Bridging the Gap:
the Greek Notation System and its Historical Development
The foundational character of the Hypolydian key discussed by Ptolemy, Porphyry, and evidenced by the Imperial musical documents, is also reflected by the basic logic that shapes the organisation of the Greek notation system.
Generally speaking, Greek melodic notation is based on groups of three related signs that originally indicated a basic, or ‘natural’, note and two ‘modifications’ of the basic pitch. This relationship is apparent in instrumental notation, where the shape of the sign that indicates the basic note (e.g. S) is often rotated and inverted to represent the two ‘modified’ notes (e.g. R P).
As shown in Figure 13, the set of basic notation signs that fall into the central octave of the Imperial harmonic system (B2–B3) form a Hypolydian octave species (B-c-d-e-f#-g-a-b), in accordance with the theoretical model provided by the Canon diagram. The Hypolydian key was therefore the basic model for the Greek notation system too.
Lynch 2024a, Figure 13: The Hypolydian framework of the Greek notation system: the basic notation signs featured in the central octave of the Imperial system (B2–B3) form a Hypolydian octave species (B-c-d-e-f#-g-a-b, mésē E3).
But the melodic notation system was not an Imperial invention, of course. In keeping with this, the set of signs reproduced in Figure 13 covers both the Dorian central octave C3–C4 that was typical of Classical Greek music and the Hypolydian central octave B2–B3 that is characteristic of Imperial music.
These notation signs account for the core set of keys featured in the two Imperial harmonic settings detailed by Porphyry and the Anonyma Bellermanniana, and are also the same signs that are needed to notate the Classical harmoníai preserved by Aristides Quintilianus (Figure 14). This correspondence suggests that the core of this Hypolydian-based notation system must have been perfected in Late Classical times at the latest.
But the Classical core of the notation system also bears witness to the original cen- trality of the Classical Dorian octave C3–C4. The shape of the instrumental note G C4, in fact, reflects its historical origins as the Nḗte (G) par excellence – the upper Dorian boundary of the Classical central octave. The lower boundary of the Dorian octave W C3 was likewise marked by the last letter of the alphabet series employed in vocal notation (A – W).
Lynch 2024a, Figure 14: The auletic Classical harmoníai preserved by Aristides Quintilianus and the Greek notation system (On the ‘silent’ mésē of the Mixolydian mode, see Lynch 2022b, 428–31. On the irregular notation signs that correspond to the higher Phrygian pyknón, Lynch 2022b, 443)
As shown in Figure 14, the first triplet that was eventually added below the lower Dorian boundary W C3 features two defining notes of the Classical Lydistí tuning–a tuning that, according to Aristoxenus, was first ‘discovered’ by Damon of Oa.
As noted elsewhere, this expression cannot mean that Damon literally invented this mode, which was already in use in archaic aulos music. Aristoxenus’ testimony rather indicates that Damon discovered how to inte- grate this traditional aulos mode into the Classical harmonic system—an innovation that is confirmed by the fact that the Hypolydian key is not included in the two ‘archaic’ systems of tónoi detailed by Aristoxenus, but appears in the set of the Classical harmoníai preserved by Aristides (Figure 14).
The first set of tónoi mentioned by Aristoxenus also indicates that the Higher Mixolydian mode was already in use in archaic times, but with a significant difference from its standard Classical counterpart, the Lower Mixolydian.
In the first ‘archaic’ system detailed by Aristoxenus, the intermediate note of the auletic Mixolydian mode was still identified with the note set a semitone lower than Dorian mésē, i.e. S E3, in keeping with the ‘naturalistic’ interpretation of this scale that was common up to the time of Pythocleides (Lynch 2022b, 427–9). Its top note therefore corresponded to what would become the highest note of the earliest core of the Classical notation system, A C#4.
But this ‘naturalistic’ interpretation of the archaic Mixolydian harmonía did not organise it into well-formed tetrachords, posing a significant obstacle to its integration into the Dorian-based, Classical modulation system. This problem was eventually solved by a grand-pupil of Pythocleides, an Athenian aulete called Lamprocles, who identified the structurally correct mésē of the Mixolydian mode with a silent note (Bb3) that falls within the undivided tritone that appears at the top of this scale (Lower Mixolydian, Figure 14). Lamprocles’ re-interpretation of the Mixolydian mode also aligned it with the central Dorian octave, producing the ‘first consonant metabolḗ’ mentioned by Ptolemy.
Lamprocles’ brilliant innovation, in turn, enabled his pupil Damon to incorporate the Lydistí mode into the Classical system by identifying its octave structure as ‘the opposite of the Mixolydian’ species that was discovered by Lamprocles himself.
Lamprocles’ identification of the Lower Mixolydian mésē with the note Bb3 also enabled Damon to employ the note S E3 as the intermediate note of the Lydistí mode, given that this note no longer represented the ‘archaic’, but structurally incorrect, mésē of the Higher Mixolydian mode.
