EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources

Descending Equi-heptatonic Circuits

An experimental composition for Classical-era auloi with diagrams and commentary by Barnaby Brown

Reeds and reproduction by Robin Howell of an aulos buried 400–350 BCE in Pydna, northern Greece.

Published for the European Music Archaeology Project by Barnaby Brown 2018

Duration: c. 5 minutes

CONTENTS

Score Version 2.2 (30 July 2018) ...... 3 Diagram 1 Version 1.2 (27 June 2018) ...... 6 Diagram 2 Version 1.1 (31 May 2018) ...... 7 Commentary Version 1.1 (4 September 2018) ...... 8 Bibliography ...... 30

Updates & open file formats: DOI 10.6084/m9.figshare.7006208 Audio, video & discussion: doublepipes.info/descending-equiheptatonic-circuits

Licence These materials are released under the Creative Commons license CC BY 4.0 to help establish an open culture of data-sharing, collaboration, and distributed testing and development in the field of Very Early music. Suggestions for best practice include: • in the case of performances, releasing audio or video documentation online and linking reciprocally between this and the development hub for this volume at doublepipes.info/descending-equiheptatonic-circuits; and • in the case of revisions and transformations of the composition or these study materials, providing a summary of the changes you make with explanations in a form that engages performers, giving bar references and citing any ancient evidence or modern scholarship that informs your decisions. For more on this series of resources and reflections on this emerging discipline, see the ‘Introduction to the EMAP Resources for Euterpe’ in Volume 1.

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources Dedicated to Stefan Hagel 3 Descending Equi-heptatonic Circuits

for Poseidonia/Pydna/Elgin aulos • composed 8–15 March, revised 18 May 2018

This composition is a training ground for producing pure intervals between the High and Low pipes. It reconstructs an auletic tonal system that supports extensive modulation: an elastic network of seven tetrachords pitched roughly a seventh-octave apart (see Diagram 1). The pitch offsets (-43, -14, etc.) should not be adhered to: the right pitch is the one at which pure fifths and fourths require the least embouchure adjustment. The hole boring of these auloi means that all fifths must be stretched and all fourths narrowed — do this by relaxing the embouchure and fractionally pulling out whichever pipe needs to be flattened. The written pitch corresponds to the Pydna aulos; the Poseidonia sounds about a semitone higher, the Elgin about a tone lower. The musical meaning of the terms Dorian, Aeolian, etc. changed over time; the usage here is a hypothesis for auletes around 500 BCE and bears no relation to the usage of medieval or modern musicians (see Diagram 2). For further information, see the Commentary.

Barnaby Brown (b. 1973) Hypodochē (summons, trumpet fanfare) ™ ™ ™ ° 4#œ™ œœœ™ œœ #œ™ œœœ™ œœ #œ œœ˙ œ#œœœ œ œœœ œ #œœœ H-0 & 4 œœ

‹ -43 Dorian 4#œ™ œœ˙ œ#œœœ œ œœœ œ™ #œœœ™ œœ #œ™ œœœ™ œœ œ™ œœ˙ L-0 ¢& 4 ‹ °6 œ™ œœ˙ œ œœœ œ œœœ œ™ œœœ™ & œ™ œœœ™ œœ œœ œ™ œœœ™ bœœ

‹ +14 Iastian (Hypophrygian) -14 Aeolian (Slack Lydian) ™ ™ ™ ™ œ ¢& œ œœœ œ œœœ œ œœœ œœ œ œœœ œ œ™ œœ˙ œ œœœ œ œœœ ‹ 11 ° ™ ™ ™ b˙ œ œ 6 & œ œ œ ˙ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ œ 8 ‹ +43 Phrygian 6 ¢& œ™ œ œ œ™ œ œ œ™ œ œ œ™ bœ œ œ™ œ œ ˙ œ™ bœ œ œ™ œbœ 8 ‹ A Spondeion (libation to the gods, dignified, disciplined) °15 ™ ™ 6#œ œ#œ ˙ œ nœ œ™ ˙™ bœ œ™ ˙™ œ œbœ™ œ™ œ œ #œ œ œ#œ & 8 J J œ J J J J J ‹ -43 Dorian -14 Aeolian +14 Iastian j +43 Phrygian -43 Dorian 6#˙™ œ #œ œ™ ˙™ nœ œ ™ ™ bœ ™ ™ ™ #œ™ œ œ ¢& 8 J J œ ˙ œ œ ˙ b˙ J ‹ °24 <#>˙™ ™ ™ #œ™ œ nœ œ œ ˙ œ bœ œ œ ˙ œ œ œbœ b˙™ #œ œ & J J J J J J J ‹ -14 Aeolian +14 Iastian +43 Phrygian -43 Dorian #œ œ œ œ™ œ™ œ nœ œ œ œ ™ ™ bœ bœ ™ ™ œ œ œbœ #œ™ œ œ ¢& J œ œ œ J œ œ œ ˙ J J J ‹

32 K ° <#>œ™ œ #œ r rK œ #œ œ ™ œœ ™ ™ œ œ™ œ™ œ œ œ œ œœ & J œ œ J œ œ œ J J œ œ™ œ J ‹ K -29 -14 Aeolian r rK 0 #œœœ œ ™ ™ œ ™ nœ œ œ ™ œ œœ œ ¢& œ œ œ J œ œ J J œ œ J œ œ œ™ œ™ œ J œ™ ‹

Updates & discussion: doublepipes.info/descending-equiheptatonic-circuits | Score Version 2.2 (30 July 2018) 4 °39 j ™ ™ bœ œ™ œ™ œ bœ œ bœ œ™ œ™ œ ˙™ & œ œ œ J J œ bœ ‹ +14 Iastian +29 Phrygian +43 œ bœ œ œ œ™ œ bœ œœbœ œ ™ ™ œ bœ œ œ™ œ bœ œbœ ¢& J J J ÔR œ œ œ J œ J œ ‹

B Harmonia (refined, educated, noble) 45 K ° r #˙™ œ™ rK #˙™ œ™ œœBœnœ #œœœœBœnœ #œ œ œ™ ˙™ œ™ œœ Bœ & J J ‹ -43 Dorian rK rK -29 Mixolydian #œ™ œnœBœnœ #˙™ œ™ œœBœnœ ˙™ œ™ œnœ Bœ nœ œ œ œ™ ˙™ ¢& ÔR J œœœ ‹

52 ° œ#œ œ rK ˙™ œ™ j & nœ œBœ ˙™ œ™ œœBœnœ œœœœBœnœ œ œ œ™ ˙™ ‹ -14 Aeolian (Slack Lydian) 0 (Tense) Lydian rK rK rK ˙™ œ™ œœBœnœ ˙™ œ™ œœBœnœ ™ ™ œbœBbœ bœ œ œ ™ ¢& ˙ œ J œ ‹

59 ° rK œ œ œ rK ˙™ œ™ ™œbœBbœ bœ œBbœ ™ ™œbœBbœbœ œ bœBbœbœ ˙™ & œ J ˙ œ œ œ ‹ +14 Iastian +29 Phrygian rK rK K œbœBbœbœ œbœBbœbœ r ¢& œœœ˙™ ˙™ œ™ ˙™ œ™ ˙™ œ™bœbœ™ ‹ °66 ˙™ bœœ˙™ ˙™ œ œœbœ™ BbœbœBbœ œ œ œ œbœœ œ™ BbœbœBbœ œ œ & J ÔR J J J ‹ +43 ¢& BbœbœBbœ œ™ œ™ bœœbœ™ BbœbœBbœ œ™ ˙™ ˙™ bœœ˙™ ˙™ ‹

73 ° B B B B 2 & œ™ œ bœ bœ œ™ œ bœ bœ œ™ œ bœ bœ œ™ œ bœ bœ 4

‹ Locrian (New Hypodorian)

œ™ bœ œ bœ œ œ™ bœ œ bœ œ œ™ bœ œ bœ œ œ™ bœ œ bœ œ œ œ 2 ¢& œbœœ R œÔR œ ÔR œ œbœœ R œÔR œ ÔR œ œbœœ R œÔR œ ÔR œ œbœœ R œÔR œ ÔR œ 4 ‹ ÔR Ô ÔR Ô ÔR Ô ÔR Ô

C Diatonos (popular, common, successful) 77 rK rK rK rK rK ° 2 nœœ#œ œ œœœ œœœ ˙ œ rK rK œ #œ œ rK rK œ #œ œ œœ & 4#œ œœœœœ œ œ œœœœœ œ œ œ œ ‹ -43 Dorian K -29 Mixolydian -14 Aeolian rK K r rK 2 œ#œœ œnœœ œ r œnœœœœœœ œ ¢& 4 œ œœœ œ œœœ ˙ ˙ œ œœœ œ ‹

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 5 83 rK rK ° œ œœœ rK rK œ rK œ rK œœœ ˙ œ bœ œ œ œ bœ œ œ œ bœœœ œ œœœbœ œœ & œ R œÔR œ œ œ œ R œÔR œ œ œ œ ‹ Ô Ô 0 Lydian +14 Iastian rK rK œ œ œœœ œœœ bœœœbœœœœœ ˙ ˙ œ œœœbœœ ¢& ÔR R œ œœœ ‹ Ô 89 ° rK bœ bœ œ œ œ bœ bœ ˙ œ œ œ nœ œœ œœ œ œ R œ œœ œ ÔR œ R œ œ R œ œœ œ œœ œœ œ & nœ œ ÔR ÔR Ô ÔR Ô Ô ÔR ÔR ÔR ‹ +29 bœ œ bœ œœ œœ œ ¢& œ R œbœœ ÔR R ˙ ˙ ˙ ‹ Ô ÔR Ô 93 rK rK rK rK rK rK ° rK bœ œ œ rK bœ œ œ 5 & ˙ ˙ œ œœ œ œ œ œ œ œœ œ œ œ œ ˙ 8

‹ +43 Locrian œ 5 bœ œ bœ œ bœ œ bœ œ b˙ b˙ œ œbœ bœœ œ bœ œœ œœ ¢& œ bœœ R œ ÔR œ ÔR œ œ bœœ R œ ÔR œ ÔR œ ÔR R ÔR ÔR 8 ‹ ÔR Ô ÔR Ô Ô D Chrōma (sweet, licentious, emotional) 98 ° 5 œ™ œ bœ œ œ œ œbœ œ bœ œ œ™ œ bœ œ œ œ œ œ œbœ &8 J bœœœ J J bœœœ J ‹ f Phrygian mf mp p 5 œ œbœ œ bœ œ œ™ œ bœ œ œ œ œbœ œbœ œ œ œ œ™ œ ¢&8 bœœœ J J J bœœœ J ‹ 105 ° bœ œ œ œ ™ ™ #œ œ #œ nœ#œ nœ #œ#œ œ™ œ œ œ#œ œ & œ œ œ œ œ œ œ œ œ #œ J J J J #œ œ œ ‹ pp -43 Dorian -29 bœ œœœœœœœœ œ œbœ nœ bœ œ #œ™ œ œ™ œ œ™ œ œ#œnœ#œ ™ ™ ¢& J J œ œ œ œ ‹ 114 ° ™ ™ #œ œ #œ nœ#œ nœ #œ œ œ™ œ œ œ œ œ & œ œ œ œ œ J J J J œ œ œ œ™ œ ‹ œ #œ nœ -14 Aeolian 0 œ œ #œ #œ œ™ œ œ™ œ œ™ œ œ#œnœ œ œ™ œ œ™ œ œ œ œ ¢& œ œ J J œœœ J ‹ 123 ° rK ™ œ œ #œ nœ œ bœ nœ œ œ™ œ œ bœ œ bœ œ bœœ œ nœ & œ œ œ J J J J œ œ J ‹ +14 Iastian +29 Phrygian #œ nœ ¢& J œ œ™ œ œ™ œ œ™ œ bœ nœbœ œ œ™ œ œ™ œ œ™ œ ‹ 131 U ° rK œbœ œ œ œœ™ œ œ™ œ bœ œ œnœ œbœ œ œ œ œ™ œ bœœ™ œ & ÔR bœ ÔR J ÔR bœ œbœ œ ÔR ‹ +43 U œ j œ j ¢& œ™ œ œbœnœbœ œ bœ œ œ™ œ œ™ œ œ œ nœœœœnœ œ bœ œ ‹

