3136/3125: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Ratio = 3136/3125 | | Ratio = 3136/3125 | ||
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'''3136/3125''', the '''hemimean comma''' or '''didacus comma''', is a [[7-limit]] [[small comma]] measuring about 6.1{{cent}}. It is the difference between five classic major thirds ([[5/4]]) and two subminor sevenths ([[7/4]]); it is also the difference between the septimal semicomma ([[126/125]]) and the septimal kleisma ([[225/224]]). | |||
'''3136/3125''', the '''hemimean comma''' | |||
== Temperaments == | == Temperaments == | ||
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* [[Hemimean family]], the rank-3 family where it is tempered out | * [[Hemimean family]], the rank-3 family where it is tempered out | ||
* [[Hemimean clan]], the rank-2 clan where it is tempered out | * [[Hemimean clan]], the rank-2 clan where it is tempered out | ||
[[Category:7-limit]] | [[Category:7-limit]] | ||
[[Category:Small commas]] | [[Category:Small commas]] | ||
[[Category:Hemimean]] | [[Category:Hemimean]] | ||
Revision as of 16:15, 7 April 2022
| Interval information |
didacus comma
3136/3125, the hemimean comma or didacus comma, is a 7-limit small comma measuring about 6.1 ¢. It is the difference between five classic major thirds (5/4) and two subminor sevenths (7/4); it is also the difference between the septimal semicomma (126/125) and the septimal kleisma (225/224).
Temperaments
In the 2.5.7 subgroup, tempering out the comma leads to the rank-2 2.5.7 subgroup temperament didacus (a variant of hemithirds without a mapping for 3) with a generator of 28/25. In the full 7-limit (2.3.5.7), tempering it out leads to the rank-3 hemimean family of temperaments, which splits the syntonic comma into two equal parts, each representing 126/125~225/224. It also splits 5/4 into two equal parts, each representing 28/25. Typical edos tempering out the comma include 68, 80, 87, 99, 111, 118 and 130, and all of them tune both 126/125 and 225/224 to a single step. Smaller edos that temper out the comma are 19, 25, 31, 37, which temper out both 126/125 and 225/224, thus also 81/80, on the 2.9.5.7 subgroup.
See also
- Hemimean family, the rank-3 family where it is tempered out
- Hemimean clan, the rank-2 clan where it is tempered out