4096/4095: Difference between revisions

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{{Infobox Interval

| Name = ~~schismina~~

| Name = minisma, minic comma

| Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma

| Comma = yes

}}

'''4096/4095''', the '''~~schismina~~''', also described as the ''tridecimal schisma'', 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]].

'''4096/4095''', the '''minisma''' or '''minic comma''', also described as the ''tridecimal schisma'' or ''tridecimal schismina''<ref>[https://sagittal.org/sagittal.pdf Sagittal – A Microtonal Notation System] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>, is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] [[comma]] 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]].

~~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.

== 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 out this comma in the full 13-limit is defined the '''minismic''' temperament, which enables the [[minismic 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

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| ⟨ || 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 }}

== Etymology ==

The names ''minisma'' and ''minic comma'' were given by [[Flora Canou]] in 2026 after the general interval size measure knowns as the ''[[mina]]'', because 4096/4095 is the default comma represented by a mina (or three [[tina]]s) in [[Sagittal notation]]. ''Mina'' is a clipping of ''schismina'', which describes a range of commas in Sagittal notation, and in turn comes from ''schisma'' (the interval region) + -in (diminutive suffix). [[Eufalesio]] proposed ''trinyblisma'', for the denominator is the largest integer that can be written in 3 {{w|nibble|nybbles}} (1.5 bytes).

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

[[Category:~~Schisminic~~]]

== References ==

[[Category:Minismic]]

[[Category:Mina]]

[[Category:Commas ~~with unknown etymology~~]]

[[Category:Commas named after their interval size]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Name = schismina
+| Name = minisma, minic comma
 | Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma
 | Comma = yes
 }}
-'''4096/4095''', the '''schismina''', also described as the ''tridecimal schisma'', 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]].
+'''4096/4095''', the '''minisma''' or '''minic comma''', also described as the ''tridecimal schisma'' or ''tridecimal schismina''<ref>[https://sagittal.org/sagittal.pdf Sagittal – A Microtonal Notation System] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>, is an [[unnoticeable comma|unnoticeable]] [[13-limit]] [[superparticular]] [[comma]] 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]].
-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.
 == 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 out this comma in the full 13-limit is defined the '''minismic''' temperament, which enables the [[minismic 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
@@ Line 29: / Line 27: @@
 | ⟨ || 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 }}
+== Etymology ==
+The names ''minisma'' and ''minic comma'' were given by [[Flora Canou]] in 2026 after the general interval size measure knowns as the ''[[mina]]'', because 4096/4095 is the default comma represented by a mina (or three [[tina]]s) in [[Sagittal notation]]. ''Mina'' is a clipping of ''schismina'', which describes a range of commas in Sagittal notation, and in turn comes from ''schisma'' (the interval region) + -in (diminutive suffix). [[Eufalesio]] proposed ''trinyblisma'', for the denominator is the largest integer that can be written in 3 {{w|nibble|nybbles}} (1.5 bytes).
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:Schisminic]]
+== References ==
+<references/>
+[[Category:Minismic]]
 [[Category:Mina]]
-[[Category:Commas with unknown etymology]]
+[[Category:Commas named after their interval size]]