Updates & discussion: doublepipes.info/descending-equiheptatonic-circuits | Score Version 2.2 (30 July 2018) L H This network of T-junctions is a Seven equidistant enharmonic tetrachords hypothetical model of how aulos players modulated in the nomos Barnaby Brown, Descending Equi-heptatonic Circuits. Diagram 1 trimelēs, the dithyramb and drama Version 1.2 (27 June 2018) | DOI: 10.6084/m9.figshare.7006208 in the period c. 550–400 BCE, i.e. EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources between Sakadas of Argos and Updates & discussion: doublepipes.info/descending-equiheptatonic-circuits Pronomus of Thebes. At each T-junction, fourth-century Greek musicians called the tetrachord to the right ‘conjunct’ (synēmmenon, a Α 1 E Fx 4 -43 Locrian fourth higher) and the tetrachord Ω (new Hypodorian) to the left ‘disjunct’ (diezeugmenon, Η a fifth higher); the tones of disjunc- 1 T E Α E4 -14 Mixolydian tion are represented by three dots. In the Roman period, the vowels Ω alpha (Α), eta (Η), omega (Ω) and Η epsilon (Ε) identified a note’s Ε Α +14 T 2 D4 Lydian position in the tetrachord, like Do Ω Ω (tense Lydian) Re Mi Fa in a movable-Do system. Η Η This was in a diatonic environment; their use in the enharmonic Α 2 3 Ε Α C4 +43 Phrygian environment of the Classical period Ω is hypothetical. Η The pitches given here are 3 4 Ε Α Ε B3 -29 Dorian approximately those of the Pydna aulos (the Poseidonia is about a Ω semitone higher, the Elgin about a Η Aeolian tone lower). The osets in cents 4 5 Ε Α 0 show the discrepancy between an A3 (slack Lydian / Ω equidistant 7-tone system and the old Hypodorian) Η equidistant 12-tone system of Aristoxenus and sta notation. Α 5 Ε G3 +29 Iastian Only the former is compatible with Ω Ω (Hypophrygian) the hole boring of Classical-era Η Η finds. For pure intervals, all fifths must be widened and all fourths Α Ε Α x -43 F 3 Locrian narrowed by roughly 16 cents. This only available when Ω hole L-5 is closed (new Hypodorian) requirement for pitch adjustment { Η on every note excludes lyres from this tonal system. Key to an evolving nomenclature: Early 5th-c. names transmitted by Heraclides et al. experimentally attached to a tonal system compatible with the Poseidonia and Pydna auloi (see Diagram 1) | Late 5th-c. names transmitted by Aristides Quintilianus The harmoniai of Plato’s of 6 scales corresponding to the harmoniai of Plato’s Republic (c. 380 BCE) | Early 4th-c. names used by aulos makers for a system of Republic: one of many 7 tonoi in which Dorian and Phrygian are spaced a tone apart, the other tonoi a ¾-tone apart | Late 4th-c. names used by Aristoxenus for a system of 13 tonoi all spaced a semitone apart. Selected reading: Stefan Hagel, Ancient Greek Music (2009), pp. 375–7 and 430–4; and possible auletic solutions Andrew Barker, Greek Musical Writings (GMW) i, pp. 163–9 , 281–4; ii, pp. 153–4, 419–22.

Scholars agree that the pitch Originally, the meaning of

drop of Dorian was the result of a L H L H the symbol C was functional. Hyperlydian paradigm shift in musical Phrygian Phrygian Attached to either mesē or behaviour between 450 and

hypatē, its pitch was (option A) (option B)

350 BCE. What exactly Dorian movable. Hagel calls this 2. changed is uncertain because Hypophrygian Lydian Hyperphrygian ‘functional notation’ (p. 383) the 12-tone system described and notes that ‘we nd by Aristoxenus proved so

Lydian Lydian Syntono-lydian Iastian Iastian Phrygian Mixolydian traces of this ‘transposing [old] Hypodorian Mixolydian Mixolydian [Low] Aeolian 1. Lydian 6. Lydian Iastian 4. Phrygian / Iastian Low 4. = subset of Phrygian Phrygian 3. / Hyperiastian High Mixolydian Locrian [new Hypodorian] Hypolydian Dorian Dorian Mixolydian 5. successful that few traces BCE, FIXED: In the 4th c. the pitch theorists xed in old of C to hypatē Lydian Dorian = new 444–5). pp. (Hagel, The notation of the Orestes of the Orestes notation The of the that matches fragment Aristides Phrygian harmonia . In the 5th c. In the 5th c. MOVABLE: these symbols BCE, musical function,indicated form original The not pitch. triplet is of the brown 367). uncertain p. (Hagel, Lydian’ approach well remain of its precursors. The into late antiquity, best evidence for them may especially in be the hole boring of instrumental 5th-century auloi. 1 Fx+50 N 툿 툸 툿 1 Fx-46 툹 툶 툼 툼 툾 scores’ (p. 445). 툈 툈 툽

buried 400 툸 Pydna aulos 툸 툼 -21 1 F -27 T 툷 툹 툹 툻 1 E T 툍 툈 툈 툺 툶 툸 툸 –350 BCE at Pydna, Greece C N -6 T Ey-14 2 툹 툹 T D 2 found 1996 툈 툈

툶 mesē 툸

+10 툶 C 툶 툸 +27 2 Cx 3 툲 툲 C 2 C 3 툎 툷

툎 툍 K C found 1969 K C 3 C-47 4 툶 mesē C 툶 3 B-33 4

툫 툫

C

C mesē 툫 C -11 C C +2 buried c. 480 BCE at Paestum, Italy 4 By 5 4 A 5 툰 툫 툓 툲 Here the harmoniai 툫 C

툯 C 툎 are paired in four

Poseidonia aulos ‘Unmodulating

+20 C mesē 툫 C C K C 5 Gx 툓 C Systems,’ each with -26 5 G -2 Gx 툮 툫 -36 its mēse on a 툫 G This diagram di erent ngering. C 툭 C modies Hagel’s White and gold circles +40 투 C 툫 -49 Diagram 11 (p. 42). Fx 툫 툓 툓 C Fx contain the notation transmit- 툫 Modications were 툫 툫 툰 ted by Aristides. Dotted lines show prompted by experiments 툯 the enharmonic, chromatic and diatonic playing reproductions by Robin notes omitted in the spondeion scale. Vertical 툫 ‘relaxed’ Lydian for drinking induces ecstasy moderate, mournful, Howell (Pydna) and Marco Sciascia (Poseidonia), mournful, 툓 spacing shows how to bend the instrument scale to invented by parties, and emotion; manly, 툓 suitable for based on measurements by Stelios Psaroudakēs and 툅 ‘tense’ Lydian; 툫 툫 produce the pure 5ths, 4ths and major 3rds of the Damon; for 툫 excessively excites to violence; steadfast, laments; used by 툮 using reeds by Howell. The views on the ethos of each drinking parties, unrestrained harmonia of compulsion magnicent, noble; blended with musical scales described by Plato’s friend Archytas Olympus for harmonia are those of Plato, Aristotle and pseudo- excessively and the dithyramb; harmonia of free choice, Dorian in tragedies; (GMW ii, pp. 47–52). Coloured bands show the his Lament for 툫 Plutarch (GMW i, pp. 130–1, 179–82 and 220–2). unrestrained used in face of danger education and libations antithesis of ‘relaxed’ approximate pitch range available on each ngering; the Python to the gods Lydian and Iastian the degree of overlap indicates how far the hole-bor- ing is from equi-heptatonic tuning. The bands are Barnaby Brown, Descending Equi-heptatonic Circuits. Diagram 2 centred on the median pitches estimated in diamonds (Hagel, in preparation). On any pipe, one of Version 1.1 (31 May 2018) | DOI: 10.6084/m9.figshare.7006208 | EMAP Resources for Euterpe 2 the two lowest pitch bands is unavailable; which, emaproject.eu/events/euterpe/resources | Updates & discussion: doublepipes.info/descending-equiheptatonic-circuits depends on whether hole 5 is open or closed. 8

Commentary

For general information about this series, see the discarded: their usage throughout this ‘Introduction to the EMAP Resources for volume is hypothetical, modeling that of Euterpe’ in Volume 1. auletes c. 510–400 BCE. The meaning of these technical terms mutated many times, the same words being reused in new musical HIS EXPERIMENTAL composition contexts. T tests a new hypothesis for the auletic Diagram 1 presents the hypothesis art of modulation. The original intention visually. It is a network of tetrachords was to compose with an understanding of arranged on a grid that divides the octave ancient Greek music theory, taking into 21 dieses – literally ‘leaks’, or small generations of scholarly endeavour into intervals roughly a quartertone in size. This account. This proved to some extent grid facilitates modulation of all kinds. It impossible, not because the literature is also means that there are, conceptually, 24 difficult (which it is) but because the notes on the type of aulos for which the archaeological finds of auloi disrupt archaeological record is strongest. The established ideas concerning musical significance of these points will be explored developments in the Classical period – below. Diagram 2 provides an overview of nominally 510–323 BCE. This is hardly how musicians’ usage of the ethnic terms surprising. Brilliant guesswork has been evolved in antiquity, sorting out the built on literary evidence that is sparse and misunderstandings any newcomer might often significantly later in date; the have in attempting to read the most scholarship is formidable. Trials making advanced work on the subject, Stefan and playing critical reproductions of Hagel’s Ancient Greek Music: A New Classical-era finds, on the other hand, are Technical History (2009). I am grateful to still in their infancy; Descending Equi- Hagel for providing substantial feedback on heptatonic Circuits is the first experiment to earlier drafts of this diagram and for be reported in any detail. comments that spurred on my own In this Commentary, I attempt a learning. For any misunderstandings or coherent synthesis of literary and material inaccuracies that remain, I accept full evidence, focusing on the tonal system of responsibility. aulos-based music in the sixth and fifth Both diagrams are designed to stand centuries BCE. It is aimed at an alone as reference sheets for practitioners, interdisciplinary audience that includes or as student handouts; they make specialist aulos learners, composers, music directors, knowledge that is scattered piecemeal across Classicists and musicologists. These groups thousands of pages more accessible to have different needs and very different levels anyone wanting to understand Classical of understanding in each other’s fields; I auloi. I would commend Diagram 2 to beg the reader’s patience with my attempts anyone who finds Hagel’s seminal book to accommodate such a diverse audience. difficult, but warn them that Diagram 1 Presenting a case for this hypothesis pushes further back in time than Hagel requires a broad survey of evidence that goes. It advances a model that is will, I hope, interest players and composers. fundamentally incompatible with the ideas It introduces the technical aspects of he inherited, not just from immediate Classical Greek music that are most predecessors, notably Andrew Barker and relevant to performers, ignoring all Martin West, but from antiquity. Most of developments after about 380 BCE. One our ancient authorities wrote on music of vital point to clarify at the outset is that the fifth century BCE without ever having modern preconceptions regarding the heard it. Conducting experimental trials on musical meaning of the terms ‘enharmonic’, instruments of the period promises to ‘Dorian’, ‘Phrygian’, etc. must be completely change what we believe.

