3136/3125: Difference between revisions
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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]] major thirds and two [[7/4]] subminor sevenths; it is also the difference between [[126/125]] (septimal semicomma), and [[225/224]] (septimal kleisma). | '''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]] major thirds and two [[7/4]] subminor sevenths; 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 [[subgroup temperaments#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), | In the 2.5.7 [[subgroup]], tempering out the comma leads to the rank-2 2.5.7 subgroup temperament [[subgroup temperaments#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|hemimean temperament]], which splits the [[81/80|syntonic comma]] into two equal parts, each representing 126/125~225/224. It also splits [[5/4]] (classic major third) 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 == | ||
Revision as of 16:44, 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 5/4 major thirds and two 7/4 subminor sevenths; 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 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 temperament, which splits the syntonic comma into two equal parts, each representing 126/125~225/224. It also splits 5/4 (classic major third) 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.