5120/5103: Difference between revisions

Line 4:

| Monzo = 10 -6 1 -1

| Cents = 5.75780

| Name = hemifamity, 7/5-kleisma

| Name = hemifamity, 5/7-kleisma

| Color name =

| FJS name = P157

Line 10:

}}

The '''hemifamity''' or '''7/5-kleisma''', '''5120/5103''', is a [[7-limit]] [[comma]] measuring about 5.8 cents. It is the difference between ~~the~~ small septimal tritone of [[7/5]] ~~and the~~ Pythagorean diminished fifth of [[~~1024~~/729]]. 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]].

The '''hemifamity''' or '''5/7-kleisma''', '''5120/5103''', 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.

@@ Line 4: / Line 4: @@
 | Monzo = 10 -6 1 -1
 | Cents = 5.75780
-| Name = hemifamity, <br>7/5-kleisma
+| Name = hemifamity, <br>5/7-kleisma
 | Color name =
 | FJS name = P1<sup>5</sup><sub>7</sub>
@@ Line 10: / Line 10: @@
 }}
-The '''hemifamity''' or '''7/5-kleisma''', '''5120/5103''', is a [[7-limit]] [[comma]] measuring about 5.8 cents. It is the difference between the small septimal tritone of [[7/5]] and the Pythagorean diminished fifth of [[1024/729]]. 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]].
+The '''hemifamity''' or '''5/7-kleisma''', '''5120/5103''', 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.