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Singing with the Muses: new paths into ancient Mousikē
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Abstract
This article completes the discussion of the Classical/Hellenistic harmonic system set out in Lynch 2022a . Taken jointly, these articles offer the first account of the use of notation keys in the Hellenistic musical documents that is fully consistent with technical evidence as well as literary testimonies about the harmonic innovations of the New Musicians. This article features practical analyses and new modern transcriptions of the Ashmolean Papyri (DAGM 5–6) and Athenaeus’ Paean (DAGM 20)—scores that reflect the modulation system of the New Music and its characteristic use of ‘exharmonic’ and ‘chromatic’ notes. The analyses offered in this article are powered by a newly-developed database (dDAGM, Lynch 2021) and show that these ‘exharmonic’ notes correspond to the chromatic ‘bends’ first identified in Lynch 2018—‘bends’ which ‘distorted’ the central pillars of the noble Dorian harmonía and turned it into its polar opposite: the Mixolydian, the emotional and lamenting mode par excellence.
References
DAGM = Pöhlmann, E. and West, M.L. (2001). Documents of Ancient Greek Music: The Extant Melodies and Fragments. Oxford.
dDAGM = Lynch, T. A.C. (2021). Database ‘Documents of Ancient Greek Music’. Version 1.1 Zenodo:https://doi.org/10.5281/zenodo.5181743
Lynch, T. (2018). ‘ “Without Timotheus, much of our melopoiia would not exist; but without Phrynis, there wouldn’t have been Timotheus”: Pherecrates’ twelve strings, the strobilos and the harmonic paranomia of the New Music’, Greek and Roman Musical Studies 6.2, 290–327. https://bit.ly/3sOsT5b
Bringing together evidence preserved by Aristoxenus, Aristides Quintilianus, Ptolemy, Porphyry and the Greek musical handbooks in a unified framework, this article and its sequels show how the Classical modulation system reconstructed in Lynch 2018 is confirmed by the melodies recorded in the Greek musical documents. Taken jointly, these articles will offer the first comprehensive account of the use of notation tónoi in the ancient Greek musical documents that is fully consistent with the extant technical evidence on ancient harmonic theory and with literary testimonies about the harmonic innovations introduced by the New Musicians. The present article will focus on the Classical/Hellenistic harmonic system, whereas its Imperial counterpart will be discussed in a forthcoming article. These theoretical analyses are based upon a newly developed database (dDAGM) that collects all the musical notes attested in the standard edition of the Greek musical fragments (DAGM), comprising over 3,400 notes.
References
DAGM = Pöhlmann, E. and West, M.L. (2001). Documents of Ancient Greek Music: The Extant Melodies and Fragments. Oxford.
dDAGM = Lynch, T.A.C. (2021). Database ‘Documents of Ancient Greek Music’. Version 1.1 Zenodo:https://doi.org/10.5281/zenodo.5181743
Lynch, T. (2018). ‘ “Without Timotheus, much of our melopoiia would not exist; but without Phrynis, there wouldn’t have been Timotheus”: Pherecrates’ twelve strings, the strobilos and the harmonic paranomia of the New Music’, Greek and Roman Musical Studies 6.2, 290–327.
Archeomusicologists commonly use methods based on the physical properties and the relative tuning system of a musical instrument in order to estimate its tones. However, because the musician often alters the tones’ frequency, for example, while playing in wind instruments by means of embouchure or by stressing the string in string instruments, the current methods that neglect the musician’s interaction with the instrument cannot provide solid results. In this work, we introduce ENTROTUNER, a computational method, based on mathematical optimization, to more accurately estimate the generated tones by considering: the instrument as a sound production mechanism, the relevant musical scale(s), and the musician’s interaction with the instrument. We simulate this interaction as a system that, by following tuning rules, aims to maximize the partials’ overlap (harmonicity), coded as entropy’s minimization of the aggregated tones’ spectrum. Last, we put ENTROTUNER into practice for the ancient Greek wind instrument Aulos. The results reveal that, compared with the traditional methods, ENTROTUNER highlights increased harmonicity (entropy decreased by 0.341bits), eleven additional consonant intervals, as well as 47.8% more tuning quality for the musical instrument.
This figure (Lynch 2023, Fig. 21) represents the basic harmoníai that could be played by the Louvre aulos in its Imperial setting, as well as some of the modulating scales that could be produced by 'expanding' the basic scales through partial-covering of up to two finger-holes of this instrument.
