3136/3125: Difference between revisions

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== 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.

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, thus also 81/80, on the 2.9.5.7 subgroup.

== See also ==

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 == 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.
+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, thus also 81/80, on the 2.9.5.7 subgroup.
 == See also ==