Holdrian comma: Difference between revisions
-"in modern music" section. There's lots of 53edo music and there's no reason why Juhan Puhm needs to be singled out. |
That "diaschisma" isn't the diaschisma in our modern sense |
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== Historical origin == | == Historical origin == | ||
The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Anicius Manlius Severinus Boethius]]). According to Boethius, [[Pythagoras of Samos |Pythagoras]]' disciple [[Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma]] | The origin of Holder's comma resides in the fact that the [[Ancient Greek]]s (or at least to the Roman [[Anicius Manlius Severinus Boethius]]). According to Boethius, [[Pythagoras of Samos |Pythagoras]]' disciple [[Philolaus of Croton]] would have said that the tone consisted in two [[diatonic semitone]]s and a comma; the diatonic semitone consisted in two [[diaschisma (Ancient Greek music)|diaschismata]], each formed of two commas.<ref>Anicius Manlius Severinus Boethius - ''De institutione musica'' - book 3 ch8</ref><ref>J. Murray Barbour - ''Tuning and Temperament: A historical survey'' (1951) - p123</ref>believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of ''5 tones + 2 diatonic'' semitones, ''5 × 9 + 2 × 4 = 53 equal'' commas. | ||
Holder<ref name=Holder-1731>William Holder - ''A Treatise of the Natural Grounds, and Principles of Harmony'' (1731) - ed3 p79</ref> attributes the division of the octave in 53 equal parts to [[Nicholas Mercator]]: "The late ''Nicholas Mercator'', a Modest Person, and a Learned and Judicious Mathematician, in a Manuscript of his, of which I have had a Sight."<ref name=Holder-1731/> who himself had proposed that 1/53 of the octave be named the "artificial comma". | Holder<ref name=Holder-1731>William Holder - ''A Treatise of the Natural Grounds, and Principles of Harmony'' (1731) - ed3 p79</ref> attributes the division of the octave in 53 equal parts to [[Nicholas Mercator]]: "The late ''Nicholas Mercator'', a Modest Person, and a Learned and Judicious Mathematician, in a Manuscript of his, of which I have had a Sight."<ref name=Holder-1731/> who himself had proposed that 1/53 of the octave be named the "artificial comma". | ||
Revision as of 05:02, 6 November 2024
| Interval information |
Holder’s comma,
Arabian comma,
1 step of 53edo
The Holdrian comma, also called Holder's comma, rarely the Arabian comma,[1] is a small interval of approximately 22.6415 cents,[1] equal to exactly one step of 53edo, or [math]\displaystyle{ \ \sqrt[53]{2\;}\ }[/math].
The name "comma", however, is technically misleading, since this interval is an irrational number and it does not describe a compromise between intervals of any tuning system. The interval gets the name "comma" because it is a close approximation of several commas, most notably the syntonic comma (21.51 cents), which was widely used as a unit of tonal measurement during William Holder’s time.
Historical origin
The origin of Holder's comma resides in the fact that the Ancient Greeks (or at least to the Roman Anicius Manlius Severinus Boethius). According to Boethius, Pythagoras' disciple Philolaus of Croton would have said that the tone consisted in two diatonic semitones and a comma; the diatonic semitone consisted in two diaschismata, each formed of two commas.[2][3]believed that in the Pythagorean tuning the tone could be divided in nine commas, four of which forming the diatonic semitone and five the chromatic semitone. If all these commas are exactly of the same size, there results an octave of 5 tones + 2 diatonic semitones, 5 × 9 + 2 × 4 = 53 equal commas.
Holder[4] attributes the division of the octave in 53 equal parts to Nicholas Mercator: "The late Nicholas Mercator, a Modest Person, and a Learned and Judicious Mathematician, in a Manuscript of his, of which I have had a Sight."[4] who himself had proposed that 1/53 of the octave be named the "artificial comma".
See also
Notes
- ↑ 1.0 1.1 Habib Hassan Touma & Laurie Schwartz - The Music of the Arabs - p23 (1993) - ISBN=0-931340-88-8
- ↑ Anicius Manlius Severinus Boethius - De institutione musica - book 3 ch8
- ↑ J. Murray Barbour - Tuning and Temperament: A historical survey (1951) - p123
- ↑ 4.0 4.1 William Holder - A Treatise of the Natural Grounds, and Principles of Harmony (1731) - ed3 p79