4096/4095: Difference between revisions

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 {{Infobox Interval
-| Ratio = 4096/4095
-| Monzo = 12 -2 -1 -1 0 -1
-| Cents = 0.42272
 | Name = schismina
-| Color name = sathurugu comma
+| Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma
-| FJS name = P1<sub>5,7,13</sub>
+| Comma = yes
 }}
-'''4096/4095''', the '''schismina''', is a [[superparticular]] [[ratio]] of about 0.42 cents. It is the difference between [[65/64]] and [[64/63]], and between [[1053/1024]] and [[36/35]].
+'''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 a [[Mersenne 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.
+== 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.
+[[Subgroup]]: 2.3.5.7.11.13
+[[Mapping]]: <br>
+{| class="right-all"
+|-
+| [⟨ || 1 || 0 || 0 || 0 || 0 || 12 || ],
+|-
+| ⟨ || 0 || 1 || 0 || 0 || 0 || -2 || ],
+|-
+| ⟨ || 0 || 0 || 1 || 0 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 1 || 0 || -1 || ],
+|-
+| ⟨ || 0 || 0 || 0 || 0 || 1 || 0 || ]]
+|}
+: 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, 9140cdef, 14463bcddeefff, 17786bccddeeefff }}
 == See also ==
@@ Line 14: / Line 36: @@
 * [[List of superparticular intervals]]
-[[Category:13-limit]]
+[[Category:Schisminic]]
-[[Category:Ratio]]
+[[Category:Mina]]
-[[Category:Unnoticeable comma]]
+[[Category:Commas with unknown etymology]]
-[[Category:Superparticular]]
-[[Category:Todo:expand]]