4096/4095 - Revision history

FloraC: + link

2026-05-04T18:41:59Z

+ link

← Older revision		Revision as of 18:41, 4 May 2026
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	== See also ==		== See also ==
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]
			* [[Tridecimal schisma]] (disambiguation page)

	== References ==		== References ==

FloraC: + factorization

2026-03-21T10:12:47Z

+ factorization

← Older revision		Revision as of 10:12, 21 March 2026
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	'''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]].		'''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]].

	It is also the smallest superparticular ratio in the [[2.3.5.7.13 subgroup]].		It factors into ([[6656/6655]])⋅([[10648/10647]]). It is also the smallest superparticular ratio in the [[2.3.5.7.13 subgroup]].

	== Temperaments ==		== Temperaments ==

FloraC: /* Temperaments */ note the rank

2026-03-04T08:00:41Z

Temperaments: note the rank

← Older revision		Revision as of 08:00, 4 March 2026
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	== Temperaments ==		== Temperaments ==
	[[Tempering out]] this comma in the full 13-limit defines the '''minismic''' temperament, or in the 2.3.5.7.13 subgroup, the '''minic''' temperament. In either case, it equates the tridecimal quartertone with the septimal one, and enables the [[minismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. You may find a list of good [[equal temperament]]s that [[support]] these temperaments below.		[[Tempering out]] this comma in the full 13-limit defines the rank-5 '''minismic''' temperament, or in the 2.3.5.7.13 subgroup, the rank-4 '''minic''' temperament. In either case, it equates the tridecimal quartertone with the septimal one, and enables the [[minismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. You may find a list of good [[equal temperament]]s that [[support]] these temperaments below.

	=== Minic ===		=== Minic ===

FloraC: /* Temperaments */ - typo

2026-03-04T07:58:33Z

Temperaments: - typo

← Older revision		Revision as of 07:58, 4 March 2026
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	[[Optimal tuning]]s:		[[Optimal tuning]]s:
	: [[WE]]: ~2 = 1199.9720{{c}}, ~3/2 = 701.9948{{c}}, ~5/4 = 386.3824{{c}}, ~7/4 = 968.9004{{c}}, ~11/8 = ~551.4020{{c}}		: [[WE]]: ~2 = 1199.9720{{c}}, ~3/2 = 701.9948{{c}}, ~5/4 = 386.3824{{c}}, ~7/4 = 968.9004{{c}}, ~11/8 = 551.4020{{c}}
	: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0114{{c}}, ~5/4 = 386.3886{{c}}, ~7/4 = 968.9218{{c}}, ~11/8 = 551.3984{{c}}		: [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0114{{c}}, ~5/4 = 386.3886{{c}}, ~7/4 = 968.9218{{c}}, ~11/8 = 551.3984{{c}}

FloraC: Expand for the no-11 subgroup temp

2026-03-04T07:47:55Z

Expand for the no-11 subgroup temp

@@ Line 4: / Line 4: @@
 | Comma = yes
 }}
 '''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]].
@@ Line 10: / Line 9: @@
 == Temperaments ==
-Tempering out this comma in the full 13-limit defines 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.
+[[Tempering out]] this comma in the full 13-limit defines the '''minismic''' temperament, or in the 2.3.5.7.13 subgroup, the '''minic''' temperament. In either case, it equates the tridecimal quartertone with the septimal one, and enables the [[minismic chords]], the [[essentially tempered chord]]s in the [[21-odd-limit]]. You may find a list of good [[equal temperament]]s that [[support]] these temperaments below.
 [[Subgroup]]: 2.3.5.7.11.13
@@ Line 29: / Line 53: @@
 : 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 }}
+[[Optimal tuning]]s:
 == Etymology ==

Tristanbay: /* Temperaments */Simpler wording

2026-03-04T00:02:10Z

Temperaments: Simpler wording

← Older revision		Revision as of 00:02, 4 March 2026
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	== Temperaments ==		== Temperaments ==
	~~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.		Tempering out this comma in the full 13-limit defines 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		[[Subgroup]]: 2.3.5.7.11.13

FloraC: Name (see talk)

2026-03-03T09:23:05Z

Name (see talk)

← Older revision		Revision as of 09:23, 3 March 2026
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	{{Infobox Interval		{{Infobox Interval
	\| Name = ~~schismina~~		\| Name = minisma, minic comma
	\| Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma		\| Color name = s3urg1, sathurugu 1sn, <br>Sathurugu comma
	\| Comma = yes		\| 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 ==		== 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		[[Subgroup]]: 2.3.5.7.11.13
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	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]		\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| ]]
	\|}		\|}

	: mapping generators: ~2, ~3, ~5, ~7, ~11		: 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 }}		{{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 ==		== See also ==
	* [[Unnoticeable comma]]
	* [[List of superparticular intervals]]		* [[List of superparticular intervals]]

	[[Category:~~Schisminic~~]]		== References ==
			<references/>

			[[Category:Minismic]]
	[[Category:Mina]]		[[Category:Mina]]
	[[Category:Commas ~~with unknown etymology~~]]		[[Category:Commas named after their interval size]]

FloraC: Restore an old descriptive name

2026-02-22T15:11:03Z

Restore an old descriptive name

← Older revision		Revision as of 15:11, 22 February 2026
Line 5:		Line 5:
	}}		}}

	'''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]].		'''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]].

	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.		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.

FloraC: Most of these relations aren't notable at all. Also do not just appropriate a name for a different temp

2026-02-22T15:09:04Z

Most of these relations aren't notable at all. Also do not just appropriate a name for a different temp

← Older revision		Revision as of 15:09, 22 February 2026
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 ==		== 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>		[[Mapping]]: <br>
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	\|-		\|-
	\| ⟨ \|\| 0 \|\| 0 \|\| 0 \|\| 1 \|\| 0 \|\| -1 \|\| ],		\| ⟨ \|\| 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 ==		== See also ==

Eufalesio: More differences!

2026-02-22T12:52:15Z

More differences!

← Older revision		Revision as of 12:52, 22 February 2026
Line 5:		Line 5:
	}}		}}

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

			* [[64/63]] and [[65/64]]
			* [[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.		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, and a [[PIFE comma\|PIFE-like comma]].~~

	== Temperaments ==		== Temperaments ==