Hyperlydian, Lydian and Hypolydian keys (Figure 4).

29

This restriction is notably observed also in the later expansion of the harmonic system, even though it would have theoretically been possible to add another key within the range of the Dorian Perfect System based on mésē Eb4paramésē F4, an octave higher than the Hypoaeolian key. But such a key would have represented the Hyper-variant of the Hyperdorian key, an addition that would have completely severed the links between notation keys and the characteristic modes of the Greek musical tradition: this move seems to have been too bold even for the ‘revolutionary’ New Musicians. This addition would not have been possible in the Imperial version of the harmonic system, which was set a semitone lower than the Classical system (cf. Lynch forthcoming 1). A hypothetical key based on mésē Eb4paramésē F4 would have crossed the higher boundary of the Hypolydian Perfect System used in Imperial music (Hypolydian nḗtē hyperbolaíōn E4).

30

The basic framework of the Dorian octave species corresponds to what Aristoxenus calls ‘immovable’ or ‘standing’ notes (φθόγγοι ἀκίνητοι, Aristox. Harm. 28.10–12, passim; φθόγγοι ἑστῶτες, Cleonides Isag. 185.16–19). The Dorian octave species was the fundamental framework of Classical lyre tunings and continued to play this role in Ptolemy’s harmogaí too: see n. 36 below.

31

Bellermann’s supplement exempli gratia.

32

The term proslambanómenos literally indicates the note or tone ‘taken in addition’ to the basic structure of a tónos and identifies its lowest note, set an octave below mésē.

33

See also Anon. Bell. §64: ‘the hyperbolic region of the voice is the whole area that starts from the Hypermixolydian’ (ὑπερβολοειδής ἐστι πᾶς ὁ ἀπὸ τοῦ ὑπερμιξολυδίου), i.e. above the upper limit of the Dorian octave C4, which corresponds to Hypermixolydian mésē.

34

Once again, the two notes that fall above the Dorian range belong to the ‘new’ high-pitched tónoi – the Hyperlydian and Hyperphrygian – that the New Musicians added to the traditional system of harmoníai: see n. 26 above.

35

Figure 4 includes only the central octave of each key, that is to say the range that is most characteristic for each key, and this suffices for the purposes of the present arguments. For the sake of completeness, diagrams displaying the diatonic variety of the Classical Dorian, Phrygian and Lydian tónoi in full, and their relationship to the Dorian range, are offered in Appendix 2. The lowest (hypatôn) tetrachord of each key is identical to its diezeugménōn tetrachord, transposed an octave lower.

36

See tables in Appendix 3. On Classical lyres and their use of the Dorian octave range, see e.g. Pl. Lach. 188d, and other evidence discussed in Lynch 2018 and Lynch 2020, esp. 131f. Hagel 2010, 58f., argued that Classical lyres were tuned to the Tense Lydian octave, but this view is rooted in a problematic interpretation of Ptolemy’s testimony concerning traditional kithara tunings. These issues and their implications for the interpretation of the Greek musical documents will be discussed in Lynch 2022, Lynch forthcoming 1 and 2.

37

DAGM 4 𝈜 𝈜, an octave above either Hyperaeolian chromatic Π (Pöhlmann and West 2001, 20) or Lydian enharmonic Π (Hagel 2010, 258). Two 𝈜 perhaps appear in DAGM 22, and are included in dDAGM in keeping with the standard edition, but the context is too uncertain to assess their harmonic significance.

38

This figure does not take into account the octave strokes featured in DAGM 17: cf. Pöhlmann and West 2001, 59; Hagel 2010, 72, n. 45, and 277–9. This papyrus is grouped with Imperial documents in dDAGM, following the dating of the papyrus itself (2–3rd cent AD) and the fact that ‘the other items on the Berlin papyrus would seem to belong to the Imperial period’ (Pöhlmann and West 2001, 59; see also Cosgrove and Meyer 2006, 74f., 80f.). It is also worth noting that DAGM 17 is written in-between two clearly Imperial instrumental interludes (DAGM 51f.; a high-resolution photo of this papyrus is available online: https://berlpap.smb.museum/01743/). In keeping with the later dating, the keys employed in these fragments are consistent with the harmonic ‘shift’ that characterises the Imperial documents discussed in Lynch forthcoming 1. But the relative percentages would not change substantially even if one took the octave strokes into account: in this case, a total of 59 notes (2.46%) would fall above Dorian nḗtē hyperbolaíōn F4, 2328 notes (97.2%) within the Dorian tónos and 8 notes (0.33%) below Dorian proslambanómenos F2.

