3136/3125: Difference between revisions
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| Monzo = 6 0 -5 2 | | Monzo = 6 0 -5 2 | ||
| Cents = 6.0832 | | Cents = 6.0832 | ||
| Name = hemimean comma, didacus comma | | Name = hemimean comma, <br>didacus comma | ||
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'''3136/3125''', the '''hemimean comma''', or the '''didacus comma''' is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between five [[5/4]] | '''3136/3125''', the '''hemimean comma''', or the '''didacus comma''' is a [[7-limit]] [[comma]] measuring about 6.1 cents. It is the difference between five [[5/4|classic major thirds (5/4)]] and two [[7/4|subminor sevenths (7/4)]]; it is also the difference between [[126/125]] (septimal semicomma), and [[225/224]] (septimal kleisma). | ||
In the 2.5.7 [[subgroup]], tempering out the comma leads to the rank-2 2.5.7 subgroup temperament [[ | == Temperaments == | ||
In the 2.5.7 [[subgroup]], tempering out the comma leads to the rank-2 2.5.7 subgroup temperament [[Hemimean clan #Didacus|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 [[81/80|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 {{EDOs| 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 {{EDOs| 19, 25, 31, 37 }}, which temper out both 126/125 and 225/224 on the 2.9.5.7 subgroup. | |||
== See also == | == See also == | ||
* [[Hemimean family]] | * [[Hemimean family]], the rank-3 family where it is tempered out | ||
* [[Hemimean clan]] | * [[Hemimean clan]], the rank-2 clan where it is tempered out | ||
* [[ | * [[Small comma]] | ||
[[Category:7-limit]] | [[Category:7-limit]] | ||
Revision as of 17:26, 5 April 2021
| Interval information |
didacus comma
3136/3125, the hemimean comma, or the didacus comma is a 7-limit comma measuring about 6.1 cents. It is the difference between five classic major thirds (5/4) and two subminor sevenths (7/4); it is also the difference between 126/125 (septimal semicomma), and 225/224 (septimal kleisma).
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 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
- Small comma