152edo - Revision history

Overthink: /* Rank-2 temperaments */ trinity

2026-06-14T16:54:28Z

Rank-2 temperaments: trinity

← Older revision		Revision as of 16:54, 14 June 2026
Line 144:		Line 144:
	\| 4/3		\| 4/3
	\| [[Kwai]]		\| [[Kwai]]
			\|-
			\| 1
			\| 65\152
			\| 513.16
			\| 52/35
			\| [[Trinity]]
	\|-		\|-
	\| 1		\| 1

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:38:09Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:38, 13 March 2026
Line 205:		Line 205:
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: /* Theory */ +a comma. Misc. cleanup

2025-03-24T13:18:58Z

Theory: +a comma. Misc. cleanup

← Older revision		Revision as of 13:18, 24 March 2025
Line 7:		Line 7:
	It has two reasonable mappings for [[13/1\|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the [[integer limit\|15-integer-limit]]. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the [[13-limit]] rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].		It has two reasonable mappings for [[13/1\|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the [[integer limit\|15-integer-limit]]. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the [[13-limit]] rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].

	Extending it beyond the 13-limit can be tricky, as the approximated [[17/1\|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[484/483]] and [[576/575]] in the 23-limit.		Extending it beyond the 13-limit can be tricky, as the approximated [[17/1\|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[300/299]], [[484/483]] and [[576/575]] in the 23-limit.

	[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].		[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
Line 18:		Line 18:

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs\| 2, 4, 8, 19, 38, 76 }}.		Since 152 factors into primes as {{nowrap\| 2<sup>3</sup> × 19 }}, 152edo has subset edos {{EDOs\| 2, 4, 8, 19, 38, 76 }}.

	== Approximation to JI ==		== Approximation to JI ==

FloraC: /* Regular temperament properties */ +no-17 19-limit and no-17 23-limit

2025-03-24T13:18:20Z

Regular temperament properties: +no-17 19-limit and no-17 23-limit

← Older revision		Revision as of 13:18, 24 March 2025
Line 48:		Line 48:
	\|-		\|-
	\| 2.3		\| 2.3
	\| {{~~monzo~~\| 241 -152 }}		\| {{Monzo\| 241 -152 }}
	\| {{~~mapping~~\| 152 241 }}		\| {{Mapping\| 152 241 }}
	\| −0.213		\| −0.213
	\| 0.213		\| 0.213
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	\| 2.3.5		\| 2.3.5
	\| 1600000/1594323, {{monzo\| 32 -7 -9 }}		\| 1600000/1594323, {{monzo\| 32 -7 -9 }}
	\| {{~~mapping~~\| 152 241 353 }}		\| {{Mapping\| 152 241 353 }}
	\| −0.218		\| −0.218
	\| 0.174		\| 0.174
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	\| 2.3.5.7		\| 2.3.5.7
	\| 4375/4374, 5120/5103, 16875/16807		\| 4375/4374, 5120/5103, 16875/16807
	\| {{~~mapping~~\| 152 241 353 427 }}		\| {{Mapping\| 152 241 353 427 }}
	\| −0.362		\| −0.362
	\| 0.291		\| 0.291
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	\| 2.3.5.7.11		\| 2.3.5.7.11
	\| 540/539, 1375/1372, 4000/3993, 5120/5103		\| 540/539, 1375/1372, 4000/3993, 5120/5103
	\| {{~~mapping~~\| 152 241 353 427 526 }}		\| {{Mapping\| 152 241 353 427 526 }}
	\| −0.365		\| −0.365
	\| 0.260		\| 0.260
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	\| 2.3.5.7.11.13		\| 2.3.5.7.11.13
	\| 352/351, 540/539, 625/624, 729/728, 1575/1573		\| 352/351, 540/539, 625/624, 729/728, 1575/1573
	\| {{~~mapping~~\| 152 241 353 427 526 563 }} (152f)		\| {{Mapping\| 152 241 353 427 526 563 }} (152f)
	\| −0.494		\| −0.494
	\| 0.373		\| 0.373
	\| 4.73		\| 4.73
			\|-
			\| 2.3.5.7.11.13.19
			\| 352/351, 400/399, 495/494, 540/539, 625/624, 1331/1330
			\| {{Mapping\| 152 241 353 427 526 563 646 }} (152f)
			\| −0.507
			\| 0.347
			\| 4.40
			\|-
			\| 2.3.5.7.11.13.19.23
			\| 300/299, 352/351, 400/399, 484/483, 495/494, 540/539, 576/575
			\| {{Mapping\| 152 241 353 427 526 563 646 688 }} (152f)
			\| −0.535
			\| 0.333
			\| 4.22
	\|}		\|}
	* 152et (152fg val) has lower absolute errors in the 11-, 19-, and 23-limit than any previous equal temperaments. In the 11-limit it is the first to beat [[130edo\|130]] and is superseded by [[224edo\|224]]. In the 19- and 23-limit it is the first to beat [[140edo\|140]] and is superseded by [[159edo\|159]].		* 152et (152fg val) has lower absolute errors in the 11-, 19-, and 23-limit than any previous equal temperaments. In the 11-limit it is the first to beat [[130edo\|130]] and is superseded by [[224edo\|224]]. In the 19- and 23-limit it is the first to beat [[140edo\|140]] and is superseded by [[159edo\|159]].
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	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
	<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal~~ lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[normal lists\|minimal form]] in parentheses if distinct