39

See tables in Appendix 4. As I will show in Lynch forthcoming 1, the central reference point of the Imperial harmonic system shifted down to Hypolydian mésē E3, i.e. a semitone lower than the Classical system centred on Dorian mésē F3. The Imperial harmonic system was therefore based on the Hypolydian tónos. Aside from occasional special effects, Imperial and Late Antique melodies do in fact move within the two-octave range of the Hypolydian tónos E2–E4 (99.16%) and especially within its central octave B2–B3 (84.18%).

40

See Dion. Hal. Comp. 19 quoted above, with Lynch 2018, 293–302.

41

Paus. 9.12.5, Ath. 14.631e. Earlier auletes had to switch between different sets of pipes to modulate between different harmoníai: cf. [Plut.] Mus. 1134a. See also Ath 14.637b–f on the experimental lyre invented by Pythagoras of Zakynthos, which allowed him to modulate between Dorian, Phrygian and Lydian tunings.

42

Data are taken from DAGM without alterations, and the grouping of scores into Dorian/Phrygian/Lydian conforms to Pöhlmann and West’s identification of different families of tónoi. Each note is counted once regardless of its dating even though repeated notes are written only once in Hellenistic scores, whereas identical notation signs are repeated above successive syllables in Imperial scores. The relative distributions of notes in Hellenistic and Imperial scores are evaluated separately in this article and its sequels, making the mathematical implications of this change immaterial. More significantly, this change in notational convention was part of the broader shift in harmonic practice that will be discussed in Lynch forthcoming 1.

43

Differences between an equally tempered fourth (=500 cents) and its closest approximation in Just Intonation (4:3 ~498 cents) are not marked in the figures offered in this article.

44

Cf. n. 22 above on the combination of vocal chromatic notes and diatonic instrumental notes in the Hypolydian fragments DAGM 15–16.

45

Cf. Winnington-Ingram 1936, 24; Hagel 2010, 34.

46

Cf. e.g. [Arist.] Prob. 19.37: ‘singing high notes is more work than singing low ones’ (ἔργον μᾶλλον ᾄδειν τὰ ὀξέα ἢ τὰ βαρέα); ‘high-pitched nómoi are hard to sing because of their tenseness’ (οἱ ὀξεῖς χαλεποὶ ᾆσαι διὰ τὸ ἀνατεταμένοι εἶναι).

47

On the kósmos of lyre tunings spanning an octave, see e.g. Theon Math. Plat. 141.7–9 (τὴν γὰρ λύραν ἑπτάχορδον λέγων εἰκόνα κόσμου συστήσασθαι τὸν Ἑρμῆν); on Plato’s use of this traditional idea and its implications, see Lynch 2020. It is noteworthy that modern scholars called Aristides Quintilianus’ transcription of the Lydian harmonía into question precisely because of its exceptionally ‘orderly’ structure (cf. n. 45), whereas Aristotle singled out this remarkable order as one of the defining traits of this mode.

48

I.e. 293 notes out of 327 Lydian instrumental notes attested in Classical/Hellenistic scores. It should also be noted that virtually all instrumental music recorded in the extant Hellenistic documents is written in Lydian tónoi, a significant coincidence that reflects the close link between this key and professional musical practice discussed at the start of this article.

49

A colourful description of the experimental nature of songs performed by these ‘leaders of a museless sort of lawlessness’ is offered in Book 3 of Plato’s Laws (Leg. 3.700a3–701b3), esp. 3.700e6–8: ‘mixing together laments with hymns, and paeans with dithyrambs, and imitating their aulos pieces with citharodic ones …’ (κεραννύντες δὲ θρήνους τε ὕμνοις καὶ παίωνας διθυράμβοις, καὶ αὐλῳδίας δὴ ταῖς κιθαρῳδίαις μιμούμενοι κτλ.). See full discussion in Lynch 2022; cf. Pöhlmann 2018, 335, who describes Athenaeus and Limenius as heirs of the New Music, ‘a musical tradition that was still accessible’ to them.

50

Cf. Telestes’ characterisation of the prototypically auletic, high-pitched Lydian nómos as a ‘nimble rival of the Dorian muse’ (PMG 806); see also Ion TrGF 19F39, Clem. Al. Strom. 1.16.76.4, Crat. ap. Ath. 14.638f, Aristox. ap. [Plut.] Mus. 1134f–1135a. On high-pitched Lydian harps, see Telest. PMG 810.

