Holdrian comma: Difference between revisions
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| Ratio = 2^{1/53} | | Ratio = 2^{1/53} | ||
| Cents = 22.6415 | | Cents = 22.6415 | ||
| Name = Holdrian comma, | | Name = Holdrian comma, Holder's comma, Arabian comma, 1 step of 53edo | ||
| Calc = 2^(1/53) | | Calc = 2^(1/53) | ||
| Comma = yes | | Comma = yes | ||
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The '''Holdrian comma''', also called '''Holder's comma''', rarely the '''Arabian comma''',<ref name=Touma>Habib Hassan Touma & Laurie Schwartz - ''The Music of the Arabs'' - p23 (1993) - ISBN=0-931340-88-8</ref> is a small [[interval]] of approximately 22.6415 [[cents]],<ref name=Touma/> equal to exactly one step of [[53edo]], or <math>\ \sqrt[53]{2\;}\ </math>. | The '''Holdrian comma''', also called '''Holder's comma''', rarely the '''Arabian comma''',<ref name=Touma>Habib Hassan Touma & Laurie Schwartz - ''The Music of the Arabs'' - p23 (1993) - ISBN=0-931340-88-8</ref> is a small [[interval]] of approximately 22.6415 [[cents]],<ref name=Touma/> equal to exactly one step of [[53edo]], or <math>\ \sqrt[53]{2\;}\ </math>. | ||
The name | The name ''[[comma]]'' describes its size and does not describe a compromise between intervals of any tuning system, since this interval is an irrational number. 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 == | == Historical origin == | ||
The origin of Holder's comma resides in 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 Pythagorean [[diatonic semitone]]s and a comma (the Pythagorean diatonic semitone consisted in two [[diaschisma (Ancient Greek music)|diaschismata]]<ref group="note">different to modern-day [[diaschisma|diaschismata]].</ref>, 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>) and believed that in the [[Pythagorean tuning]] the tone could be divided in nine commas, four of which forming the Pythagorean diatonic semitone and five the Pythagorean [[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. | |||
The origin of Holder's comma resides in | |||
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". | ||
== Mercator's comma, | == Mercator's comma, Mercator's old comma, and the Holdrian comma == | ||
'''Mercator's old comma''' is a name sometimes used for a closely related interval because of its association with Nicholas Mercator. | '''Mercator's old comma''' is a name sometimes used for a closely related interval because of its association with Nicholas Mercator. | ||
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William Holder, for whom the ''Holdrian'' comma is named, favored this latter unit because the intervals of 53edo are closer to [[just intonation]] than to [[55edo]]. Thus Mercator's old comma and the Holdrian comma are two distinct but nearly equal intervals. | William Holder, for whom the ''Holdrian'' comma is named, favored this latter unit because the intervals of 53edo are closer to [[just intonation]] than to [[55edo]]. Thus Mercator's old comma and the Holdrian comma are two distinct but nearly equal intervals. | ||
There is another comma named | There is another comma named ''[[Mercator's comma]]'' which receives much more usage in modern musical tuning. It a small comma of 3.615 cents which is the amount by which 53 [[perfect fifth]]s exceed 31 [[octave]]s, in other words (3/2)<sup>53</sup>/2<sup>31</sup>. It has its own dedicated article. | ||
== See also == | == See also == | ||
* [[Historical temperaments]] | * [[Historical temperaments]] | ||
* [[Interval size measure]]: both the Holdrian comma and Mercator's old comma are examples of this | |||
== Notes == | == Notes == | ||
<references group="note"/> | |||
== References == | |||
<references/> | |||
[[Category:53edo]] | [[Category:53edo]] | ||
[[Category:Small commas]] | [[Category:Small commas]] | ||
[[Category:Commas named after individuals]] | [[Category:Commas named after individuals]] | ||