Nanisma - Revision history

FloraC: - "xenharmonic bridge" (term doesn't quite catch on). Update data

2026-01-18T09:32:09Z

- "xenharmonic bridge" (term doesn't quite catch on). Update data

← Older revision		Revision as of 09:32, 18 January 2026
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	The '''nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is an [[unnoticeable comma\|unnoticeable]] [[7-limit]] (also [[2.3.7 subgroup\|2.3.7-subgroup]]) [[comma]] measuring about 0.189 [[cent]]s. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor seventh of ratio [[7/4]].		The '''nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is an [[unnoticeable comma\|unnoticeable]] [[7-limit]] (also [[2.3.7 subgroup\|2.3.7-subgroup]]) [[comma]] measuring about 0.189 [[cent]]s. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor seventh of ratio [[7/4]].

	The nanisma ~~is considered as a 3=7 [[xenharmonic bridge]]. It~~ also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and ~~also~~ the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. ~~It can also be thought~~ of as the difference between [[Mercator's comma]] and the [[garischisma]].		The nanisma also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. In terms of commas, it is the difference between [[Mercator's comma]] and the [[garischisma]].

	== Temperaments ==		== Temperaments ==
	The nanisma is tempered out in such notable [[edo]]s as {{EDOs\| 306~~, 612~~, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.		The nanisma is tempered out in such notable [[edo]]s as {{EDOs\| 306, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

	=== Nanic ===		=== Nanic ===
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	{{Mapping\|legend=1\| 1 0 0 109 \| 0 1 0 -67 \| 0 0 1 0 }}		{{Mapping\|legend=1\| 1 0 0 109 \| 0 1 0 -67 \| 0 0 1 0 }}
			: mapping generators: ~2, ~3, ~5

	: ~~sval mapping generators~~: ~2, ~3, ~5		[[Optimal tuning]]s:
			* [[WE]]: ~2 = 1199.999111{{c}}, ~3/2 = 701.957264{{c}}, ~5/4 = 386.315493{{c}}
	[[~~Optimal tuning~~]] ([[~~CTE~~]]): ~2 = 1200.~~0000~~, ~3/2 = 701.~~9578~~, ~5/4 = 386.~~3137~~		: [[error map]]: {{val\| -0.0009 +0.0014 -0.0000 +0.0001 }}
			* [[CWE]]: ~2 = 1200.000000{{c}}, ~3/2 = 701.957796{{c}}, ~5/4 = 386.315103{{c}}
			: error map: {{val\| 0.0000 +0.0028 +0.0014 +0.0018 }}

	{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}		{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}

	[[Badness]]: ~~6.09 × 10<sup>-3</sup>~~		[[Badness]] (Sintel): TBD

	== Etymology ==		== Etymology ==

FloraC: -duplicate data

2025-03-16T15:53:00Z

-duplicate data

← Older revision		Revision as of 15:53, 16 March 2025
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	\| Comma = yes		\| Comma = yes
	}}		}}
	'''~~Nanisma~~''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is ~~a no~~-~~five~~ [[7-~~limit~~]] [[~~unnoticeable~~ comma]] measuring about 0.189 [[cent]]s ~~in size~~. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor~~-7th~~ of ratio [[7/4]].		The '''nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is an [[unnoticeable comma\|unnoticeable]] [[7-limit]] (also [[2.3.7 subgroup\|2.3.7-subgroup]]) [[comma]] measuring about 0.189 [[cent]]s. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor seventh of ratio [[7/4]].

	The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[garischisma]].		The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[garischisma]].

	== Temperaments ==		== Temperaments ==
	The nanisma is tempered out in such notable ~~edos~~ as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.		The nanisma is tempered out in such notable [[edo]]s as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

			=== Nanic ===
			See [[Very high accuracy temperaments #Nanic]].