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 9

Classical-era finger-hole boring (Pydna). Regarding equidistant spacing, Martin West makes an important point: In 2016, thanks to the support of the Actors Touring Company and the European Music Ethnomusicologists have found that in most Archaeology Project, I commissioned pipes in most countries the spacing of finger- critical reproductions of two auloi buried at holes is not calculated so as to produce a either end of the fifth century: one in rational series of intervals but is governed by the principle of equidistance. ... Some southern Italy in the Greek colony of correction of notes may be made by adjusting Poseidonia (later called Paestum), the other the sizes or contours of holes, but for the rest it in northern Greece in the Macedonian port is taken for granted that the player will make of Pydna. Their scales agree with reassuring the necessary corrections by such techniques as exactitude but not with modern or indeed have been mentioned above. (1992, p. 96) scholarly expectations. At first, it appeared These techniques are the ones described by impossible to reconcile their finger-hole Aristoxenus: boring with any of the interval structures described in detail by the late fourth- It is not because the aulos has bore-holes and century musicologist, Aristoxenus. To make cavities and so forth that it plays fourths or sense of the hole boring, we must discard fifths or octaves in true accord or gives each of conceptions that have shaped Western the other intervals its due size, but because of skilful operation, partly by the hands, partly music for over two millennia. by the other parts with which the player has Aristoxenus and the school of harmonic the power to raise or lower pitch. For theory that he followed divided the octave although all the holes etc. are provided, none into twelve equidistant steps. This is the the less auletes mostly miss the proper octave division that enjoys global intonation, for all their taking the pipes away dominance today: every scale is fitted to a (from each other?) and setting them parallel, 12-tone grid. The fit of some scales can be blowing harder or less hard, and modifying quite loose, acoustically, but the grid works other factors. ... Just as there is no in practice because the fit is conceptual, not attunement in strings unless one applies skill physical. The human brain is adept at and tunes them, so there is none in bore-holes unless skilful operation brings them into tune. fitting stimuli to the closest familiar pattern and tolerating considerable discrepancies. El. Harm. 2.42; West 1992, p. 96 The 12-tone grid was developed by In other words, the ‘true accord’ of fourths, Aristoxenus’ predecessors – fourth-century fifths and octaves depends on the player’s harmonikoi. Hagel calls it the ‘old skill more than the instrument’s hole commensurable’ system (2009, p. 390). boring. What is puzzling is that this system is Be that as it may, the hole boring of finds incompatible with the finger-hole boring of has much to tell us. It provides a scaffolding auloi made in the Classical period. The only that supports and constrains the player’s grid that fits their hole boring satisfactorily movements in the realm of pitch. Most of is represented in Diagram 1. This divides the numerous auletic finds dated to the the octave into seven equidistant steps and Classical period are fragmentary or, in the it emerged as a better option through case of the Elgin aulos, seriously distorted; practical experiment: a slow process of trial reconstructing them involves high degrees and error composing music on of interpretation and creativity. The reproductions of the Pydna and Poseidonia Poseidonia and Pydna auloi are in auloi. exceptionally good condition – the only Kathleen Schlesinger devoted a massive serious guesswork concerns the reeds. To book to equidistant hole boring in 1939. evaluate the way in which their hole boring The archaeological evidence available to her supports and constrains the player, I then and her handling of ethnographic and followed Hagel’s advice: literary evidence did not yield compelling results. The case presented here is built on A replica, as I have argued previously (and finds from 1969 (Poseidonia) and 1996 others have before me), is, however, not the best way to determine the intended pitches of

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an aulos. Apart from the practical sequence of experiments altering one inconveniences involved in experimenting parameter at a time: the find, the with different sizes of reeds, the unconscious reproduction of the find, the reeds and the efforts of any player to produce a familiar player. Descending Equi-heptatonic Circuits scale present a real obstacle. If possible, an allows such an experiment to begin. It evaluation should therefore start by contains cells in each of the three genera of determining an ‘ideal’ scale by means of calculations based on the instrument’s layout; ancient Greek music – enharmonic, diatonic as a second step, a replica is of course most and chromatic – and transposes these cells welcome to confirm the conclusions. to three descending scale degrees. I have no doubt that much will be learned by Hagel 2010, p. 71 changing the most complex parameter of My trials playing reproductions confirm that all: the player. Auletes who have developed it is disconcertingly easy to lip pitches to a some competence producing pure intervals scale that accords with the cultural between the pipes will notice the slightest conditioning of the player, particularly on deviation from equi-heptatonic tuning. Classical-era auloi. Even with ‘stiff’ reeds, Starting the same polyphonic cell on the pitch-platforms provided by these another finger-hole feels slightly different: if instruments are unsteady. They have an the octave divisions are not exactly alarming wobble, confirming Aristoxenus’ equidistant, the pattern of embouchure statement that good intonation depends on adjustments required to achieve pure the player’s skill. I am therefore grateful to intonation differs. In the cases of the Pydna, Hagel for sharing his predictions, generated Poseidonia and Elgin auloi (with hole 6 using his dedicated aulos software, which is open on both pipes), we are close enough to a tool of the utmost brilliance. Adjusting equidistant tuning for cyclic modulation to virtual reed sizes to obtain a maximum be entirely practical. If hole 6 is closed, this number of fourths and fifths (to within 20 introduces a gap of a third and the cents of pure), the predicted intonation for polyphonic cells can no longer be so freely the Pydna and Poseidonia auloi is transposed. remarkably close. Ignoring an overall Between the Pydna and Poseidonia, difference of a semitone, seven of the eight musical repertoire and reeds are almost low-register pitches coincide with a completely transferable. There are only standard deviation of 2–7 cents. three significant acoustic differences: the Trials playing reproductions by Robin Poseidonia sounds a semitone higher; the Howell (Pydna), Marco Sciascia Pydna is a little louder and more pitch- (Poseidonia) and Chrestos Terzēs (Pydna flexible (because it has a wider bore); and and Poseidonia), all based on the notes labeled G in Diagram 2 are about measurements by Stelios Psaroudakēs 27 cents flatter on the Pydna. As can be (2008, 2014), confirm Hagel’s predictions. seen from the coloured horizontal bands in What playing reproductions reveals is that Diagram 2, these instruments are not tuned Classical aulos pitches should be to have tones and semitones; the intervals understood as broad ranges, not as narrow between finger-holes are all much the same points. Values to the nearest cent are size, particularly on the far left of the misleading: the broad coloured bands in diagram, which corresponds to the Diagram 2 are a better representation of Poseidonia low pipe. pitches that are notoriously bendy. I This equidistant spacing does not match therefore treat Hagel’s optimal estimates as the tonoi system developed ‘with an eye to midpoints. They are shown at each end of the boring of the finger-holes of auloi’ the horizontal bands in coloured diamonds. reported by Aristoxenus (translated on page The best way to test predictions of the 26 below). The scholarly consensus midpoints, I suggest, is to memorise a interpreting this system is as follows: composition that transposes polyphonic Although some of the scales stand in cells (both pipes sounding together) to harmonic relations of fifths and fourths as different scale degrees; then to run a

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required for modulation, such a pattern is not While it is true that Thai instruments of fixed implemented throughout. Consequently, pitch are tuned to be functionally equidistant, modulation for instance between Phrygian allowing compositions to be played starting on and Lydian, or between Dorian and [old] any of the seven pitches, equidistant tuning is Hypodorian, is impossible. not encountered with the voice, winds or string instruments, except when they must Hagel 2009, p. 382 conform to the keyed percussion. The instrument-led process of composing Church 2015, pp. 188–90 Descending Equi-heptatonic Circuits suggests otherwise. It was developed on the Pydna This observation is crucial – it led me to the and Poseidonia auloi, committing to paper understanding presented here. only a small proportion of what was tried Bending an equi-heptatonic scale to and tested. Playing reproductions produce pure intonation between the two establishes that bending pitches a pipes of the aulos involves making quartertone in either direction is easy. What adjustments of around 16 cents – no larger has not been appreciated by writers since than the adjustments woodwind players Aristoxenus is that this inherent instability, make in a Mozart symphony, or viol players or available breadth in a note, makes cyclic in a Byrd fantasia. In the paneuropean modulation perfectly possible. Hagel’s musical tradition that is now global, singers, statement above is true for lyres and harps winds and string instruments do not aim to throughout history and for the mechanised produce equidistant 12-tone tuning except, auloi of the Roman Imperial period, but not as in Thailand, when playing with for the aulos tradition that the keyboards and other fixed-pitch archaeological record suggests was instruments. In smaller ensembles (anything prominent and panhellenic in the Classical one-to-a-part), skilled performers will lower period. major thirds by about 14 cents, so that sustained chords sound more in tune and harmonic resolutions are sweeter. Plato’s Equi-heptatonic systems friend Archytas gives us good evidence that For assistance interpreting the hole boring ancient Greek musicians did likewise, of these two finds, let us fast forward 2500 aiming for pure fifths, fourths and major years to living musical traditions. The global thirds, at least in the Dorian harmonia success of the 12-tone grid has pushed the (GMW ii, p. 50). On a roughly equi- equidistant 7-tone scale to the margins of heptatonic aulos, producing pure intervals musical awareness. It is so undervalued means widening the fifths (narrowing the today that to suggest it prevailed in the fourths) by about 16 cents, and widening leading forms of Classical Greek music – the major thirds (narrowing the minor the dithyramb and tragedy – seems sixths) by about 14 cents. Even with ludicrous. The xylophones and gong circles inflexible reeds, this is easily done, as I of West Africa and Southeast Asia, like demonstrate in this video: Classical auloi, traditionally divide the https://youtu.be/PtqUvZsW0XY?t=13m31s. octave into seven roughly-equal steps. The testimony of Classical-era writers Describing the West African balo, Roderic confirms that flexibility of intonation was a Knight notes that ‘a builder tunes the keys defining characteristic of the aulos. with the intention of making each ascending Discussing attunement, Aristoxenus notes step the same size. For a player, this that auloi ‘are especially susceptible to translates into the ability to start a tune on variation, introduced through the craft of any note and it will sound the same’ aulos-making, through manual techniques, (Church 2015, p. 36). Terry Miller notes an and through their own peculiar nature’ (El. equivalent functionality in the tuning of Harm. 2.43; GMW ii, p. 158). The allusions xylophones and gong circles in Thailand, to it being ‘many-noted’ in earlier literature Laos, Vietnam and Cambodia, but he adds are numerous (GMW i, p. 57, n. 10). My an important detail: own experience playing reproductions leads

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me to suggest that the fundamental link in makers of the Poseidonia and Pydna auloi the Classical imagination between the aulos had been aiming for equidistant tuning, and a multiplicity of notes would have then all the coloured bands would overlap arisen from composers’ exploitation of its equally. They do not. To understand why proclivity for pitch-bending. The chromatic not, and to explain the extraordinarily close and mimetic opportunities are rich because, match in tuning between two instruments as Aristoxenus says, the instrument was separated chronologically by about a made that way. century and in ancient journey time by at When modulating by fifths and fourths least a fortnight, it may help us to consider on these auloi, the average discrepancy of unequal temperaments in the less remote 16 cents per step is not the impediment to 12-tone tradition. modulation that I expected it to be. This When keyboards are tuned to European was a real surprise. Music directors who try Renaissance or Baroque temperaments, the to prevent choirs from drifting sharp or flat twelve semitones are functionally equal but view any gradual tightening or slackening of may be audibly unequal. When some keys pitch negatively for cultural reasons. In are used more frequently than others, Classical Greece, however, choirs were unequal steps may be desirable. For accompanied by auloi, not by organs or example, in the Renaissance temperament lyres. An abhorrence of pitch drift may be ‘¼-comma Meantone,’ F major is one of the reasons that modulation was gorgeously in tune at the expense of F sharp taboo, shamelessly and famously broken by major, which sounds hideous and was never the fifth century’s avant-garde composers. used by Renaissance composers. The But if one employs the characteristic Baroque temperament ‘Werkmeister III’ techniques of Eastern double-reed distributes acceptable intonation more traditions – such as portamento, timbral evenly, permitting the use of all twelve keys, contrasts (fingering the same pitch two each in two modes (major and minor); different ways) and vibrato (using a hand however, it still favours the most popular movement rather than the diaphagm, which keys of C, G and D major. What draws means each pipe can be assigned vibrato aficionados to unequal temperaments is that independently) – the 16-cent discrepancies they give each key a different colour or ethos are really not so disturbing. Although they (‘character’). are easily veiled by larger manipulations of We know that dramatic realism was pitch, I suspect the cumulative rise or fall in pursued by Classical Greek composers in pitch was exploited, not masked, by ways that gave modulation a notorious composers pursuing the expressive realism prominence, like any new fashion attracting that came into vogue in the late sixth ridicule and contempt, adulation and century. This is when the Poseidonia aulos commercial success (GMW i, pp. 93–8; was made, not in a cultural backwater but Kowalzic & Wilson 2013, part III). I in one of the most prosperous colonies of propose that 7-tone unequal temperaments Magna Graecia. flourished in the fifth century BCE for precisely the same reasons that 12-tone Unequal temperaments unequal temperaments flourished in the eighteenth century CE. They enable Equidistant tuning does not entirely explain extensive modulation, favour the most the hole boring of finds. In Diagram 2, popular keys, and contribute to the horizontal coloured bands of identical width formation of a distinctive ethos for each key approximate the pitch range available on without the player needing to change each fingering – without leaking air from the instrument or retune. A 12-tone grid is finger-hole below, purely through excluded by the archaeological finds embouchure adjustment. Using ‘stiff’ reeds, because, as a revival player trained in a 12- the range is about a tone; with ‘flexible’ tone world, you find yourself wishing the reeds that require less pressure but more holes were bored in different places. The skill, the range is easily a minor third. If the problem disappears when you switch to a 7-