51

See Ptol. Harm. 39.12–14 Düring (‘the mixture of tense diatonic with tonic will fit the metabolika characters, which the kitharodoi call Lydian and Iastian’, transl. Barker 1989, 312), Ptol. Harm. 80.14f., and Porph. in Harm. 156.8–10, with Barker 2015 ad loc. The ‘modulating’ character of these tunings is related to the fact that they both include a ‘ditonic diatonic’ tetrachord in their instrumental version, featuring two 9:8 tones at the top. As will be shown in Lynch forthcoming 2, this sequence allowed kitharodes to join up different tunings with ease (cf. Ptol. Harm. 54.7–9). Lynch forthcoming 1 and 2 will also show how Porphyry’s identification of Ptolemy’s Lýdia tuning with the Hypolydian notation tónos has major implications for the interpretation of the Imperial musical documents and allows us to establish a consistent link between the traditional names of Classical and Imperial tunings: just as Ptolemy’s Lýdia corresponded to the Classical Lydistí harmonía that came to be assigned to the Hypolydian notation tónos for the reasons discussed in §§1–2 above, Ptolemy’s Iástia corresponded to the Classical Iastí harmonía, which was assigned to the Hypophrygian notation tónos. Unlike the hypothesis that Ptolemy’s Lýdia corresponded to the Lydian notation tónos put forward in Hagel 2010, 57f., Porphyry’s identification of the kitharodic tuning Lýdia with the Hypolydian tónos (and, therefore, with the Classical Lydistí) allows us to bridge the gap between the harmonic systems employed in Hellenistic and Imperial scores, reconstructing a continuous tradition that links Classical to Late Antique musical practice (Lynch forthcoming 1 and 2).

52

See transcription in West 1994, 293–9, which features several octave leaps B2–B3 corresponding to DAGM 21, lines 10, 13, 20, 23, and 31. This octave interval was known as kompismós: cf. Anon. Bell. §93 (Προκρούσεως δὲ γενομένης ἐκ τοῦ διὰ πασῶν κομπισμὸς γίγνεται), with West 1994, 204 and 268. On the harmonic importance of opening and closing sections, see West 1994, 294–300.

53

I.e. notes that fall above the higher boundary of the central octave C4 Ν – namely D4 𝈼, E4 𝈿, and F4 𝉀 (attested in DAGM 21 line 3, 6, 14, 15, 31–3 and 38).

54

Athenaeus’ Paean, in contrast, features ‘hyperbolic’ notes above (and not including) C4 Г (=instrumental Ν) in 23 lines out of 40 (57.5%).

55

Hence the range defined by the two auletic Lydian harmoníai preserved by Aristides plus Ptolemy’s Lýdia covers 95% of all the Lydian notes attested in the Hellenistic documents. From a strictly harmonic point of view, 3.8% of these notes belong to the Hyperlydian tónos (namely Θ 𝈍, Η 𝈷, and Г Ν, cf. Figure 10) but the overwhelming majority is clearly rooted in the original Lydian range of Aristides Quintilianus’ Lydistí, slightly expanded by Syntonolydistí. The Lydian vocal notes represented in Figure 9 largely belong to tragic music and, therefore, may also include notes belonging to Aristides’ Mixolydian mode – cf. Lynch 2022.

56

Dorian, Hypodorian, and Hyperdorian scores include 382 vocal notes, Phrygian, Hypophrygian, Hyperphrygian scores 256 vocal notes, and Lydian/Hypolydian scores 144 vocal notes and 327 instrumental ones (for a total of 471). Pieces that modulate between tónoi belonging to different groups have been assigned to the one that is prevalent. In practice, this affects only a handful of notes and therefore does not have a significant impact on the overall percentages.

57

E.g. Cleonid. 201.14–18 Jan, quoted and discussed in Lynch 2018, 302.

58

On mésē as the ‘origin’ of the notes of a tuning (archḗ), cf. [Arist.] Prob. 19.44 with Lynch 2020, 129f. The genitive plural τῶν καλῶν could alternatively be taken as a reference to beautiful melodies (e.g. Barker 1984, 195), but this reading is unlikely given that the word melos occurs only at the start of this quotation, whereas τῶν φθόγγων occurs immediately before τῶν καλῶν.

59

Cf. Melidis 2020; Hall 2002.

60

Cf. [Arist.] Prob. 19.15.

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