	=== Nanismic ===		=== Nanismic ===
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	: sval mapping generators: ~2, ~3, ~5		: sval mapping generators: ~2, ~3, ~5

	[[Optimal tuning]] ([[CTE]]): ~2 = ~~1\1~~, ~3/2 = 701.9578, ~5/4 = 386.3137		[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9578, ~5/4 = 386.3137

	{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}		{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}

	[[Badness]]: 6.09 × 10<sup>-3</sup>		[[Badness]]: 6.09 × 10<sup>-3</sup>

	~~=== Nanic ===~~
	~~[[Subgroup]]: 2.3.7~~

	~~[[Comma list]]: {{monzo\| 109 -67 -1 }}~~

	~~{{Mapping\|legend=2\| 1 0 109 \| 0 1 -67 }}~~

	~~: sval mapping generators: ~2, ~3~~

	~~[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578~~

	~~{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}~~

	~~[[Badness]]: 0.0138~~

	== Etymology ==		== Etymology ==
	This comma was named by [[Margo Schulter]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38852.html#38854 Yahoo! Tuning Group \| ''Proposal: a high-order septimal schisma'']</ref>.		This comma was named by [[Margo Schulter]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38852.html#38854 Yahoo! Tuning Group \| ''Proposal: a high-order septimal schisma'']</ref>.

	~~== See also ==~~
	* [[Unnoticeable comma]]

	== External links ==		== External links ==

BudjarnLambeth at 23:40, 3 November 2024

2024-11-03T23:40:12Z

← Older revision		Revision as of 23:40, 3 November 2024
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	[[Category:Nanismic]]		[[Category:Nanismic]]
	[[Category:Commas ~~named after individuals~~]]		[[Category:Commas with unknown etymology]]

BudjarnLambeth at 23:38, 3 November 2024

2024-11-03T23:38:40Z

← Older revision		Revision as of 23:38, 3 November 2024
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	[[Category:Nanismic]]		[[Category:Nanismic]]
			[[Category:Commas named after individuals]]

AthiTrydhen at 06:56, 4 April 2024

2024-04-04T06:56:41Z

← Older revision		Revision as of 06:56, 4 April 2024
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	'''Nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].		'''Nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].

	The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[~~septimal schisma~~]].		The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[garischisma]].

	== Temperaments ==		== Temperaments ==

AthiTrydhen at 06:56, 4 April 2024

2024-04-04T06:56:15Z

← Older revision		Revision as of 06:56, 4 April 2024
Line 7:		Line 7:
	'''Nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].		'''Nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].

	The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]].		The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]]. It can also be thought of as the difference between [[Mercator's comma]] and the [[septimal schisma]].

	== Temperaments ==		== Temperaments ==

Francium: Added color name

2023-09-08T05:58:04Z

Added color name

← Older revision		Revision as of 05:58, 8 September 2023
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	\| Monzo = 109 -67 0 -1		\| Monzo = 109 -67 0 -1
	\| Name = nanisma		\| Name = nanisma
			\| Color name = s<sup>10</sup>r7, quinbisaru 7th
	\| Comma = yes		\| Comma = yes
	}}		}}

FloraC: Normalize the mapping; +naming

2023-06-05T11:17:25Z

Normalize the mapping; +naming

← Older revision		Revision as of 11:17, 5 June 2023
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	[[Comma list]]: {{monzo\| 109 -67 0 -1 }}		[[Comma list]]: {{monzo\| 109 -67 0 -1 }}

	{{Mapping\|legend=1\| 1 0 0 109 \| 0 -1 0 67 \| 0 0 1 0 }}		{{Mapping\|legend=1\| 1 0 0 109 \| 0 1 0 -67 \| 0 0 1 0 }}

	: sval mapping generators: ~2, ~3, ~5		: sval mapping generators: ~2, ~3, ~5
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	[[Comma list]]: {{monzo\| 109 -67 -1 }}		[[Comma list]]: {{monzo\| 109 -67 -1 }}

	{{Mapping\|legend=2\| 1 0 109 \| 0 -1 67 }}		{{Mapping\|legend=2\| 1 0 109 \| 0 1 -67 }}

	: sval mapping generators: ~2, ~3		: sval mapping generators: ~2, ~3
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	[[Badness]]: 0.0138		[[Badness]]: 0.0138

			== Etymology ==
			This comma was named by [[Margo Schulter]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_38852.html#38854 Yahoo! Tuning Group \| ''Proposal: a high-order septimal schisma'']</ref>.