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 13 tone grid. Its platforms are conceptual, rising are minimal and powers of timbral and and falling in pitch with an elasticity for dynamic expression are optimal. I am which the aulos was designed, enabling it to grateful to Robin Howell for this sage lead musical fashion in the direction of a advice. To counteract the tendency of more colourful dramatic expressiveness, beginners to play too near the ‘onion’ of the indulging in all kinds of modulation. The reed, I advise relaxing the embouchure and reason the kithara was initially excluded pulling out the reed that needs to be from this crowd-pleasing style, I suggest, is flattened, rather than tightening and because its pitches are inelastic. To pushing in the reed that needs to be compete, it had to add more strings. The sharpened, as far as possible, in the pursuit date when strings were added is significant: of pure intonation. the number increased from seven to eleven When I started learning to play Classical- between the late-sixth and mid-fifth era auloi in August 2016, I struggled to centuries (West 1992, p. 62). make sense of them because I was trained in an equidistant 12-tone system. For over a An inconvenient outcome year, I was bewildered and confused. All results were unsatisfactory. Only when I An octave has 1200 cents. In a 7-tone started exploring the 7-tone system did the system, the keys are roughly 171 cents apart instruments make sense. This result was (1200 ÷ 7). On a piano, they are multiples neither expected nor desirable. I had of 100 cents apart. This is a problem for commissioned the reproductions imagining aulos learners and composers today: that Callum Armstrong and I would be able equidistant 7-tone tuning is fundamentally to use them in a new production of The incompatible with all mainstream Suppliant Women by Aeschyllus. The Actors instruments except the voice and unpitched Touring Company kindly gave us financial percussion. Adding it to the options in support to expand our instrumentarium and digital tuning aps would make life slightly our Pydna auloi arrived six weeks before easier. In order to give 7-tone music a opening night at the Edinburgh Royal chance of being understood and appreciated Lyceum Theatre. It was acutely in a musical culture ruled by keyboards and embarrassing that we could not make sense staff notation, this score gives pitch offsets of the instrument in time to use it in the as they would appear on digital meters: production. We had to abandon the idea of multiples of 14.3 cents rounded to the playing fifth-century instruments in a fifth- nearest whole number (14, 29 or 43). 14.3 century play, and instead use a much later cents is the pitch creep that must be made instrument, the Louvre aulos. The Louvre at every step moving round the circle of is perfect for accompanying solo singers but fifths in order to end back at the same pitch really too quiet for theatre work. you started at. These pitch offsets should be With hindsight, there were two problems disregarded by players – they require no that prevented us from using Classical auloi action, they are simply a reminder that this in The Suppliant Women. First, we were is not 12-tone music. They estimate of what playing in ensemble with pitched percussion the aulos will do naturally of its own accord. instruments tuned to 12-tone Equal For players of Descending Equi-heptatonic Temperament, accompanying singers who Circuits, there are two things that I consider rehearsed with keyboards. Secondly, as are of prime importance. Firstly, pure Highland pipers, our brains were intonation between the pipes. When the conditioned to the idea that pipes are tuned harmonics lock, the aulos casts a magical to a musical scale, rather than to an elastic spell that is intoxicating; in combination grid that must be moulded by the player to with circular breathing, the effect is conform to any culturally-approved scale. consistent with the role that the aulos The need to impose a musical scale on the played in ancient rituals, ecstatic and instrument by making embouchure demure. Secondly, playing near the tips of adjustments every fraction of a second was the reeds is where intonation adjustments

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terrifying. Like learning the violin, this takes Each tuning basis is defined by the interval six years to master, not six weeks. structure of the tetrachord (literally ‘four strings’) – specifically, by the tuning of the Three types of modulation two internal notes. The outer notes of the tetrachord are fixed, tuned to a pure fourth. It is helpful to clarify what modulation may In Descending Equi-heptatonic Circuits, have encompassed in Classical Greek section B is enharmonic, section C is music. The sources indicate the co- diatonic, and section D is chromatic. This existence of three types. Modulation by kind of modulation is like switching from genus involves changing the interval major to minor in the now-global tradition, structure of the basic building block, the except that the chromatic genus before tetrachord. Modulation by tonos involves Aristoxenus was probably more a style than transposing any interval structure to a new a particular interval structure – one that pitch. Modulation by harmonia involves relished the inflection of pitches away from switching between the six modes that we their expected position (GMW i, p. 225, n. understand poorly from the Aristides scales 132). The earliest evidence of this threefold (see Volume 3 in this series, Vocables for classification of melody is an anonymous Learning the Aristides Scales). These three papyrus, written at around the same time as types of modulation would originally have Plato’s Republic (c. 380 BCE): been stratified – chronologically, regionally, They say that some melodies make people or socially – but they evidently commingled self-controlled, some prudent, some just, some in the course of the sixth and fifth centuries brave and some cowardly, failing to with results that progressed from being understand that the chromatic (chrōma) innovative to fashionable to cosmopolitan. cannot make cowards of those who employ it, Descending Equi-heptatonic Circuits explores and the enharmonic (harmonia) cannot the first two types of modulation only; the make them brave. For who does not know third type is explored in Volume 3. Several that the Aetolians and the Dolopes and all witnesses indicate that modulation by genus the [. . .], who use diatonic music (diatonos and harmonia was originally between pieces, mousikē), are much braver than tragedy- not within them. In the fifth century BCE, singers, who always follow the practice of singing in the enharmonic? Hence it is chromaticism and modulation mid-strophe obvious that the chromatic does not make became a defining trait of the self-styled people cowardly, and neither does the ‘New Music’ that emerged in Athens. This enharmonic make them brave. attracted fierce criticism as it rejected the ‘noble style’ established by competitive P. Hib. i.13–22; Barker 2007, pp. 69–70 events at the Olympic and Pythian Games. Like tragedy singers, harmonic theorists There are, however, reasons to suspect that before Aristoxenus devoted themselves it was not as new as its protagonists entirely to the enharmonic genus, which boasted. A gradual evolution, building on was regarded by cognoscenti as ‘the noble an equally-innovative sixth century, may be style of music that is specifically Greek’ (ps- nearer the truth. Plut. 1135b; GMW i, p. 218). All six of the The first type of modulation, by genus, is Aristides scales are enharmonic because introduced by Aristoxenus as follows: they contain clusters of quartertones. This Any given melody which is attuned on a style was cultivated between the seventh single basis is either diatonic or chromatic or and fifth centuries, but by the mid-fourth enharmonic. Of these the diatonic, since century had gone out of fashion. According human nature comes upon it first, must be to Aristoxenus, it was displaced by the reckoned the first and oldest, the chromatic chromatic genus on account of composers’ second, and the enharmonic third and most ‘endless pursuit of sweetness’ (GMW ii, p. sophisticated, since perception becomes 141). accustomed to it at last, with difficulty, and The first two sections of Descending Equi- through much hard work. heptatonic Circuits use the spondeion El. Harm. 19.20–29; GMW i, p. 139 (‘libation’) scale. This is similar to the

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 15 enharmonic genus but omits the aulos, this makes perfect sense. The quartertones. In modern terms, it is enharmonic genus requires the greatest pentatonic (using five notes per octave), but precision, the diatonic the least. Aristides in ancient Greek thinking it is trichordal, continues, shedding light on the second using three notes per tetrachord. It was type of modulation (by tonos): associated with an orderly and dignified one kind of melody is called ‘direct’, one ‘few-note’ style that was upheld in ‘returning’ and one ‘circular’. The direct opposition to the crowd-pleasing theatrical moves from low to high, and the returning in ‘many-note’ style (GMW i, pp. 218–9, n. the opposite direction; while the circular is 96, and p. 223). Using modern note names that which modulates, as for example when to indicate its interval structure, the one moves up a tetrachord in conjunction and spondeion scale is: then descends it in disjunction. E F A B C E Arist. Quint. I.9; GMW ii, p. 418 This has two semitones, E-F and B-C. This description of a ‘circular’ melody is According to some musical experts who respected in each section of Descending informed Aristoxenus, the Phrygian ‘father’ Equi-heptatonic Circuits. The modulations of the Greek aulos tradition, Olympus, are descending because a rise of a fourth invented the enharmonic style by splitting followed by a fall of a fifth results in a fall of one of these semitones in two (GMW i, pp. a tone. This modulation route is 92, 212, 215–7). Taking the Aristides scales represented visually in Diagram 1, reading into account, evidence weighs in favour of it from left to right: the tetrachords rise in being the lower semitone, E-F, that he split, conjunction and descend in disjunction. sometime in the seventh century. This is the The compass restriction of Classical auloi, semitone split more frequently in the however, means it is impossible to transpose melodies attributed to Olympus three a melody up or down a fourth without centuries later (GMW i, pp. 223–4). clipping. Melodic units can only rise or fall The spondeion scale continued to be used by tones and, even then, their compass is well into the Roman era for libations and limited to a fifth (permitting three keys) or a paeans to the gods. It corresponds to scale sixth (permitting two). The ancient structures still used today in China and conception of a systēma amatebolon Japan. The only ancient Greek scale (‘Unmodulating System’) reflects this structure to have enjoyed continuous limitation: a piece has not fully modulated transmission in the West is the diatonic until it has travelled two tetrachords in genus. In the following passage, thought to either direction, shifting hypatē (literally the have been written in the third century CE, ‘head’ or ‘principal’ note of the key) up or Aristides sums up views that almost down one finger-hole. This kind of certainly derive from Aristoxenus: modulation is limited to the low register because overblowing produces the interval There are three genera of melody, the of a twelfth, not an octave, leaving a gap in enharmonic, the chromatic and the diatonic, the scale. This gap was bridged in later which acquire their distinctions from the narrowness or largeness of their intervals... types of aulos, such as the Berlin and Of these the diatonic is more natural, since it Louvre, presumably because composers can be performed by everyone, even the wanted to transpose melodic cells of greater wholly untutored: the chromatic is more compass. technically sophisticated, being performed As the direction of modulation that only by those who have been trained: and the Aristides describes in the passage above is enharmonic demands stricter precision, being ubiquitous in European Baroque music, accepted only by the most outstanding musicians reared in the Western tradition musicians, while for most people it is should note that the conventional route in impossible. the sixth century BCE was in the opposite If we interpret ‘difficulty’ here as the direction. A tradition related by Plato’s accurate control of pitch on a Classical elder brother, Glaucon, concerning the