Each of these modes is matched to the corresponding Greek notes employed in the Imperial musical documents, as well as the corresponding tunings recorded by Aristides Quintilianus and Ptolemy. The practical use of these modes in the Imperial musical documents shall be discussed in detail in a book currently in preparation (https://zenodo.org/record/7524698#.Y-oUwy8w1pR).
As discussed on my website, this reconstruction is based on the 3D model I produced in 2021: https://www.emousike.com/louvreaulos
For the sake of methodological rigour, my analysis of the Louvre aulos scale is based on the frequencies published in Hagel 2014. Thanks to the chamber pitch calculator included in Lynch 2021b, the musical value of these frequencies is however established on the basis of the standard pitch set by the Koilē flute (~432 Hz, Terzēs 2020).
Among other things, this diagram shows the basic scales produced by the Louvre aulos conform to the Phrygian and Hypophrygian tunings recorded by Ptolemy (Hypértropa and Iástia) not only with regard to their general octave species but also in connection with the fine tuning of key intervals. For instance, the septimal tone d–e (8:7) that is featured in Ptolemy’s Phrygian tuning (Hypertropa) corresponds to the interval produced by the relative holes of the L pipe of the Louvre aulos (Φ and C). Likewise, the septimal tone A–B that was distinctive of the ‘relaxed’ Iastian mode (Iastia) is produced by the lowest holes of the H pipe.
This diagram also shows that the Imperial kithára tunings were doubled an octave higher by the Louvre Aulos. This octave shift suggests that the Louvre aulos was a ‘kitharistic’ aulos (kitharistḗrios), which was also known as mágadis (Ath. Deipn. 14.634e–35c) after the special ‘harp-like’ effect produced by playing melodies in parallel octaves (magadízein).
Unlike the note-for-note (próschorda) accompaniment that was typical of traditional lyre playing, ‘kitharistic’ auloi replicated the male register characteristic of kithara scales an octave higher (cf. e.g. Ps.-Plut. De Mus. 1141b).
Callum Armstrong will produce audio recordings of these scales in the near future, and they will be made available on the website in due course.
References:
Lynch, T. A.C. (2023) 'Singing with the Muses: new paths into ancient Mousikē'. Dramaturgias (forthcoming). https://www.researchgate.net/publication/368832615_Singing_with_the_Muses_new_paths_into_ancient_Mousike
Hagel, S. (2014b). Better Understanding the Louvre Aulos. In Eichmann, R., Jianjun, F., Koch, L.- Ch. (eds), Papers from the 8th Symposium of the International Study Group on Music Archaeology. Rahden, Westf.: Marie Leidorf, pp.131–142.
Terzēs, C. (2020). Musical Instruments of Greek and Roman Antiquity. In Lynch, T. A.C. and Rocconi, E. (eds), A Companion to Ancient Greek and Roman Music, Malden: Blackwell, pp. 213-227.
This database has been created by Dr Tosca A.C. Lynch (https://oxford.academia.edu/ToscaLynch) and includes all the notes attested in the ancient Greek musical documents collected in the standard edition (DAGM = Pöhlmann, E. and West, M.L., 2001, Documents of Ancient Greek Music, Oxford: OUP).
Dr Lynch will present historically informed interpretations of these data in a series of articles devoted, respectively, to the Classical/Hellenistic harmonic system and the relative documents (marked as BC in this database), and the Imperial harmonic system and the relative documents (marked as AD in this database).
Dubious readings follow Pöhlmann and West; DAGM 17-18 are grouped with Imperial documents, as discussed in the articles.
This database will be released under CC License Attribution-NonCommercial-NoDerivatives 4.0 International upon publication of the articles that offer historically-informed interpretation of the data.
The Database 'Documents of Ancient Greek Music' shall be licensed by Tosca A.C. Lynch under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License for academic research purposes (https://creativecommons.org/licenses/by-nc-nd/4.0/).
A COMPANION TO ANCIENT GREEK AND ROMAN MUSIC
A comprehensive guide to music in Classical Antiquity and beyond
Drawing on the latest research on the topic, A Companion to Ancient Greek and Roman Music provides a detailed overview of the most important issues raised by the study of ancient Greek and Roman music. An international panel of contributors, including leading experts as well as emerging voices in the field, examine the ancient ‘Art of the Muses’ from a wide range of methodological, theoretical, and practical perspectives.
Written in an engaging and accessible style, this book explores the pervasive presence of the performing arts in ancient Greek and Roman culture—ranging from musical mythology to music theory and education, as well as archaeology and the practicalities of performances in private and public contexts. But this Companion also explores the broader roles played by music in the Graeco-Roman world, examining philosophical, psychological, medical and political uses of music in antiquity, and aspects of its cultural heritage in Mediaeval and Modern times.