	== See also ==		== See also ==
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	== External links ==		== External links ==
	* [http://tonalsoft.com/enc/n/nanisma.aspx Tonalsoft Encyclopedia\| ''Nanisma'']		* [http://tonalsoft.com/enc/n/nanisma.aspx Tonalsoft Encyclopedia\| ''Nanisma'']

			== Notes ==

	[[Category:Nanismic]]		[[Category:Nanismic]]

FloraC at 07:58, 2 June 2023

2023-06-02T07:58:38Z

← Older revision		Revision as of 07:58, 2 June 2023
Line 8:		Line 8:
	The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]].		The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]].

	== ~~Temperament~~ ==		== Temperaments ==
	The nanisma is tempered out in such notable edos as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.		The nanisma is tempered out in such notable edos as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the '''nanismic temperament''', in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

	=== Nanismic ===		=== Nanismic ===

FloraC: Expansion

2023-06-02T07:49:31Z

Expansion

← Older revision		Revision as of 07:49, 2 June 2023
Line 4:		Line 4:
	\| Comma = yes		\| Comma = yes
	}}		}}
	'''Nanisma''' (~~[[monzo]]:~~ {{monzo\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].		'''Nanisma''' ({{monzo\|legend=1\| 109 -67 0 -1 }}) is a no-five [[7-limit]] [[unnoticeable comma]] measuring about 0.189 [[cent]]s in size. It is the tiny interval between the pythagorean ratio {{monzo\| 107 -67 }} and the harmonic minor-7th of ratio [[7/4]].

	The nanisma is considered as a 3=7 xenharmonic-bridge. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]].		The nanisma is considered as a 3=7 [[xenharmonic bridge]]. It also describes the difference between {{monzo\| 108 -68 }} (a stack of four [[17-comma]]s) and the septimal minor third of ratio [[7/6]], and also the difference between {{monzo\| -109 69 }} and the wide septimal major third of ratio [[9/7]].

	== Temperament ==		== Temperament ==
	The nanisma is tempered out in such notable edos as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.		The nanisma is tempered out in such notable edos as {{EDOs\| 306, 612, 1277, 1583, 2860, 4137, 4802, 5414, 6079, 6691, 11493, 12105, and 12770 }}, leading to the nanismic temperament, in which sixty-seven fifths make up a septimal whole tone [[8/7]] with octave reduction.

	=== No-~~five nanismic~~ (1277~~&2860)~~ ===		=== Nanismic ===
			[[Subgroup]]: 2.3.5.7

			[[Comma list]]: {{monzo\| 109 -67 0 -1 }}

			{{Mapping\|legend=1\| 1 0 0 109 \| 0 -1 0 67 \| 0 0 1 0 }}

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

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578, ~5/4 = 386.3137

			{{Optimal ET sequence\|legend=1\| 53, 147d, 200, 253, 306c, 359, 412, 506d, 559, 612, 1277, 1889, 3525, 4137, 4190, 4802, 5414, 6079, 6691, 18184, 24875, 92809, 117684, 142559 }}

			[[Badness]]: 6.09 × 10<sup>-3</sup>

			=== Nanic ===
	[[Subgroup]]: 2.3.7		[[Subgroup]]: 2.3.7

	[[Comma list]]: {{monzo\| 109 -67 -1 }}		[[Comma list]]: {{monzo\| 109 -67 -1 }}

	~~[[Sval]] [[mapping]]: [~~{{~~val~~\| 1 ~~2 -25 }}, {{val~~\| 0 -1 67 }}]		{{Mapping\|legend=2\| 1 0 109 \| 0 -1 67 }}

			: sval mapping generators: ~2, ~3

			[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9578

	[[Optimal ~~tuning]] ([[POTE]]): ~3/2~~ = ~~701.9578~~		{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}

	~~{{Optimal ET sequence\|legend=1\| 53, 200, 253, 306, 665, 971, 1277, 4137, 5414, 6691, 7968 }}~~		[[Badness]]: 0.0138

	== See also ==		== See also ==