Amity - Revision history

FloraC: Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

2026-06-06T12:39:44Z

Text replacement - "Category:Hemifamity temperaments" to "Category:Aberschismic temperaments"

← Older revision		Revision as of 12:39, 6 June 2026
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	[[Category:Amity family]]		[[Category:Amity family]]
	[[Category:Ragismic microtemperaments]]		[[Category:Ragismic microtemperaments]]
	[[Category:~~Hemifamity~~ temperaments]]		[[Category:Aberschismic temperaments]]

FloraC at 08:54, 9 February 2026

2026-02-09T08:54:53Z

← Older revision		Revision as of 08:54, 9 February 2026
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	\| Edo join 1 = 46 \| Edo join 2 = 53		\| Edo join 1 = 46 \| Edo join 2 = 53
	\| Mapping = 1; -5 -13 17		\| Mapping = 1; -5 -13 17
	\| ~~Generator~~ = 243/200		\| Generators = 243/200
	\| ~~Generator~~ tuning = 339.4		\| Generators tuning = 339.4
	\| Optimization method = CWE		\| Optimization method = CWE
	\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]		\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]

FloraC: Cleanup on infobox

2026-02-09T08:54:24Z

Cleanup on infobox

← Older revision		Revision as of 08:54, 9 February 2026
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	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = [[1600000/1594323]] (2.3.5); <br>[[4375/4374]], [[5120/5103]] (2.3.5.7)		\| Comma basis = [[1600000/1594323]] (2.3.5); <br>[[4375/4374]], [[5120/5103]] (2.3.5.7)
			\| Edo join 1 = 46 \| Edo join 2 = 53
			\| Mapping = 1; -5 -13 17
	\| Generator = 243/200		\| Generator = 243/200
	\| ~~Mapping~~ = 1; ~~-5 -13 17~~		\| Generator tuning = 339.4
			\| Optimization method = CWE
			\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]
	\| Pergen = (P8, cP4/5)		\| Pergen = (P8, cP4/5)
	\| Color name = Saquinyoti		\| Color name = Saquinyoti
	~~\| Edo join 1 = 46 \| Edo join 2 = 53~~
	~~\| Optimization method = CTE~~
	~~\| Generator tuning = 339.4~~
	~~\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]~~
	~~\| Ploidacot = gamma-pentacot~~
	\| Odd limit 1 = 5 \| Mistuning 1 = 0.47 \| Complexity 1 = 18		\| Odd limit 1 = 5 \| Mistuning 1 = 0.47 \| Complexity 1 = 18
	\| Odd limit 2 = 9 \| Mistuning 2 = 1.68 \| Complexity 2 = 32		\| Odd limit 2 = 9 \| Mistuning 2 = 1.68 \| Complexity 2 = 32

Overthink: fix name

2025-12-27T08:38:16Z

fix name

← Older revision		Revision as of 08:38, 27 December 2025
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	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), ~~catamite~~ ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), stalagmite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.

Overthink: oops

2025-12-01T03:15:32Z

oops

← Older revision		Revision as of 03:15, 1 December 2025
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	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in ~~catamite~~, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.

Overthink: new name

2025-12-01T03:14:45Z

new name

← Older revision		Revision as of 03:14, 1 December 2025
Line 17:		Line 17:
	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. ~~Catamite~~ tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.

Overthink: Made target scale size based on harmonics rather than the whole diamond

2025-10-29T21:50:49Z

Made target scale size based on harmonics rather than the whole diamond

← Older revision		Revision as of 21:50, 29 October 2025
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	\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]		\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]
	\| Ploidacot = gamma-pentacot		\| Ploidacot = gamma-pentacot
	\| Odd limit 1 = 5 \| Mistuning 1 = 0.47 \| Complexity 1 = 32		\| Odd limit 1 = 5 \| Mistuning 1 = 0.47 \| Complexity 1 = 18
	\| Odd limit 2 = 9 \| Mistuning 2 = 1.68 \| Complexity 2 = 99		\| Odd limit 2 = 9 \| Mistuning 2 = 1.68 \| Complexity 2 = 32
	}}		}}
	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