As shown in Figure 14, the Classical Lydistí mode spanned an octave but was effectively placed in between the Dorian and the Hypolydian notation keys. Damon’s integration of the Lydistí mode, and the relative Hypolydian key, into the Classical system therefore required the addition of a new pyknón gba immediately below the Dorian boundary W C3. This new triplet clearly mirrors the top triplet GBA that is based on Dorian Nḗte G G C4, and features the first derivative signs that were produced by modifying the standard letter shapes used in vocal notation.
In keeping with this, the vocal note a is first attested in a Hypolydian document dated to the third century BC (P. Vindob. G 13763/1494), and is employed alongside b in accordance with the structure of the Classical Lydistí mode (DAGM 15.5 ba and 15.7 a).
In similar vein, the instrumental counterpart of vocal a, a, first appears in the accompaniment to the tragic lament that is preserved in one of the earliest extant musical documents, the Orestes papyrus (P. Vindob. G 2315, third–second century BC).
Figure 14 also shows that Damon’s integration of the Lydistí mode required the introduction of a new fixed note, Z B3, and the relative pyknón—notes that were not previously featured in the Classical core of the harmonic system (Dorian–Phrygian–Lydian plus Lower Mixolydian). But the integration of the Lydistí mode, and the relative Hypolydian octave, within a harmonic system that included the Higher Mixolydian key posed a new, and unprecedented, challenge to the central role of the Classical Dorian mode.
Prior to the integration of the Lydistí mode, the Dorian had been the only Classical scale that featured a note set a fifth above its mésē F3. In this context, the Dorian was also the only mode that could modulate seamlessly with the Lower version of the Mixolydian mode via the common tone F3 and a shared pyknón.
The integration of Lydistí, however, undermined the previously unique status of the Dorian, given that Lydistí also included a note set a fifth above its mésē E3 and could modulate with the Higher Mixolydian mode via two common tones (E3 and B3) as well as a shared pyknón. As we shall see in a moment, these competing tensions would eventually shift the centre of the harmonic system to Imperial mésē E3.
Lynch 2024a, Figure 7: The changing alignment of the Mixolydian mode (mésai are marked in bold and underlined; half-sharp signs indicate quarter-tone intervals, sharp-and-a-half signs raise the relative note by three quarter-tones)
For now, however, let us keep our focus on the late Classical developments of the Greek harmonic system and the issues raised by the unwieldy structure of the Mixolydian mode. Even though the Mixolydian mode had largely been integrated into the harmonic system by now, a problem still remained unsolved – namely the fact that one of its pykná did not correspond to a single notation triplet but featured a mixture of signs taken from neighbouring triplets (Figure 15).
Lynch 2024a, Figure 15: Both the Lower Mixolydian and the Higher Mixolydian modes featured a ‘mixed’ pyknón (marked in bright pink). These mixed pykná do not correspond to standard notation triplets but mix signs belonging to different groups. The Lydian ‘Mixolydian’ harmonía, by contrast, does not include any mixed pykná and uses Lydian signs throughout.
Damon’s integration of the Lydistí mode allowed late Classical musicians to find a solution to this lingering problem by setting the Mixolydian in the new Hypolydian octave B2–B3, i.e. a semitone lower than the Classical Lower Mixolydian mode. Thanks to this semitone shift, the structural mésē of the Mixolydian mode came to correspond to a note that was in common use, I A3, overcoming the theoretical abstraction of the ‘silent’ mésē introduced by Lamprocles. This shift also made it possible to represent the ‘archaic’ mésē of this mode with a standard diatonic sign, F D3, as opposed to the irregular ‘exharmonic’ solution entailed in earlier versions of this mode.
This Lydian version of the Mixolydian mode is employed in the vocal part of the Euripidean lament preserved in the Orestes papyrus (DAGM 3), in accordance with the typically tragic character of this mode. In keeping with the Mixolydian model preserved by Aristides Quintilianus, this lament features the characteristically Mixolydian tritone at the top of the scale (Z B3–P F3).
But this mode could not properly be called ‘Mixo-lydian’ (Mixolydistí) any more, because its core Lydian elements were no longer ‘mixed’ with the Dorian system, as in its previous incarnations. As shown in Figure 15, all the notes of the new Lydian ‘Mixolydian’ mode correspond to standard notes of the Lydian tónos, producing a conjunct variant of the Lydistí octave.
As shown in Figure 16, the series of inverted signs that was inaugurated by the Lydian pyknón gba was extended in order to notate the extra ‘fixed’ note of the Dorian mode set ‘beyond hypátē’ (hyperhypátē Bb2 d). In keeping with this, the note Bb2 d corresponds to the ‘additional tone’ of the Hyperdorian key that was used to notate the Classical Lower Mixolydian mode (mésē Bb3), and is also the note that aulos players would overblow in order to produce the highest note of the Classical harmonic system: the ‘hyperbolic’ nḗtē of the Dorian key (F4 Ó ).
The note Bb2 d also marks the beginning of the second inverted pyknón zed, which is included in the lowest mode of the Classical system, the Iastian, and was notated by the Classical Hypophrygian key. The series of inverted vocal signs was therefore extended down to Hypophrygian proslambanómenos s D2, the modified and inverted sigma sign that represents the lowest note of the Hypophrygian key.