This book debunks common myths about Greek and Roman music, casting light on yet unanswered questions thanks to newly discovered evidence. Each chapter includes a discussion of the tools or methodologies that are most appropriate to address different topics, as well as detailed case studies illustrating their effectiveness.
This book
• Offers new research insights that will contribute to the future developments of the field, outlining new interdisciplinary approaches to investigate the importance of performing arts in the ancient world and its reception in modern culture
• Traces the history and development of ancient Greek and Roman music, including their Near Eastern roots, following a thematic approach
• Showcases contributions from a wide range of disciplines and international scholarly traditions
• Examines the political, social and cultural implications of music in antiquity, including ethnicity, regional identity, gender and ideology
• Presents original diagrams and transcriptions of ancient scales, rhythms, and extant scores that facilitate access to these vital aspects of ancient music for scholars as well as practicing musicians
Written for a broad range of readers including classicists, musicologists, art historians, and philosophers, A Companion to Ancient Greek and Roman Music provides a rich, informative and thought-provoking picture of ancient music in Classical Antiquity and beyond.
TOSCA A.C. LYNCH has been Junior Research Fellow in Classics at Jesus College, Oxford (2016–19). She is Visiting Professor in Greek Literature, Metre and Music at the Department of Cultures and Civilisations, University of Verona, and Research Associate at the Classics Faculty, University of Oxford.
ELEONORA ROCCONI is Associate Professor of Greek Language and Literature, Department of Musicology and Cultural Heritage, University of Pavia (Cremona), and editor‐in‐chief of the journal Greek and Roman Musical Studies.
This appendix presents transcriptions and diagrams of the most recent scholarly reconstructions of the ancient modes (harmoniai) attested in ancient musical treatises—especially Aristides Quintilianus’ De musica and Ptolemy's Harmonics—with further references to publications that give details on the sources, methodology, and rationales of these reconstructions. It is intended as a way to facilitate access to the most recent scholarship on this vital aspect of ancient music for a variety of readers, including musicologists and professional musicians.
Modern scholarship, starting with literary evidence, deploys theories concerning physical materials, shape and dimensions, tensions, junctions between parts, absolute pitch, scales, and tunings, as well as playing techniques, mostly by employing methods and tools from other disciplines (acoustics, statistics, computer science), and evaluates these theories by applying them on statistically weighted iconographical evidence and available archaeological finds of musical instruments. Importantly, the study of new finds enlightens missing links in the chain of instruments’ technical history. Either printed out from 3D models or handmade reconstructions of historically documented and technically restored models, Greek and Roman musical instruments illustrate our understanding of the music of the past.
Computer-Aided Estimation of the Athenian Agora Aulos Scales Based on Physical Modelling
- A Andreopoulou
- A Roginska
Andreopoulou, A., and Roginska, A. (2012). Computer-Aided Estimation of the Athenian Agora
Aulos Scales Based on Physical Modelling. Audio Engineering Society Convention Papers
8695, pp. 1-10.
Music-Archaeological Sources: Excavated Finds, Oral Transmission, Written Evidence
- S Hagel
Hagel, S. (2004). Calculating Auloi-The Louvre Aulos Scale. In Hickmann, E. and Eichmann, R.
(eds), Music-Archaeological Sources: Excavated Finds, Oral Transmission, Written Evidence,
Studien zur Musikarchäologie 4.15, Rahden: Leidorf, pp. 373-90.
(eds) Musical Perceptions-Past and Present: On Ethnographic Analogy in Music Archaeology
- S Hagel
Hagel, S. (2010). Understanding the Aulos Berlin Egyptian Museum 12461/12462. In Eichmann,
R., Hickmann, E. and Koch, L.-C. (eds) Musical Perceptions-Past and Present: On
Ethnographic Analogy in Music Archaeology, Rahden, Westf.: Verlag Marie Leidorf GmbH,
67-87.
Data for Reconstructing the Louvre aulos
- S Hagel
Hagel, S. (2014a). Data for Reconstructing the Louvre aulos. EMAP. Vienna.
http://www.doublepipes.info/wp-content/uploads/2014/04/Louvre-Aulos.pdf
Better Understanding the Louvre Aulos
- S Hagel
Hagel, S. (2014b). Better Understanding the Louvre Aulos. In Eichmann, R., Jianjun, F., Koch, L.-Ch. (eds), Papers from the 8th Symposium of the International Study Group on Music
Archaeology. Rahden, Westf.: Marie Leidorf, pp.131-142.