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invention of the nomos trimelēs suggests that spent playing Baroque music? Had I been a the orthodox progression was Dorian– Turkish or Iranian piper, I suspect I would Phrygian–Lydian, with the keynote hypatē have composed ‘Ascending’ circuits. A climbing finger-hole by finger-hole. This descending direction may, of course, have route – up by a fifth, down by fourth – is been orthodox in another genre of aulos- mentioned by Aristides when he returns to based music, in which case the lament modulation three chapters later: would be a strong candidate. the production of a melody in a particular way ... has three forms of agōgē [‘rearing,’ a Five types of aulos disciplined and prestigious training], direct, returning and circular. Direct agōgē is that One of the insights gleaned from playing which makes an ascent through successive several types of aulos in the same concert, notes, returning agōgē is that which brings each with different finger-hole spacing, is about depth of pitch through notes that follow that the hours of training and reed each other, while circular agōgē is that which maintenance required rise in direct proceeds upwards in conjunction and proportion to the number of instruments downwards in disjunction, or conversely, and being played. A single aulos seems more is also treated as a type of modulation. plausible for amateur and educational Arist. Quint. I.12; GMW ii, p. 431 contexts, even for the average professional, multiple instruments being realistic only for The converse direction is represented in the most dedicated individual who trains Diagram 1 by reading from right to left. several hours a day. Without this level of The practice of ascending by adjacent finger ongoing training, the fingers will revert holes, incrementally raising the intensity under stress to whichever hole spacing is over several minutes, is highly esteemed in most deeply embedded: the autopilot of a the pibroch and launeddas traditions. The woodwind player’s neuromuscular most impressive example I have heard, conditioning. Moving a finger hole by so however, was a neyjofti solo performed by much as 1mm can be catastrophic, such is the Iranian piper, Saeid Shanbehzadeh, at the precision gained – and neuroplasticity the William Kennedy Piping Festival in lost – through years of practising. It is much 2005. Due to the restricted compass of the easier to switch to an instrument that neyjofti, the number of notes available produces a higher or lower pitch than to one gradually reduced from six to five to four as that produces a different scale. the focal tone rose. The result was thrilling. This perspective alters how we interpret Shuttling back and forth between two focal the vital scraps of literary evidence tones is the more conventional harmonic concerning aulos classification. There are behaviour, pervasive in most musical basically five sources giving substantial traditions; rising twice in a row provokes an details, two from the fourth century BCE exhilarating emotion because it is unusual. and three from around five hundred years If I were designing an experiment later. The first is by Aristotle, who informs reconstructing the nomos trimelēs, I would us that ‘girl’ auloi were higher-pitched than complement Shanbehzadeh’s single-reed ‘boy’ auloi (GMW i, p. 267, n. 30). The tradition from the Persian Gulf with double- second is a lost work by Aristoxenus, On the reed traditions from elsewhere in Asia to hole boring of auloi, which Athenaeus quotes avoid the very real problem of cultural bias. as follows: It is no good replacing one limited perspective with another: in the discipline of there are five sorts of aulos: girl [parthenios], Very Early music, intercultural boy [paidikos], kitharist [kitharistērios], collaboration is as important as grown-up [teleios], hyper-grown-up interdisciplinary teamwork for the [hyperteleios]. credibility of results. To what extent does Ath. 634e; Hagel 2010, p. 74, n. 22 Descending Equi-heptatonic Circuits reflect my This quotation survives in a colossal musical formation, much of which was compendium of ‘table-talk’ compiled in

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Egypt, probably in the early third century There is a statue of Pronomus, a very great CE. The same list appears hundreds of favourite with the people for his playing on pages earlier, probably derived from the the aulos. For a time auletes had three forms same source: of the aulos. On one they played Dorian music; for Phrygian melodies auloi of a [The Alexandrians] are highly musical in different pattern were made; what is called respect of auloi too, not only those called the Lydian mode was played on auloi of a ‘maiden-pipes’ and ‘child-pipes’, but also the third kind. It was Pronomus who first devised man-pipes, which are called ‘complete’ and an aulos equally suited for every kind of ‘extra-complete’, as well as the kitharistērioi melody, and was the first to play on the same and the dactylic. instrument music so vastly different in form. Ath. 176f; GMW i, p. 266–7 Paus. IX.12.5; W.H.S. Jones (1918) The addition of dactylic is puzzling – it is The ethnic terms are clearly being used for unclear how a ‘finger’ aulos would differ musical styles here – modes not keys – from the other types listed. Perhaps it does rather than the Aristoxenian usage, which is not belong in this classification system. for transpositions of the Dorian interval Comparing Hagel’s and Barker’s structure. The same modal classification is translations is instructive. Both could be found in our fifth and final source, which misleading, however, were it not for our like the first survives in Athenaeus’ third source, written in the second century compendium. This time, the author is CE by Julius Pollux. His ten-book unidentified: Onomasticon quotes numerous lost works In the old days, a noble beauty was carefully concerning Classical Attic culture. Barker preserved in music, and every aspect kept to summarises the relevant information as the orderliness proper to it, in conformity with follows: the principles of the art. That is why there Pollux (IV.81) tells us that [kitharistērioi were special auloi, one for each harmonia, auloi] were called by this name because they and in the competitions each aulete had auloi accompanied the kithara; and he adds to suit each of the harmoniai. It was (IV.83) that there were nomoi Pronomos of Thebes who first played all the kitharistērioi, pieces for kithara without the harmoniai on the same auloi. voice, called iamboi and pariambides, Ath. 631e; GMW i, p. 291 which were accompanied by auloi. ... Pollux also says (IV.81) that parthenioi auloi There must be some kernel of truth in this, accompanied the choral songs of maidens, but I am more inclined to take the earlier paidikoi those of boys, hyperteleioi those of sources at face value. The only fourth- men, while teleioi, also called Pythikoi, were century evidence that has come to my used for the ‘chorusless’ pythikon aulēma, attention for classifying auloi by mode, i.e. the auletic solos typified by the Pythikos rather than by performing context, is a nomos, and also to accompany paeans. passage by Aristoxenus that mentions the GMW i, p. 267, n. 30 ‘Hypophrygian aulos’ (quoted on page 26 below). The context in which this occurs This may be our most valuable source as it implies that each of the six harmoniai had its clarifies the earlier two. The fourth source, own special aulos. There was a Phrygian written at about the same time, introduces aulos, without doubt, visually identifiable by confusion by classifying auloi in what the curved horn attached to its lower pipe. appears to be a radically different way. Was a Hypophrygian aulos effectively a bass Aristotle, Aristoxenus and Pollux agree in version, adding lower notes out of reach of classifying them by performing context: the the fingers? The evidence surveyed by genres prescribed for competitive or Martin West for what was almost religious occasions. Pausanias classifies universally regarded as the ancestor of all them using the ethnic terms that distinguish Greek auloi includes an eighth-century either interval structures (harmoniai) or keys bronze figurine and this letter: (tonoi). In a ten-book description of Greece, essentially a travel guide, he writes:

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In about 245 BC a Greek official in an it; to be in charge of the instrument rather Egyptian town was making arrangements for than it imposing its wild ways on you. a party, and wrote to a colleague, ‘Make When we take into consideration the fact every effort to send me the aulete Petous with that the colourful, dramatic style associated both his Phrygian and his other pipes.’ with the aulos became fashionable in the West 1992, p. 91 late sixth century, this dual assumption The question is, which of all these types concerning the history of modulation are our finds from Poseidonia and Pydna? collapses. This composition supports the Regional types and musical dialects would hypothesis that theatrical harmonic twists have persisted long after the development of flourished in the dithyrambs and tragedies a panhellenic aulos. The idea prompted by of Attic Dionysia. Lyre players, however, my practical experiments of a compositional would be excluded from the colourful tonal nature is that what defined the world of aulos-based music because they cosmopolitan instrument was a hole-boring cannot bend pitches. The immense that abandoned ethnic identity in favour of popularity of the emerging dramatic style modulating capacity. The introduction of triggered an ‘aulisation’ of the kithara in the solo aulos contests at the Pythian games in late sixth century. This involved increasing 586 BCE potentially marks the emergence the number of strings from seven to around of a panhellenic style, or at least the eleven (Kowalzic & Wilson 2013, p. 243). I beginning of this process. The date suggest that what Timotheus succeeded in proposed in previous studies for the doing in his ‘New Music’ was not inventing assimilation of ethnic scale structures is the extensive modulation, but imitating what late fifth century. Pronomus and Eratocles the aulos had already been doing for a are given credit for different stages in a couple of generations, applying new process of systematisation and the harmonic excitement to tired, ancient conjecture that a relatively disorganised set kitharodic genres that were loosing of modes were tidied up to fit on a 12-tone audience. If this interpretation is correct, grid in a cyclic fashion is widely accepted as then the Poseidonia and Pydna auloi would fact. An assumption related to this is that be examples of the teleios or Pythikos aulos composers who boasted about their ‘New used for solo pieces, for accompanying Music’ were the first to modulate paeans, for men’s dithyrambic contests and extensively. What troubles me about these for tragedy before Pronomos. two assumptions is that auloi appear to have What, then, is the instrument developed been intentionally designed to have a note- by Pronomus in the late fifth century? If it is breadth of around 200 cents since the late one of the five types listed by Aristoxenus, it sixth century. With training, this makes any could only be the hyperteleios aulos and the scale possible. All the notes overlap. un-extended teleios aulos would be its Diagram 2 suggests where the precise predecessor. I conjecture that what interval structures of the Aristides scales Pronomus did was to extend its low register could be played, but in practice they easily downwards, adding keys that enabled a slip a little higher or lower in pitch, which more expansive melody to be transposed means that a player may hop from any scale without clipping the top or bottom notes. In to any other and back again with complete this case, the aulos that accompanied freedom. This requires training but gives choruses of men in the dithyramb and auletes rich opportunities for chromaticism drama before Pronomus would be the same and modulation. In fact, the pitches are so as the solo instrument: the teleios aulos. wobbly that modulation happens Although this interpretation involves unintentionally when you are learning. I considerable speculation, it has the merit of spent eighteen months not knowing what being supported both by the archaeological mode the instrument was in. Skill is record and by a comprehensive assembly of required to prevent modulation and control literary evidence. We do not have to invent missing instruments, persuading ourselves that the auletic finds are unrepresentative;

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 19 reject some historical tales as fictional while record. The competitive advantage of a accepting others; or confer higher levels of single-mode aulos comes at a price: more achievement to the later period, which is instruments to purchase, maintain and easy to do because the quality of practice. It would open up new musical information is more impressive. possibilities from which a distinct style Nevertheless, just as previous scholars have would evolve, one that was no longer been influenced by Aristoxenus and ‘old’ encumbered by constant embouchure history skewed by his superlative writings, adjustments. so this ‘new’ history may be skewed by my Knowing what French horn players and attraction to the Pydna and Poseidonia violinists can achieve, even by the age of 13, auloi. it would be foolish to imagine that having to To explain the modal classification of make pitch adjustments on a note-by-note our fourth and fifth sources, we have two basis lowers the potential for artistic options. We could view Pausanias’ report as achievement or virtuosity; it changes what is relating to a seventh-century reality, in possible stylistically. I suspect that the which case the word harmonia in the microtones of the enharmonic style were an anonymous fifth source would be a simple artistic solution that made a virtue out of mistake. Replacing it with the word ‘event’ intonation discrepancies. On the solves the problem because each of the auloi Poseidonia, Pydna and Elgin auloi, you in Aristoxenus’ list was used in a different always get a salty dissonance if you don’t lip panhellenic event. Alternatively, we could the intervals into tune, or lip them the posit the following hypothetical scenario for wrong way. Relishing interference beats around 530 BCE, a century before would explain why the enharmonic style Pronomus. An ambitious competitive aulete was so highly revered: the peaks of sensory becomes frustrated with having to lip dissonance are higher and controlling them intervals into tune. To beat his competitors, tastefully demands consummate skill. he wants to play faster without compromising his intonation. He realises Pitch creep that the embouchure adjustments traditional on a standard aulos are a Diagram 1 shows how cyclic modulation by hindrance to this ambition. He therefore conjunction (fourths) and disjunction takes a knife to enlarge two finger-holes, (fifths) is possible on a grid that divides the sharpening the notes he has to lip up in one octave into seven functionally-equidistant particular harmonia – or he asks his aulos steps. On any instrument that supports maker to produce a new instrument with pitch bending, the adjustment required the holes in the optimal positions for that when modulating to the next tetrachord in mode. His efforts are rewarded: he wins the either direction is trivial: on average, only panhellenic prize. Pleased with his success, 14 cents. Progressing further in either he ends up with a fleet of special direction, this accumulates to produce a instruments – one for each mode – and pitch creep. Handled skilfully, this creep other auletes quickly catch on because could be imperceptible, spread out over a competition is intense and the stakes are passage of music or masked by vibrato and high. Pindar’s ode celebrating the victor portamento. Alternatively, it could be from Akragas (Agrigento, Sicilly) in 490 harnessed to theatrical or religious purpose, BCE indicates the level of prestige involved provoking emotions such as anguish or – as much for the city state as the ecstasy. competitor, as in football or the Olympic I discovered that a 7-tone circle of fifths games today (see Volume 4 in this series, was viable by accident, first playing the Pindar’s 12th Pythian Ode). For a century or aulos then by singing unaccompanied, solo so, these harmonia-specific auloi co-exist and with an unsuspecting community with the older panhellenic aulos. The latter chorus. I would never have predicted that is more widespread and the only one (so equi-heptatonic tuning could support far) represented in the archaeological extensive modulation of polyphonic cells in