Lynch 2024a, Figure 16: The second stage in the development of the Greek notation system is marked by the addition of inverted vocal signs. These inverted signs cover the ‘relaxed’ register that is set immediately below Dorian C3 W, starting from a and reaching down to s (=Hypophrygian proslambanómenos D2), as well as the new, ‘hyperbolic’ keys set above A C#4.
The Classical harmonic system was further expanded in late Classical times by the introduction of two high-pitched keys set above Dorian nḗtē C4, the upper boundary of the central octave. The remaining inverted letters were therefore used to notate these new ‘hyperbolic’ keys:
Phrygian nḗtē D4 1 (= Hyperlydian mésē)
with the relative Hyperphrygian pyknón 123
and
Lydian nḗtē E4 4 (=Hyperlydian paramésē)
with the relative Hyperlydian pyknón 456
As shown in Figure 16 above, the sign that is set immediately above the core Classical system A–W is D4 1 , a note that completes the central octave of the Phrygian key (D3–D4) and, at the same time, made it possible to introduce a new key based on mésē C4, which was defined by the disjunctive tone C4–D4. This notation key was called Hyperphrygian, or Hypermixolydian in Aristoxenian parlance, and corresponded to the Locrian mode that Philoxenus introduced into the late Classical kithara system (Lynch 2018).
But the note D4 1 plays two other important roles. On the one hand, it is two octaves above the note that is represented by the lowest inverted sign of the Greek notation system, Hypophrygian proslambanómenos s D2.. On the other, D4 1 corresponds to the intermediate note of the new Hyperlydian key–the highest key included in the Greek notation system as a whole. In order to be defined as a new mésē in the Classical sense of the term, D4 1 had to be accompanied by a note set a tone above it, E4 4 —a note that represents Hyperlydian paramésē and, at the same time, completes the central octave of the Lydian key (=Lydian nḗtē). The top note of the Hyperlydian pyknón, 6 F4, likewise corresponds to the ‘hyperbolic’ nḗtē of the Dorian key, the very top boundary of the Classical, Dorian-based harmonic system (Figure 16).
A new register was eventually added above the upper Dorian boundary F4 6, and comprises notes that could be produced as overtones on professional lyres. In keeping with this, the signs featured in this new register are identical to the ones that appear in the central Classical range with the addition of octave strokes (e.g. O’ K’ F#4 vs O K F#3).
The fourth, and final, stage in the development of the Greek notation system entailed the addition of six new letter-based signs at the very bottom of the system. As shown in Figure 17 below, the basic note of the higher of these triplets (f C2) defines the ‘additional tone’ of the formalised Hypodorian key (C2–D2), and the basic note of the lowest triplet (w Bb1) mirrors the inverted omega that sits at the very top of the notation system (1’ D5), but was not included in any notation keys. In keeping with this, none of the keys featured in the Greek melodic system is lower than Dorian hypátē (W C3), confirming that the Dorian key was the original point of reference for the Classical harmonic system (Figure 17).
Lynch 2024a, Figure 17: The final stages of the development of the Greek notation system:
3. addition of the overtone register set above the hyperbolic Dorian tetrachord;
4. addition of six sideways letters that represent the ‘additional’ tone of the Hypodorian key
As mentioned above, the structural rivalry created by the late Classical introduction of the Lydistí mode into the Classical harmonic system undermined the primacy of the Classical Dorian key.
As shown in Figure 18, the new Lydistí mode could in fact modulate seamlessly with the Higher Mixolydian mode as well as the new Lydian version of the Mixolydian mode, establishing the fifth S E3–Z B3 as a new point of reference that competed with the Classical fourth defined by the Dorian and Lower Mixolydian mode (P F3–H Bb3).
These competing harmonic tensions eventually led to the birth of the new Hypolydian-centred system that is employed in the Imperial musical documents, where Lýdia became the new Dorian (Figure 18).
Lynch 2024a, Figure 18: Bridging the gap: the structural rivalry between the Classical Dorian mode and Lydistí eventually led to the birth of the new Imperial system, where Lýdia became the new Dorian and the structural fifth S E3–Z B3 replaced the Classical fourth P F3–H Bb3.
In keeping with its new Hypolydian framework, only three families of notation keys are employed in the Imperial musical documents: Lydian, Iastian and (very occasionally) Aeolian. As shown in Figure 9 and 19, these are precisely the Imperial counterparts of the Dorian, Phrygian and Lydian keys that formed the core of the Classical modulation system.
Lynch 2024a, Figure 19: The notation keys employed in the Imperial musical documents and the underlying Hypolydian tónos.
Errata Corrige (Advance Article)
p. 35, line 5: please insert missing ‘grand-’ after pupil’ (revised sentence: ‘This problem was eventually solved by a grand-pupil of Pythocleides, an Athenian aulete called Lamprocles’.
p.38, lines 5–7: please delete the following sentence: ‘and the same interval is emphasised an octave lower in the instrumental accompaniment (a B3–P F3)’. I misread the notation sign relative to the lowest note (which ought to have been printed in its instrumental version a) for g B2.
The actual sign recorded in the Orestes papyrus is a C3 (as reported in note 86 on the same page), and forms a fourth with the note P F3