5120/5103: Difference between revisions

Line 12:

'''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.

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, 118, 140, 239, 292, 391}}, etc.

== See also ==

@@ Line 12: / Line 12: @@
 '''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.
+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, 118, 140, 239, 292, 391}}, etc.
 == See also ==