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Just Intonation and only recommend it as a 7-tone modulation, whereas a mixture of practical solution because it is easy to tones and semitones supports 12-tone execute, surprisingly so for musicians reared modulation. What previous studies have not in a 12-tone world. Although it feels like understood is that both systems support what the instrument was designed for, this extensive modulation of all three types. is not sufficient reason to believe it. It is a This hypothesis overturns conventional guess, informed by playing these thinking, which is that auletes before instruments. Testing by others is now Pronomus could not participate in the required to identify weaknesses that I have ‘exharmonic twists’ and ‘perverted ant- not seen. This may interest researchers in crawlings’ of the so-called New Music other fields because every music director (GMW i, pp. 236–7). Descending Equi- and vocal coach struggles to prevent singers heptatonic Circuits demonstrates that this is from drifting sharp or flat. My informal wrong. Depending on whether our experiments, leading audiences of untrained witnesses resisted or welcomed change, singers in the warm-up included in Volume what was ‘New’ here was either the 3, suggest that the 7-tone circle of fifths corruption of kitharodic nomoi by the aulos, with elastic gridlines accommodates the or the revitalising of an illustrious genre that evolutionary predispositions of singers at had become tedious (GMW i, p. 96). least as well as the 12-tone system with rigid Extensive, indeed infinite possibilities of gridlines. modulation are as available on the aulos as The teachings of Pythagoras and they are on the violin. The auletic record calculations of Plato’s friend Archytas proves that this had been the case since at suggest that Classical auletes and their least the sixth century. It is modulation on audiences cherished pure intervals between an elastic 7-tone, not a rigid 12-tone grid, pipes. If we accept this, then the auletic and doing it proficiently takes years of finds from their lifetimes indicate that pure training. The compass of a polyphonic cell intervals required embouchure adjustments transposable into three keys is limited to a all the time. Boring finger-holes a seventh- fifth, but this limitation does not, of course, octave apart makes cyclic modulation easier apply to singers. because it keeps the size of these embouchure adjustments to a minimum. How big is a diesis? Going round the circle of fifths in 7-tone equal temperament – playing pure intervals On a doublepipe with launeddas-style single and returning to the starting point – involves reeds, pitch adjustment using the adjusting one pipe by 14 cents and the other embouchure is impossible – the only way to by 2 cents, stretching fifths and narrowing bend a pitch is to uncover a finger-hole fourths by 16 cents. This gives a pitch creep slightly, so that it leaks air. The word diesis of, on average, 14 cents per step. If the (literally a ‘leak’) may have acquired its temperament is unequal, then the musical meaning in a single-reed embouchure adjustments will be larger in environment, before double reeds became some places, smaller in others. The standard in the Greek aulos tradition. Pitch temperament reveals which keys were adjustment by embouchure becomes favoured. possible with double reeds. If the pitch Between the Pydna aulos (made in the platforms are unsteady, because the reeds late fifth century) and the Megara auloi are flexible and easier to blow, then (made in the late fourth century) the embouchure adjustments become essential principle of hole-boring changed. Two to produce pure consonances between the interval categories begin to emerge: tones pipes. Double reeds offer greater ranges of and semitones. The most compelling pitch, dynamics, timbre and articulation; explanation for this change, I suggest, is but fundamentally they gives pipers greater that an auletic 7-tone cycle of fifths was harmonic freedom, abandoning a fixed eclipsed by a kitharodic 12-tone cycle of drone. It is acoustically impossible to fifths. Equi-heptatonic hole boring supports produce pure consonances using single

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 21 reeds unless there is a fixed drone against developed in the fourth century. Writing in which all notes are tuned – a single the late second or early third century CE, reference point. If you change the drone, Sextus Empiricus transmits the following: you have to retune the instrument. To The Pythagoreans ... are in the habit of execute the hundreds of intonation sometimes saying ‘All things resemble adjustments required in Descending Equi- number’, and of sometimes swearing this most heptatonic Circuits, I find it easier to use the fundamental oath: ‘No, by him that gave to embouchure, but I have no doubt that us the tetraktys, which contains the fount partially uncovering finger-holes was an and root of ever-flowing nature.’ By ‘him additional technique used by some if not all that gave’ they mean Pythagoras (for they Classical auletes. The embouchure method, deified him); and by ‘tetraktys’ they mean a however, supports greater speed and agility number which, being constituted out of the because the movements are smaller and the first four numbers, fits together the most perfect number, as for instance ten: for one mechanical operations of note change and plus two plus three plus four makes ten. This note inflection are physically separated. number is the first tetraktys, and is described As Hagel notes, the diesis was as the ‘fount of ever-flowing nature’ in as established as the unit of measurement for much as the whole universe is organised on interval structures at least a generation the basis of these numbers according to before Aristoxenus: harmonia; and harmonia is a system of three concords, the fourth, the fifth and the Aristotle cites the díesis as the measure in octave; and the proportions of these three music among measures of daily use such as concords are found in the four numbers the foot for distances or the mina for weights: previously mentioned, in one, two, three and An. post. 84b; Met. 1016b; 1053ab. four. Hagel 2009, p. 152, n. 39 Adv. Math. vii.94–5; GMW ii, p. 30 When a set of disparate scale structures On a monochord, string lengths in the ratios have been aligned to a regular grid, 4:3, 3:2 and 2:1 produce the intervals of an rationalising every interval as a multiple of octave, fifth and fourth respectively. This one diesis, the scale structures are information concerning the Pythagoreans ‘commensurable’. This has practical as well enables us to interpret the passage by as philosophical merits. If the triplets of the Aristotle. It concerns a traditional way of ancient instrumental notation were dividing up the tonal space available on the developed by auletes and represent pitches aulos: one diesis apart, it is reasonable to suppose that they originally divided the octave into Some people say that there are many such 21 dieses (3 × 7), conceptually splitting [numerical correspondences]: for instance the equidistant scale steps in three. Aristoxenus, mesai are respectively 9 and 8 [i.e. monochord string lengths for the notes mesē however, adopted the octave division of 24 and paramesē are in the ratio 9:8]. They dieses (2 × 12), splitting twelve semitones point out also that the interval from alpha to in two, which would reflect kitharodic omega in the alphabet is equal to that from practice. The difference in size is barely the lowest note to the highest in auloi, whose perceptible: only 7 cents. The ‘auletic’ number is equal to the whole system of the diesis would be 1200 cents ÷ 7 equidistant heavens. steps ÷ 3 dieses per step = 57 cents. The Metaphysics 1093a 29-b4; GMW ii, p. 73 universally-recognised ‘kitharodic’ diesis is 1200 cents ÷ 12 equidistant steps ÷ 2 dieses In Pythagorean philosophy, the ‘whole per step = 50 cents. system of the heavens’ has ten spheres: the A passage by Aristotle supports this earth, counter-earth, moon, sun, Venus, conjecture. Before reading it, however, we Mercury, Mars, Jupiter, Saturn and the need some understanding of Pythagorean stars. Aristotle says that they added the teachings. These may in any case be more counter-earth in order to explain eclipses of relevant to the Poseidonia aulos, probably the moon and ‘to raise the number of made in Pythagoras’ lifetime, than ideas heavenly bodies around the central fire from

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nine to ten, which the Pythagoreans (2007, pp. 45–8) and Hagel offers a regarded as the perfect number’ reconstruction (2009, p. 377). Barker’s (Metaphysics 986a 8–12). The basic tetraktys suggestion is consistent with a division of is 1+2+3+4, which equals 10, but the the octave into 21 dieses because the notes reference here here is to its other out of range in Diagram 2 require an manifestation, 1×2×3×4, which is 24. extension of four dieses to fit within the For the correspondence these system. Perhaps this captured on papyrus Pythagoreans saw between the 24 letters of what Pronomus achieved in practice, adding the alphabet and the notes of the aulos, a lever-mechanisms that extended the low- division of the octave into 24 dieses proves register compass from 24 notes to 29. The unsatisfactory for two reasons. First, the low number of notes is always one higher than registers of the Pydna and Poseidonia auloi the number of intervals. would have 25 notes (a complete octave, counting extremities). Secondly, even using The fourth-century reform inflexible reeds, the low register comfortably exceeds an octave owing to the range of Previous scholars have unanimously agreed pitch available on each fingering. A 21- that the fifth-century fashion for diesis division is much more satisfactory. A ‘exharmonic twists’ and ‘ant-crawlings’ led single octave gives us 22 notes and to a tidy-up operation by the school of stretching this by a diesis at either end Eratocles – the harmonikoi referred to by brings the total to 24. Diagram 1 shows Aristoxenus. Organizing a disparate precisely this number of notes, not because collection of ethnic modes into a unified, I had interpreted this passage by Aristotle in cyclic system of keys appeared to be a neat this way, but because when composing musical corollary to the Greek spelling enharmonic music on the Pydna and reform (the Athenians voted to introduce a Poseidonia auloi, 24 is the number of notes standardised alphabet in 403/2 BCE and I found I could comfortably play. during the fourth century this displaced The practice of stretching a compass by local alphabets throughout the Greek- one diesis at either end finds oblique speaking world). Above, I argued that the support in the first Aristides scale, which is evidence points to a considerably earlier called (Slack) Lydian. In Diagram 2, it is date for the assimilation of regional interval numbered 1 and the stretched notes, top structures (Phrygian, Lydian, etc.) into a and bottom, are coloured gold. Stronger ‘commensurable’ system that supported support for this interpretation may lie in the modulation. The aulos was originally a sequence of 24 letters (alpha to omega) foreign instrument, played by Phrygians and assigned to pitches one diesis apart in the Lydians, but it had taken root in Greek ancient vocal notation. Did these pitches musical culture by the mid seventh century originally correspond to the low register of (GMW i, p. 51; West 1992, p. 82). If a grid an aulos? If so, then the Elgin is a supporting extensive modulation emerged candidate. When the symbols are used in a in the sixth century, at least for auletes, then fixed-pitch sense (which is not always the the fourth-century reform must have been case), the pitch of sigma (C) is thought to lie of a different nature. between F and F sharp (Hagel 2009, p. 93, Mode-related and key-related notions of Diagram 22). This brings the low register of tonos are intertwined in the literary sources. the Elgin into alignment with the sequence Sense can be teased from the confusion if alpha to omega in Hagel’s diagram of the tonos is understood as one of a progression fully developed notation system (2009, pp. of concepts, evolving, accumulating and co- 13 and 93). existing. In chronological order, these Aristoxenus refers to a 28-diesis diagram concepts would include focal tone, produced by Eratoclean theorists, probably tetrachord, octave and the two-octave in the first half of the fourth century. Barker interval structure called the ‘Greater Perfect considers it most likely that the Aristides System’. Barker concludes: scales were extracted from this diagram

