5120/5103: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Ratio = 5120/5103

| Monzo = 10 -6 1 -1

| Cents = 5.75780

| Name = hemifamity comma, 5/7-kleisma

| Name = hemifamity comma, 5/7-kleisma

| Color name =

| FJS name = P157

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'''5120/5103''', the '''hemifamity comma''' or '''5/7-kleisma''', is a [[7-limit]] [[small comma]] measuring about 5.8 cents. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]].

Tempering it out leads to the rank-3 [[hemifamity family]], which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. Edos that temper it out include {{EDOs| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 239, 292, 391 }}, etc.

== Temperaments ==

Tempering it out leads to the rank-3 [[hemifamity family]], which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. Edos that temper it out include {{EDOs| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc.

== See also ==

* [[Hemifamity family]]

* [[Hemifamity family]], the rank-3 family where it is tempered out

* [[Hemifamity temperaments]]

* [[Hemifamity temperaments]], a collection of rank-2 temperaments where it is tempered out

* [[~~Comma~~]]

* [[Small comma]]

[[Category:7-limit]]

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 {{Infobox Interval
-| Icon =
 | Ratio = 5120/5103
 | Monzo = 10 -6 1 -1
 | Cents = 5.75780
-| Name = hemifamity comma, <br> 5/7-kleisma
+| Name = hemifamity comma, <br>5/7-kleisma
 | Color name =
 | FJS name = P1<sup>5</sup><sub>7</sub>
@@ Line 12: / Line 11: @@
 '''5120/5103''', the '''hemifamity comma''' or '''5/7-kleisma''', is a [[7-limit]] [[small comma]] measuring about 5.8 cents. It is the difference between [[7/5]] (small septimal tritone) and [[1024/729]] (Pythagorean diminished fifth), or between [[10/7]] (large septimal tritone) and [[729/512]] (Pythagorean augmented fourth). It is also the difference between [[15/14]] and [[2187/2048]], between [[21/20]] and [[256/243]], between [[80/63]] and [[81/64]], etc., hence, between the septimal comma of [[64/63]] and the syntonic comma of [[81/80]].
-Tempering it out leads to the rank-3 [[hemifamity family]], which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. Edos that temper it out include {{EDOs| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 239, 292, 391 }}, etc.
+== Temperaments ==
+Tempering it out leads to the rank-3 [[hemifamity family]], which splits the septimal quartertone [[36/35]] into two equal parts, each representing 81/80~64/63. Rank-2 temperaments that temper it out include [[hemififths]] and [[amity]], to name two. Edos that temper it out include {{EDOs| 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 145, 152, 239, 292, 391 }}, etc.
 == See also ==
-* [[Hemifamity family]]
+* [[Hemifamity family]], the rank-3 family where it is tempered out
-* [[Hemifamity temperaments]]
+* [[Hemifamity temperaments]], a collection of rank-2 temperaments where it is tempered out
-* [[Comma]]
+* [[Small comma]]
 [[Category:7-limit]]