5120/5103: Difference between revisions
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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]]. | '''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 | 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. | ||
== See also == | == See also == | ||
Revision as of 12:01, 7 November 2021
| Interval information |
5/7-kleisma
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 29, 34, 41, 46, 53, 58, 87, 94, 99, 111, 140, 239, 292, 391, etc.