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what [Aristoxenus] wrote was sufficiently have composed a choral ode (an ‘aulodic’ obscure or involved to breed nonsense in the nomos) and Clonas a solo piece (an ‘auletic’ minds of some of his later followers. Given the nomos). Nomos (literally a ‘custom’ or ‘law’) use of the same term, tonos, in the two in this context means a type of composition different contexts [mode and key], and the given canonical status by its selection for use of the same names both for harmoniai competitive or religious occasions (GMW i, and for tonoi in either of their roles, the ambiguities were always likely to create p. 249). It appears that the issue here is not confusion. the story transmitted by pseudo-Plutarch, GMW i, pp. 26–7 but the scholarly model – over two thousand years of Western musicological We can bring some clarity to the picture by belief, as crystallised in the cyclic positing that the octave concept of tonos arrangements of tones and semitones known coincides with the Dorian harmonia, or as the seven octave species (GMW ii, pp. central octave of the Greater Perfect 15–21). Projecting this conception onto System. Interpreted thus, we need no longer aulos-based music is incompatible with the dismiss the following story as corrupt: hole boring of Classical finds, as Schlesinger Sacadas of Argos, who composed songs and guessed in 1939 but with insufficient elegaic poems set to music ... was also a fine archaeological evidence to prove her case. aulete, and it is recorded that he won the A more resilient model emerges when we Pythian contest three times [in 582, 578 and first give the key-related notion of tonos a 574 BCE]. He is mentioned by Pindar. In deeper history; and then recognise that the the time of Polymnestus and Sacadas, there enharmonic octave species of Eratocles (c. were three tonoi, Dorian, Phrygian and Lydian: and it is said that Sacadas composed 400 BCE) did not necessarily fit the same a strophe in each of them, and taught the grid as the diatonic octave species of chorus to sing the first in the Dorian tonos, Cleonides (? first century BCE) and the second in the Phrygian, and the third in Ptolemy (second century CE). The notion the Lydian: this nomos is said to have been that mode-related aspects of harmonia had called Trimelēs because of the modulation. chronological precedence to key-related But in the document at Sicyon concerning the aspects of tonos is undermined by practical poets, Clonas is recorded as being the inventor experiment and all forms of evidence: ē of the Trimel s nomos. literary, material and ethnographic. Ps-Plut. 1134a–b; GMW i, pp. 213–4 Transforming the melody by altering its scale structure is what happens when you This was written in about the second set off in the wrong tuning, or a lyre string century CE and is thought to quote or slips in mid-performance; transposing the paraphrase a historical work by Plato’s elder same melody to a new pitch happens when brother, Glaucon. Projecting the two-octave you set off on the wrong note (on an equi- meaning of tonos from the late fourth heptatonic instrument), or your voice finds century onto a tradition that has its origins a lower or a higher pitch more comfortable. 150 years earlier has caused both Barker I suspect that musicians were exploring and Hagel to reject this tradition as both possibilities (modes and keys) for mistaken. As witnesses of musical thousands of years before the Classical behaviour, physical instruments are period. What Diagram 1 offers is a practical certainly more reliable than stories written framework that allows three things to co- generations later, but this particular exist: octave species (a cyclic reordering of tradition, unlike that for classifying auloi by intervals); transpositions of the same mode, has no contradictory witnesses. interval structure (tonoi); and different scale Although we cannot be sure it is by structures (harmoniai). The gridlines are Glaucon, this appears likely. It may be more elastic than Aristoxenus could accept interpreted in a way that is entirely and, after the rejection of the aulos by consistent with the auletic record and the Acibiades and Plato, it is no wonder that dispute between Clonas and Sacadas is elite citizens were more receptive to lyre- easily resolved. For example, Sacadas may based conceptions.

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Adding a deprecated sixth-century This may be the strongest single piece of auletic grid to our historical model enables literary evidence supporting the hypothesis us to accept the traditions that Sacadas and that emerges from this compositional Clonas could modulate between three tonoi, experiment. Playing pure fourths and fifths without changing instrument, respectively a on a 7-tone grid is only possible if the notes century and two centuries before have breadth. The elasticity required is 16 Pronomus. It would be modulation in a 7- cents on average, which is significantly tone system, transposing a polyphonic cell greater than the 2 cents required on a 12- spanning a fifth or less to consecutive tone grid. Without bending any gridlines, finger-holes. The vocal melody would not the sizes in cents of the fourths and fifths be limited to a fifth, only the aulos are 514:686 on a 7-tone grid and 500:700 accompaniment. Two centuries later, this on a 12-tone grid; for pure intonation, they might be perceived as having ‘a noble must be bent to 498:702. Pure consonances beauty’ because significantly fewer notes are are critical on an aulos because, when the involved than in the 12-tone ‘bending and tuning is imperfect, the interference beats twisting’ that earned the kithara players are more audible than between two lyre Timotheus and Philoxenus the contempt of strings. Hagel sets the tolerance for pure conservative critics (GMW i, p. 237). intervals to ± 20 cents when using his The historical model emerging from this dedicated software to predict optimal reed compositional experiment is that the lengths. I wonder if this may be telling us Poseidonia-type aulos evolved to suit the something significant. It is consistent with nomos trimelēs and the expressive an average note-breadth of 16 cents – a modulations of other auletic genres, above breadth that excludes lyres and harps from all the Pythikos and polykephalos nomoi. It is using the 7-tone grid because bending notes the theatrical use of rhythm and harmony all the time is impractical. Not so on an that the leading composer, Lasus of aulos, although it demands years of training. Hermione, appears to have taken from According to this hypothesis, what competitive auletic culture, introducing it to Pronomus did was to add the Dorian and the dithyramb in the late sixth century: Iastian harmoniai (as transmitted by Aristides) to an instrument that was already Lasos of Hermione, by altering the rhythms for the movement of the dithyramb, and by capable of playing in (Slack) Lydian, Tense pursuing the example of the muliplicity of Lydian, Phrygian and Mixolydian (see notes belonging to the aulos (and so making Volume 3 for details). Modulation mid- use of more notes, widely scattered about), piece would have been made easier by the transformed the music that existed before him. addition of lever mechanisms to operate Ps.-Plut. 1141c; GMW i, p. 235 three lower holes, out of reach of the fingers, as found on the Megara auloi. The Lasus was a contemporary of the player of names of tonoi may have been re-used (? by the Poseidonia aulos. He wrote the first Damon or Lasus) as the names of harmoniai ‘treatise’ (logos) on music, but precious little that had focal tones on corresponding scale is known about its contents (GMW ii, pp. degrees but possessed different interval 31; West 1992, p. 225; Barker 2007, p. 19). structures. The notes Pronomus added, if What we do know is highly significant: this model is correct, are shown in Diagram Aristoxenus criticises him and some others 2, below the range shared by the Poseidonia for thinking that notes had breadth: and Pydna auloi. These developments ... if [pitch] is not defined, it is not at all easy would all have taken place long after the to say what a note [phthongos] is. Anyone aulos tradition was cosmopolitan. The date who does not want to be forced into the proposed for the assimilation of ethnic scale position of Lasus and certain of the followers structures, establishing an instrument of of Epigonus, who thought that a note has panhellenic identity, is pushed back to the breadth, must say something rather more early sixth century: sometime between the precise about it. widespread adoption of the 7-string lyre and El. Harm. 3.19–24; GMW ii, p. 128

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 25 the introduction of aulos competitions at makers or players of the aulos into the city? the Panhellenic Games. Or isn’t it the most numerous-noted of all, This historical model leads me to suggest and aren’t the ‘panharmonic’ instruments that the paradigm shift taking place between themselves simply an imitation of the aulos?’ Timotheus and Aristoxenus – at the same ‘Obviously,’ he said. time as the Greek alphabet was being Plato, Rep. 399d; GMW i, p. 132 standardised – was not about enabling Plato is not saying that harps imitate a cyclic modulation, as previously thought, specific type of aulos, nor is it plausible that but about abandoning a dual-grid system these types of harp were developed in and replacing it with a single grid. Barker imitation of the new aulos that Pronomus writes: ‘Reputedly the most ancient and had developed only a few decades earlier. certainly the most respected class of nomos Plato can only be referring to the standard, was the kitharodic (treated e.g. by Plato, conventional Greek aulos that Pronomus Laws 700b, as the only class worth inherited and both Socrates and Plato had mentioning)’ (GMW i, p. 250). It is probably studied as teenagers. Plato is therefore natural that the kitharodic grid excluding the aulos generically. The should oust the auletic one, particularly different types used to accompany girls, when auletes already had an instrument boys, men and kithara players are all refused adapted to suit the kithara: the kitharistērios entry to his ideal city-state. What this aulos. Abandoning the 7-tone grid meant implies is that it was not a particular type of that pipes and lyres could perform together aulos that modulated between harmoniai, it more easily, there was only one tonal system was all of them. They were all capable of to teach and learn, and notes did not ‘exharmonic twists’ because, as Lasus and require so much breadth. A 12-tone grid the followers of Epigonus believed, each increases the number of keys available, note had a breadth of pitch. changes the pitch relations between them Over a thousand years later, Proclus of and, most significantly for auletes, reduces Athens (412–485 CE) wrote: the amount of lip bending required to play in tune. they say that each aulos-hole yields three notes at least, and more if the side-holes are opened too. A coherent solution Commentary on Plato’s Alcibiades I, 3.41; The ancient materials that have come down West 1992, p. 95 to us may be unrepresentative or unreliable Compared to fixed-pitch instruments for a variety of reasons (discussed by (harps, lyres and panpipes) the greater Barker: 2007, pp. 5–6). The hypothesis harmonic versatility of the aulos provides an generated by this composition makes sense excellent explanation for the moral of conflicting stories, drawing out of a judgement cast by Socrates, Alcibiades and problematic evidence base a more Plato. The aulos was unsuitable for an elite compelling solution. The central issues have citizen’s education because playing it been addressed above. Here I raise involved bending pitches, leading to awareness of four points that add coherence associations not with steadfastness and to the picture. restraint but impulsive, uncontrolled and First, when Socrates famously rejects the emotional behaviour. aulos in Plato’s Republic, he does so because The second point adding coherence is it is the original instrument guilty of that one of Aristoxenus’ contemporaries, modulating mid-piece in the pursuit of Heraclides of Pontus, differs from all other expressive realism: authorities in giving primacy to the triad ‘Then we shall not bring up craftsmen to Aeolian-Iastian-Dorian, rather than Dorian- make trigōnoi or pēktides [two forms of Phrygian-Lydian. Athenaeus writes: harp] or any of the instruments that have many strings and all harmoniai.’ Heraclides of Pontus, in the third book of his ‘Apparently not.’ ‘Well, will you admit On Music, says that Phrygian should not

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even be called a harmonia, and no more semitone higher, the Dorian a semitone above should Lydian. There are, he says, three that, the Phrygian a tone above the Dorian, harmoniai, since there are three races of and similarly the Lydian another tone above Greeks: Dorians, Aeolians and Ionians. the Phrygian. Others add below the ones mentioned the Hypophrygian aulos; while Ath. 624c; GMW i, p. 281 others again, with an eye to the boring of the Heraclides may have been a nationalist, finger-holes of auloi, separate the three lowest wanting to cleanse Greek music of its tonoi, the Hypophrygian, the Hypodorian associations with Lydia and Phrygia (in and the Dorian, by three dieses from one what is now western Turkey), but this another, and the Phrygian from the Dorian apparent disagreement may amount to by a tone, placing the Lydian at a distance of another three dieses from the Phrygian, and nothing. Diagram 1 shows how the pairs of the Mixolydian at the same distance from the tetrachords labelled Aeolian-Lydian and Lydian. Iastian-Phrygian each form an Unmodulating System, or one key brought De Musica 37.15ff; GMW ii, pp. 153–4 to life by the tonal contrast between two We can date these two tonoi systems to tetrachords (conjunct and disjunct). The some time before 322 BCE. By then, pair Dorian-Mixolydian forms a third Aristoxenus had achieved an eminence that Unmodulating System. When pairs of tonoi fuelled his ambitions he might succeed are married in this way, forming a single key Aristotle. Headship of the Lyceum, defined by its tonal dynamism, then the however, passed to Theophrastus (GMW ii, auletic grid supports three keys a tone apart, p. 119). Hagel suggests a date of ‘not long rather than seven keys a fourth apart. This after 400’ for these tonoi systems (2009, p. would explain the low profile of the seventh 389). Anyone dipping into Hagel’s book tonos, Locrian, in ancient literature: it does should note that he switches his not participate in the triad of keys terminology: the ‘Second’ system in the established in the sixth century by Sacadas diagrams on pages 379–80 is renamed the and possibly in the seventh century by ‘old auletic’ system from page 390 onwards. Clonas. In the Plutarchian treatise De ‘Old’ in this instance means early fourth Musica, immediately before the story about century. Another potential source of the invention of the nomos trimelēs, we learn confusion is that Hypodorian is below a little more from Glaucon: Dorian by a finger-hole, not by a fourth, in Clonas, the composer of nomoi sung to the both tonoi systems. This is why I call it ‘old’ aulos, who lived a little later than Terpander, Hypodorian in Diagrams 1 and 2, like was a Tegean according to the Arcadians, a Hagel using ‘old’ to mean before Theban according to the Boeotians. Aristoxenus, whose work obliterated what came before. ps-Plut. 1133a; GMW i, pp. 210–11 The interval of three dieses in the second This places Clonas in the seventh century system (‘with an eye to the boring of the and identifies him as a Greek of Aeolian finger-holes of auloi’) must involve 12-tone identity, unlike the semi-mythical inventor dieses of 50 cents, rather than 7-tone dieses of the enharmonic style, Olympus, who was of 57 cents, because of the larger interval a Phrygian. between Phrygian and Dorian: a tone (four The third point concerns a disagreement dieses). This system is almost equi- between Aristoxenus’ predecessors: heptatonic, except that the scale step The exposition of the tonoi by the corresponding to the tone of disjunction in harmonicists is just like the way the days of the Dorian tonos is larger. This is highly the month are counted, where, for example, significant: it eliminates the need for what the Corinthians call the tenth the embouchure adjustment when moving Athenians call the fifth, and others again the between the concords hypatē-mesē and eighth. In just the same way, some of the hypatē-paramesē – the fourth and fifth that harmonicists say that the Hypodorian is the define the key. I would interpret this tonoi lowest of the tonoi, the Mixolydian a system as an unequal 7-tone temperament,

