3136/3125: Difference between revisions

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| Monzo = 6 0 -5 2

| Cents = 6.0832

| Name = hemimean comma, didacus comma

| Name = hemimean comma, <br>didacus comma

| Color name =

| FJS name =

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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|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 [[~~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.

== 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 ==

* [[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

* [[~~Comma~~]]

* [[Small comma]]

[[Category:7-limit]]

@@ Line 4: / Line 4: @@
 | Monzo = 6 0 -5 2
 | Cents = 6.0832
-| Name = hemimean comma, didacus comma
+| Name = hemimean comma, <br>didacus comma
 | Color name =
 | FJS name =
@@ Line 10: / Line 10: @@
 }}
-'''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|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 [[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.
+== 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 ==
-* [[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
-* [[Comma]]
+* [[Small comma]]
 [[Category:7-limit]]