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).

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.

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 ==

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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).
-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.
+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 ==