Overthink: fixed color name

2025-10-20T22:45:38Z

fixed color name

← Older revision		Revision as of 22:45, 20 October 2025
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	\| Mapping = 1; -5 -13 17		\| Mapping = 1; -5 -13 17
	\| Pergen = (P8, cP4/5)		\| Pergen = (P8, cP4/5)
	\| Color name = ~~Saquinyo~~		\| Color name = Saquinyoti
	\| Edo join 1 = 46 \| Edo join 2 = 53		\| Edo join 1 = 46 \| Edo join 2 = 53
	\| Optimization method = CTE		\| Optimization method = CTE

Overthink: Tweaked the optimization to be 7-limit instead of 5-limit

2025-09-21T06:23:28Z

Tweaked the optimization to be 7-limit instead of 5-limit

← Older revision		Revision as of 06:23, 21 September 2025
Line 9:		Line 9:
	\| Edo join 1 = 46 \| Edo join 2 = 53		\| Edo join 1 = 46 \| Edo join 2 = 53
	\| Optimization method = CTE		\| Optimization method = CTE
	\| Generator tuning = 339.5		\| Generator tuning = 339.4
	\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]		\| MOS scales = [[7L 4s]], [[7L 11s]], [[7L 18s]], [[7L 25s]]
	\| Ploidacot = gamma-pentacot		\| Ploidacot = gamma-pentacot

Overthink: linked commas

2025-09-21T04:04:47Z

linked commas

← Older revision		Revision as of 04:04, 21 September 2025
Line 2:		Line 2:
	\| Title = Amity		\| Title = Amity
	\| Subgroups = 2.3.5, 2.3.5.7		\| Subgroups = 2.3.5, 2.3.5.7
	\| Comma basis = 1600000/1594323 (2.3.5); <br>4375/4374, 5120/5103 (2.3.5.7)		\| Comma basis = [[1600000/1594323]] (2.3.5); <br>[[4375/4374]], [[5120/5103]] (2.3.5.7)
	\| Generator = 243/200		\| Generator = 243/200
	\| Mapping = 1; -5 -13 17		\| Mapping = 1; -5 -13 17

← Older revision		Revision as of 08:38, 27 December 2025
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	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), ~~catamite~~ ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), stalagmite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.

← Older revision		Revision as of 03:15, 1 December 2025
Line 17:		Line 17:
	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in ~~catamite~~, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in stalagmite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.

← Older revision		Revision as of 03:14, 1 December 2025
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	'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.		'''Amity''' is a [[regular temperament\|temperament]] that divides a [[8/3\|perfect eleventh]] into 5 [[generator]]s of acute minor thirds. A stack of 13 generators [[octave reduction\|octave reduced]] represents [[8/5]], [[tempering out]] the [[amity comma]], 1600000/1594323. This article also assumes the canonical [[extension]] to the [[7-limit]], where a stack of 17 generators octave reduced represents [[7/4]], tempering out [[4375/4374]] and [[5120/5103]]. [[Equal temperaments]] that [[support]] amity include {{EDOs\| 46, 53, 99, 152, and 205 }}.

	Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. ~~Catamite~~ tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].		Extending amity from the 7-limit to the 11-limit is not so simple. There are three mappings that are comparable in complexity and error: undecimal amity ({{nowrap\| 53 & 152 }}), catamite ({{nowrap\| 46 & 145 }}), and hitchcock ({{nowrap\| 46 & 53 }}). Undecimal amity tempers out 540/539 and has the harmonic 11 mapped to −62 generator steps. Stalagmite tempers out 441/440 and has the harmonic 11 mapped to +37 generators steps. Hitchcock tempers out 121/120 and has the harmonic 11 mapped to −9 steps. They can be extended to the 13-limit through [[352/351]], and results in [[625/624]] and [[729/728]] being tempered out in 13-limit amity, [[196/195]] and [[364/363]] being tempered out in catamite, and [[169/168]] and [[325/324]] being tempered out in hitchcock. Hitchcock has an extra extension to the 17-limit where it tempers out [[154/153]], [[256/255]], and [[273/272]].

	Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.		Amity was named by [[Gene Ward Smith]] in 2001–2002 as a restructuring of the phrase ''acute minor third''<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group \| ''Kleismic & co'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group \| ''32 best 5-limit linear temperaments redux'']</ref>.