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 27 favouring Dorian but still supporting Conclusions excursions to other keys and twists of For this experimental composition, my goal chromaticism. It would be an intermediate was to respect everything scholars knew stage, halfway between the auletic 7-tone about Greek music in the period when the system and the kitharodic 12-tone system. Poseidonia and Pydna auloi were being Finally, this hypothesis potentially offers played (roughly 510–380 BCE). As a a simpler explanation for the Dorian composer bringing critical reproductions of enigma. How did the scale that occupied a these finds to life, I wanted to constrain my central place in Classical music education creativity by taking every scrap of ancient and theory end up in a marginalised evidence into account. I did not anticipate position? Hagel’s book provides a solution. that the hole boring of these instruments He defines the problem as follows: would contradict both the thinking of in the notation, it is by no means the natural ancient Greek music scholars and a scale, as one should expect, but lies at the fundamental tenet of Western music – the outskirts of the diagram, to be transcribed division of the octave into twelve semitones. with five flats. This was naive. The musical tradition we Hagel 2009, p. 10 are dealing with experienced profound Exploring how the collapse of a 7-tone grid changes in the two centuries before and rise of the 12-tone grid may explain the Aristoxenus. Dorian enigma more successfully is a topic Descending Equi-heptatonic Circuits for a future study. I will simply point out submits for distributed testing and that in Diagrams 1 and 2, the interval development what may prove to be better structures with ethnic labels in blue, black solutions to a number of puzzling questions. and red are transposed three aulos scale- It gives due weight to the auletic record and steps higher, to what Hagel concludes was looks to unfamiliar classical music cultures their ‘old’ pitch, again meaning before to help interpret two outstanding Aristoxenus. This is convincing. With ‘old’ archaeological finds. Previous studies have Dorian at the pitch of ‘new’ Lydian asserted that cyclic modulation by fifths and (labelled in green), the low register of the fourths was impossible on Classical auloi Pydna aulos can be reconciled with the before Pronomus; that before the late fifth musical genres for which professional century changing mode or key meant auletes were most in demand. When the changing aulos. This composition two holes out of reach of the fingers are demonstrates that extensive modulation open (the basic setup, which I use for may be much older and is entirely viable on Descending Equi-heptatonic Circuits), the instruments contemporary with Lasus of instrument is optimised for the Phrygian Hermione, provided the tonal gridlines are tonos with focal tones a little sharper than elastic and notes are understood as having G–C–D; when they are closed, the breadth. It suggests that fourth-century instrument is optimised for Dorian with theorists favoured the modulatory focal tones somewhat flatter than F♯–B–C♯. framework developed by kithara players in Everything makes sense. The only proposed the first half of the fifth century. This did refinements to Hagel’s model are the nature not require pitches to have breadth; instead, of the paradigm shift (deprecation of an it involved increasing the number of strings elastic 7-tone grid) and the perspective of from seven to eleven. According to this ‘Lasus and certain of the followers of hypothesis, an auletic system of seven Epigonus, who thought that a note has functionally-equidistant tetrachords breadth’. The lack of written evidence for a (Diagram 1) was gradually eclipsed by a musical behaviour contemporary with tonal grid that enabled kithara players to be Pythagoras and Socrates is unsurprising. as crowd-pleasing as auletes in a period What we have are the physical instruments when theatrical realism was leading musical and their testimony deserves greater fashion (GMW i, p. 300). attention.

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The aulos had been calling the tune for training beyond what anyone in the aulos Greek musical culture as a whole since the revival has reached at the present time, late sixth century thanks to the popularity of including myself, but this level is no greater the dithyramb and the rise of drama in than what any professional skill demands. Athens. But the balance of power and The primary purpose of this composition, direction of influence seems to change in therefore, is to raise the bar and provide a the second half of the fifth century. rewarding training experience for all Timothy Power writes: learners, raising our competence levels and filling a void: players of Classical auloi By the 420s Panathenaic kitharoidoi were somehow felt to be intruding on the territory currently have no repertoire to practise. In of the aulete – making themselves at home in the absence of living masters, Descending the Dionysiac realm, posing an imitative Equi-heptatonic Circuits is a substitute for a challenge to the aulos-based music of strict teacher. For students of any dithyramb and drama. ... Plato disdains the instrument, the path to excellence involves way (Dionysiac, aulodic) dithyramb absorbs venturing out of one’s depth, aiming at (Apolline, lyric) paian – but to have something slightly beyond one’s current kitharodic music itself imitating aulodic capacities. Descending Equi-heptatonic music is too disturbing a symptom of late Circuits provides a training ground for democratic cultural perversity. playing pure intervals between pipes. I have Kowalzic & Wilson 2013, p. 244 uploaded recordings and videos at various The terms need to be clarified: ‘aulodic’ points in its development process (and mine and ‘kitharodic’ refer to music that involved playing it) and intend to continue doing so the voice, whereas ‘auletic’ and ‘kitharistic’ in order that others struggling can take refer to music that was purely instrumental. heart in the knowledge that the impossible It was kitharodic culture that commanded does become possible with practise. the highest prestige, tied to the performance Proponents of an open fingering system of Homeric epic. Traditionalists found its may or may not reach my conclusion, which theatrical turn in the Classical period vulgar is that closed fingering (generally opening and deeply disturbing. one finger-hole at a time) avoids dropping A scaffolding of seven wobbly platforms the instrument and significantly reduces the would be restricted to a double-reed tension and physical effort that leads to doublepipe tradition that exploited pitch injury and technical awkwardness. I like to bending to produce pure concords between have as much surface area in contact with the pipes. It would support three tonoi a the pipes as possible, so that finger pressure scale-step apart, each with a compass of a can be reduced and the pipes are held fifth (a vocal melody could be more lightly, not gripped. expansive). A 12-tone grid, by contrast, is Descending Equi-heptatonic Circuits is compatible with the inflexible pitches of simultaneously a cultural product, serving harps and lyres. It supports twelve tonoi in aulos learners, and a research output in the theory (in practice, only about seven were discipline of Very Early music (see Volume used) and a highly chromatic harmonic 1, p. 6). As a cultural product, I hope it language. The driving force behind this opens up new musical territory for aulisation of the kithara was pleasing crowds composers and paves the way for at Dionysia: lyre players’ desire to be intercultural collaborations, perhaps with fashionable, doing what virtuoso auletes like musicians from West Africa, Thailand, Sacadas, Lasus and Epigonus had started Laos, Cambodia or Vietnam, whose doing in the sixth century. Ultimately, instruments are also tuned to a functionally- however, the kitharodic tonal system won: a equidistant 7-tone system. As a research dual-grid musical culture collapsed to a output, I trust it provokes performers, single-grid one. Classicists and musicologists to look again Playing a composition like Descending at ancient Greek materials, asking new Equi-heptatonic Circuits requires a level of questions and reaching deeper insights. Learning to play Classical auloi sheds light

EMAP Resources for Euterpe 2 | emaproject.eu/events/euterpe/resources 29 on the deep history of music: east, west, 10.6084/m9.figshare.7006208. This is so north and south. that performers with different cultural The most serious limitation with this training – for example, players of the composition is my own cultural Croatian sopele, Azerbaijani balaban, or conditioning. I was reared in the Scottish Chinese guan – can recompose it easily. I pibroch and paneuropean orchestral and would strongly encourage them to do so, Baroque flute traditions. Descending Equi- exploring other possibilities and sharing heptatonic Circuits reflects this heritage as results online. I would also encourage those powerfully as it reflects anything ancient designing future projects to take Greek. Rather than attempting to undo my intercultural collaboration to a higher level. training, which I do not think is possible, I This could mean budgeting properly for: 1) would recommend that future research and learning to play, such as full-time 3-year cultural projects make it a priority to recruit studentships; 2) composing new music, and cultivate brilliant players with roots which has to be by dedicated players elsewhere on the planet: virtuoso musicians through practical experiment; and 3) from Mediterranean islands, the Balkans, producing scores or videos that capture new the Near, Middle and Far East. A more compositions, a greater diversity of playing fruitful journey will begin when we stop techniques, and explain the decision- claiming that we know best or that what we making process in detail. This would build are doing is ancient Greek music. Aulos on the remarkable achievements of the players should keep their minds open, European Music Archaeology Project, recognising that all authorities, ancient and which has brought interdisciplinary modern, have cultural prejudices. There are collaboration in the aulos revival to new other solutions to be found and the aulos heights. Doing the same thing for revival will be healthier when it is being fed intercultural collaboration would put the by a broader spectrum of piping traditions. aulos revival on an even more powerful In order to encourage others to keep on trajectory, generating new knowledge and pushing boundaries, I have shared editable enriching cultural life. file formats for this composition at the DOI

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Bibliography

BARKER, A. (2007) The Science of Harmonics in Classical Greece. Cambridge: Cambridge University Press. CHURCH, M. (ed.) (2015), The Other Classical Musics: Fifteen Great Traditions. Woodbridge: The Boydell Press. GMW i. A. Barker (1984), Greek Musical Writings I: The Musician and his Art. Cambridge: Cambridge University Press.

GMW ii. A. Barker (1989), Greek Musical Writings II: Harmonic and Acoustic Theory. Cambridge: Cambridge University Press.

HAGEL, S. (2009) Ancient Greek Music. A New Technical History. Cambridge: Cambridge University Press. —— (2010), ‘Understanding the aulos Berlin Egyptian Museum 12461/12462’. In Ricardo Eichmann, Ellen Hickmann and Lars-Christian Koch (eds), Studien zur Musikarchäologie 7. Orient-Archäologie 25, pp. 67–87. KOWALZIG, B. and P. Wilson (eds) (2013), Dithyramb in Context. Oxford: Oxford University Press. PSAROUDAKĒS, S. (2008), ‘The aulos of Pydna’. In Arnd Adje Both, Ricardo Eichmann, Ellen Hickmann and Lars-Christian Koch (eds), Studien zur Musikarchäologie 6. Orient- Archäologie 22, pp. 197–216. —— (2014) ‘The aulos of Poseidōnia’. In Angela Bellia (ed.), Musica, culti e riti nell’Occidente greco. Telestes. Studi e ricerche di archeologia musicale nel Mediterraneo 1. Pisa and Rome: Istituti Editoriali e Poligrafici Internazionali, pp. 117–29. WEST, M. L. (1992) Ancient Greek Music. Oxford: Oxford University Press.

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