A History of Performing Pitch: The Story of 'A'
- B Haynes
Haynes, B. (2002). A History of Performing Pitch: The Story of 'A'. Scarecrow Press.
Review of A Companion to Ancient Greek and Roman Music
- W Levitan
Levitan, W. (2023). Review of A Companion to Ancient Greek and Roman Music. Blackwell
Companions to the Ancient World, edited by Lynch, T.A.C., and Rocconi, E. Greek and
Roman Musical Studies (Online first). doi: https://doi.org/10.1163/22129758-bja10057
Why are only the Dorian and Phrygian harmoniai accepted in Plato's Kallipolis? Lyre vs. Aulos
- T Lynch
Lynch, T. (2016). Why are only the Dorian and Phrygian harmoniai accepted in Plato's Kallipolis?
Lyre vs. Aulos. In Bravi, L., Lomiento, L., Meriani, A. and Pace, G. (eds), Tra lyra e aulos.
Tradizioni musicali e generi poetici, Pisa-Bari: Fabrizio Serra Editore, 267-84.
Tuning the Lyre, Tuning the Soul: Harmonía and the kósmos of the Soul in Plato's Republic and Timaeus. Greek and Roman Musical Studies 8
- T A C Lynch
Lynch, T. A.C. (2020a). Tuning the Lyre, Tuning the Soul: Harmonía and the kósmos of the Soul
in Plato's Republic and Timaeus. Greek and Roman Musical Studies 8.1, 111-55.
The Louvre aulos-interactive 3D Model
- T A C Lynch
Lynch, T. A.C. (2021a). The Louvre aulos-interactive 3D Model.
https://www.emousike.com/louvreaulos
Louvre Aulos scale calculator 1.0
- T A C Lynch
Lynch, T. A.C. (2021b). Louvre Aulos scale calculator 1.0. Zenodo.
https://doi.org/10.5281/zenodo.5515303
Rhythms "in armour" and rhythms "by the finger
- T A C Lynch
Lynch, T. A.C. (2022c). 'Rhythms "in armour" and rhythms "by the finger": Socratic humour
and rhythmic sophistry in Aristophanes' Clouds (636-53)'. In Gostoli, A.,
Zimmermann, B. (eds), Nuove volute di versi. Poesia e musica nella commedia greca di V
e IV sec. a.C., Göttingen: Vandenhoek & Ruprecht, 245-66.
The Canon' diagram (Heidelbergensis Palatinus gr. 281, fol. 173 v) and the structure of the Hypolydian Unchanging Perfect System
- T A C Lynch
Lynch, T. A.C. (2022d). 'The Canon' diagram (Heidelbergensis Palatinus gr. 281, fol. 173 v) and
the structure of the Hypolydian Unchanging Perfect System. Zenodo.
https://doi.org/10.5281/zenodo.6627046
Louvre aulos: basic scales and keys, Classical setting
- T A C Lynch
Lynch, T. A.C. (2022f). Louvre aulos: basic scales and keys, Classical setting. Zenodo.
https://doi.org/10.5281/zenodo.7213545
Unlocking the Riddles of Imperial Greek Melodies: the 'Lydian' Metamorphosis of the Classical Harmonic System. Under evaluation
- T A C Lynch
Lynch, T.A.C. (2023a). Unlocking the Riddles of Imperial Greek Melodies: the 'Lydian'
Metamorphosis of the Classical Harmonic System. Under evaluation. Preprint on
Zenodo. https://doi.org/10.5281/zenodo.6927929
Plato's Musical ēthos and Classical Greek modes, instruments and rhythms
- T A C Lynch
Lynch, T.A.C. (forthcoming 1). Plato's Musical ēthos and Classical Greek modes, instruments and
rhythms [2023 draft].
Ancient Greek melodies and the Invention of the Harmonic System: from Euripides to Early Christianity
- T A C Lynch
Lynch, T.A.C. (forthcoming 2). Ancient Greek melodies and the Invention of the Harmonic System:
from Euripides to Early Christianity. [2023 draft]. Zenodo.
https://doi.org/10.5281/zenodo.7524698
The Auloi of Pydna. Studien Zur Musik-Archäologie 6
- S Psaroudakēs
Psaroudakēs, S. (2008). The Auloi of Pydna. Studien Zur Musik-Archäologie 6.22: 197-216.