4096/4095: Difference between revisions

Line 9:

The name lends itself to the general interval size measure knowns as the [[mina]]. In [[Sagittal notation]], 4096/4095 is the default comma represented by a mina or three [[tina]]s.

It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup.

It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup, and a [[PIFE comma|PIFE-like comma]].

== Temperaments ==

By tempering it out is defined the '''schisminic temperament''', which enables the [[schisminic chords]], the essentially tempered chords in the 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.

By tempering it out is defined the '''schisminic temperament''', which enables the [[schisminic chords]], the essentially tempered chords in the no-11 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.

[[Subgroup]]: 2.3.5.7~~.11~~.13

[[Subgroup]]: 2.3.5.7.13

[[Mapping]]: <br>

Line 26:

|-

| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],

|-

~~| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]]~~

|}

: mapping generators: ~2, ~3, ~5, ~7~~, ~11~~

: mapping generators: ~2, ~3, ~5, ~7

{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, ~~9140cdef~~, ~~14463bcddeefff~~, ~~17786bccddeeefff~~ }}

{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, 9140cdf, 14463bcddfff, 17786bccddfff }}

== See also ==

@@ Line 9: / Line 9: @@
 The name lends itself to the general interval size measure knowns as the [[mina]]. In [[Sagittal notation]], 4096/4095 is the default comma represented by a mina or three [[tina]]s.
-It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup.
+It is also the smallest superparticular ratio in the 2.3.5.7.13 subgroup, and a [[PIFE comma|PIFE-like comma]].
 == Temperaments ==
-By tempering it out is defined the '''schisminic temperament''', which enables the [[schisminic chords]], the essentially tempered chords in the 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.
+By tempering it out is defined the '''schisminic temperament''', which enables the [[schisminic chords]], the essentially tempered chords in the no-11 21-odd-limit. You may find a list of good equal temperaments that support this temperament below.
-[[Subgroup]]: 2.3.5.7.11.13
+[[Subgroup]]: 2.3.5.7.13
 [[Mapping]]: <br>
@@ Line 26: / Line 26: @@
 |-
 | ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
-|-
-| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]]
 |}
-: mapping generators: ~2, ~3, ~5, ~7, ~11
+: mapping generators: ~2, ~3, ~5, ~7
-{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, 9140cdef, 14463bcddeefff, 17786bccddeeefff }}
+{{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 84, 87, 118, 130, 183, 217, 224, 270, 494, 764, 935, 1012, 1236, 1506, 3236, 3323, 3817, 5323f, 9140cdf, 14463bcddfff, 17786bccddfff }}
 == See also ==