4096/4095: Difference between revisions

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}}

'''4096/4095''', the '''schismina''', is a [[13-limit]] [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between:

'''4096/4095''', the '''schismina''', is a [[13-limit]] [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between the [[64/63|septimal comma (64/63)]] and the [[65/64|wilsorma (65/64)]], and between the [[36/35|septimal quartertone (36/35)]] and the [[1053/1024|tridecimal quartertone (1053/1024)]]. It is also a [[Mersenne comma]].

* [[~~64/63~~]] ~~and~~ [[~~65/64~~]]

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.

* [[27/26]] and [[8505/~~8192]]~~

* [[36/35]] and [[1053/1024]]

* [[35/32]] and [[128/117]]

* [[39/32]] and [[128/105]]

* [[45/32]] and [[128/91]]

* [[13/8]] and [[512/315]]

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

~~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.

== Temperaments ==

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.

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.

[[Subgroup]]: 2.3.5.7.13

[[Subgroup]]: 2.3.5.7.11.13

[[Mapping]]: <br>

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|-

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

|-

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

|}

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

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

{{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~~ }}

{{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 }}

== See also ==

@@ Line 5: / Line 5: @@
 }}
-'''4096/4095''', the '''schismina''', is a [[13-limit]] [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between:
+'''4096/4095''', the '''schismina''', is a [[13-limit]] [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between the [[64/63|septimal comma (64/63)]] and the [[65/64|wilsorma (65/64)]], and between the [[36/35|septimal quartertone (36/35)]] and the [[1053/1024|tridecimal quartertone (1053/1024)]]. It is also a [[Mersenne comma]].
-* [[64/63]] and [[65/64]]
+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.
-* [[27/26]] and [[8505/8192]]
-* [[36/35]] and [[1053/1024]]
-* [[35/32]] and [[128/117]]
-* [[39/32]] and [[128/105]]
-* [[45/32]] and [[128/91]]
-* [[13/8]] and [[512/315]]
-It is also a [[Mersenne comma]], and the smallest superparticular ratio in the [[2.3.5.7.13 subgroup]] on which it is also a [[PIFE comma|PIFE-like comma]].
-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.
 == Temperaments ==
-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.
+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.
-[[Subgroup]]: 2.3.5.7.13
+[[Subgroup]]: 2.3.5.7.11.13
 [[Mapping]]: <br>
@@ Line 34: / Line 26: @@
 |-
 | ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]]
 |}
-: mapping generators: ~2, ~3, ~5, ~7
+: mapping generators: ~2, ~3, ~5, ~7, ~11
-{{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 }}
+{{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 }}
 == See also ==