Didymus the Musician: Difference between revisions
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== Theory == |
== Theory == |
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We know of his theory only indirectly from the works of Porphyry and Ptolemy. There, one finds examples of his [[tetrachord]]s as measured string lengths from which the following proportions can be calculated: |
We know of his theory only indirectly from the works of Porphyry and Ptolemy. There, one finds examples of his [[tetrachord]]s as measured string lengths from which the following proportions can be calculated: |
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:{| style="text-align:center;" |
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|- style="vertical-align:bottom;" |
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!align="right"|  [[tetrachord]]<br/> type |
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!  [[musical interval|interval]]<br/>  1st–2nd |
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!  [[musical interval|interval]]<br/>  2nd–3rd |
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!  [[musical interval|interval]]<br/>  3rd–4th |
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|- |
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!align="right"| diatonic |
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|  {{big|{{sfrac| 16 | 15 }} }} ||  {{big|{{sfrac| 10 | 9 }} }} ||  {{big|{{sfrac| 9 | 8 }} }} |
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|- |
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!align="right"| chromatic |
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|  {{big|{{sfrac| 16 | 15 }} }} ||  {{big|{{sfrac| 25 | 24 }} }} ||  {{big|{{sfrac| 6 | 5 }} }} |
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|- |
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!align="right"| enharmonic |
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|  {{big|{{sfrac| 32 | 31 }} }} ||  {{big|{{sfrac| 31 | 30 }} }} ||  {{big|{{sfrac| 5 | 4 }} }} |
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|} |
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| ⚫ | Like [[Archytas]], he used a [[major third]], but appears to have been the first to use it in the [[Diatonic scale|diatonic]] as the sum of the [[major tone|major]] (9:8) and [[minor tone|minor]] (10:9) [[Major second|whole tones]] as for the proportions produced by {{nobr| {{big|{{math| {{sfrac| 10 | 9 }} × {{sfrac| 9 | 8 }} {{=}} {{sfrac| 5 | 4 }} }} }} .}} The ratio of these whole tones {{nobr| {{big|{{math| {{sfrac| 9 | 8 }} {{small|''⧸''}} {{sfrac| 10 | 9 }} {{=}} {{sfrac| 9 | 8 }} × {{sfrac| 9 | 10 }} {{=}} {{sfrac| 81 | 80 }} }} }} ;}} is the so-called ''[[syntonic comma]]'', also referred to as ''Didymos' comma''.{{sfn |Chappell |1874 |p=[https://hdl.handle.net/2027/coo1.ark:/13960/t6k07nk8q?urlappend=%3Bseq=304 204]}}{{sfn |Hubbard |1910 |p=[{{Google Books URL |id=H7FhAAAAIAAJ |p=121}} 121]}} |
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* diatonic tetrachord: (16:15)(10:9)(9:8) |
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* chromatic tetrachord: (16:15)(25:24)(6:5) |
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* enharmonic tetrachord: (32:31)(31:30)(5:4) |
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| ⚫ | Like [[Archytas]], he used a [[major third]], but appears to have been the first to use it in the [[Diatonic scale|diatonic]] as the sum of the [[major tone|major]] (9:8) and [[minor tone|minor]] (10:9) [[Major second|whole tones]] as for the proportions |
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==References== |
==References== |
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Revision as of 05:16, 24 March 2024
Didymus the Musician (Greek: Δίδυμος) was a music theorist in Rome of the end of the 1st century BC or beginning of the 1st century AD, who combined elements of earlier theoretical approaches with an appreciation of the aspect of performance. Formerly assumed to be identical with the Alexandrian grammarian and lexicographer Didymus Chalcenterus, because Ptolemy and Porphyry referred to him as Didymus ho mousikos (the musician), classical scholars now believe that this Didymus was a younger grammarian and musician working in Rome at the time of Emperor Nero.[1] He was a predecessor of Ptolemy at the library of Alexandria. According to Andrew Barker,[2] his intention was to revive and produce contemporary performances of the music of Greek antiquity. The syntonic comma of 81/80 is sometimes called the comma of Didymus after him.[1]
Among his works was On the Difference between the Aristoxenians and the Pythagoreans (Περὶ τῆς διαφορᾶς τῶν Ἀριστοξενείων τε καὶ Πυθαγορείων).
Theory
We know of his theory only indirectly from the works of Porphyry and Ptolemy. There, one finds examples of his tetrachords as measured string lengths from which the following proportions can be calculated:
tetrachord
typeinterval
1st–2ndinterval
2nd–3rdinterval
3rd–4thdiatonic 16 / 15 10 / 9 9 / 8 chromatic 16 / 15 25 / 24 6 / 5 enharmonic 32 / 31 31 / 30 5 / 4
Like Archytas, he used a major third, but appears to have been the first to use it in the diatonic as the sum of the major (9:8) and minor (10:9) whole tones as for the proportions produced by 10 / 9 × 9 / 8 = 5 / 4 . The ratio of these whole tones 9 / 8 ⧸ 10 / 9 = 9 / 8 × 9 / 10 = 81 / 80 ; is the so-called syntonic comma, also referred to as Didymos' comma.[3][4]
References
- ^ a b Richter 1995, pp. 462–463.
- ^ Barker 1994, [page needed].
- ^ Chappell 1874, p. 204.
- ^ Hubbard 1910, p. 121.
Sources
- Barker, Andrew (1994). "Greek Musicologists in the Roman Empire". Apeiron. 27 (4). Walter de Gruyter GmbH: 53–74. doi:10.1515/apeiron.1994.27.4.53. ISSN 2156-7093. OCLC 8306313368. S2CID 170415282.
- Chappell, William (1874). "The History of Music (Art and science)". London: Chappell & Co – via HathiTrust Digital Library.
- Hubbard, W. L., ed. (1910). The American history and encyclopedia of music. Vol. 10. New York: Irving Squire. OCLC 1194188882. Archived from the original on 2022-02-22. Retrieved 2022-09-30. Reprinted ISBN 1-4179-0200-0
- Katz, Ruth; Dahlhaus, Carl (1987). Contemplating Music: Source Readings in the Aesthetics of Music. Pendragon. p. 30. ISBN 9780918728609.
- Richter, Lukas (1995) [1980]. "Didymus [Didymos ho mousikos]". In Sadie, Stanley; Grove, George (eds.). The New Grove Dictionary of Music and Musicians. London: Oxford University Press. pp. 462–463. doi:10.1093/gmo/9781561592630.article.07752. ISBN 0-333-23111-2. OCLC 1245646411.