	== Music ==		== Music ==

FloraC: /* Theory */ discuss the extensions beyond the 13-limit

2025-03-24T13:10:10Z

Theory: discuss the extensions beyond the 13-limit

← Older revision		Revision as of 13:10, 24 March 2025
Line 3:		Line 3:

	== Theory ==		== Theory ==
	152edo is a strong [[11-limit]] system, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] slightly sharp. It [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]) in the [[5-limit]]; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the [[7-limit]]; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit rank-2 temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit rank-3 temperament [[laka]].		152edo is a strong [[11-limit]] system, with the [[harmonic]]s [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] slightly sharp. It [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]) in the [[5-limit]]; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the [[7-limit]]; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit rank-2 temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit rank-3 temperament [[laka]].

	It has two reasonable mappings for [[13/1\|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the 15-integer-limit. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].		It has two reasonable mappings for [[13/1\|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the [[integer limit\|15-integer-limit]]. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the [[13-limit]] rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].

			Extending it beyond the 13-limit can be tricky, as the approximated [[17/1\|harmonic 17]] is almost 1/3-edostep flat of just, which does not blend well with the sharp tendency from the lower harmonics. The 152fg val in turn gives you an alternative that is more than 2/3-edostep sharp. However, if we skip prime 17 altogether, we can treat 152edo as a no-17 [[23-limit]] system with the 152f val, where it is strong and almost consistent to the no-17 [[23-odd-limit]] with the sole exception of [[13/8]] and its [[octave complement]]. It tempers out [[400/399]] and [[495/494]] in the [[19-limit]] and [[484/483]] and [[576/575]] in the 23-limit.

	[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].		[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].

FloraC: /* Theory */ +octave stretch

2025-03-24T13:00:57Z

Theory: +octave stretch

← Older revision		Revision as of 13:00, 24 March 2025
Line 5:		Line 5:
	152edo is a strong [[11-limit]] system, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] slightly sharp. It [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]) in the [[5-limit]]; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the [[7-limit]]; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit rank-2 temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit rank-3 temperament [[laka]].		152edo is a strong [[11-limit]] system, with the [[3/1\|3]], [[5/1\|5]], [[7/1\|7]], and [[11/1\|11]] slightly sharp. It [[tempering out\|tempers out]] 1600000/1594323 ([[amity comma]]) and {{monzo\| 32 -7 -9 }} ([[escapade comma]]) in the [[5-limit]]; [[4375/4374]], [[5120/5103]], [[6144/6125]] and [[16875/16807]] in the [[7-limit]]; [[540/539]], [[1375/1372]], [[3025/3024]], [[4000/3993]], [[5632/5625]] and [[9801/9800]] in the 11-limit. It provides the [[optimal patent val]] for the 11-limit rank-2 temperaments [[amity]], [[grendel]], and [[kwai]], and the 11-limit rank-3 temperament [[laka]].

	It has two reasonable mappings for 13, with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the 15-integer-limit. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].		It has two reasonable mappings for [[13/1\|13]], with the 152f val scoring much better. The 152f val tempers out [[352/351]], [[625/624]], [[640/637]], [[729/728]], [[847/845]], [[1188/1183]], [[1575/1573]], [[1716/1715]] and [[2080/2079]], [[support]]ing and giving an excellent tuning for amity, kwai, and laka. The optimal tuning of this temperament is [[consistent]] in the 15-integer-limit. The [[patent val]] tempers out [[169/168]], [[325/324]], [[351/350]], [[364/363]], [[1001/1000]], [[1573/1568]], and [[4096/4095]], providing the optimal patent val for the 13-limit rank-5 temperament tempering out 169/168, as well as some further temperaments thereof, such as [[octopus]].

	[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].		[[Paul Erlich]] has suggested that 152edo could be considered a sort of [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3038.html#3041 universal tuning].
Line 11:		Line 11:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|152}}		{{Harmonics in equal\|152}}

			=== Octave stretch ===
			152edo's approximated harmonics 3, 5, 7, 11 can all be improved, and moreover the approximated harmonic 13 can be brought to consistency, if slightly [[stretched and compressed tuning\|compressing the octave]] is acceptable. [[241edt]] is a great example for this.

	=== Subsets and supersets ===		=== Subsets and supersets ===

ArrowHead294: /* Zeta peak index */

2025-03-20T15:16:39Z

Zeta peak index

← Older revision		Revision as of 15:16, 20 March 2025
Line 17:		Line 17:
	== Approximation to JI ==		== Approximation to JI ==
	=== Zeta peak index ===		=== Zeta peak index ===
	{~~\| class="wikitable center-all"~~		{{ZPI
	\|-		\| zpi = 965
	~~! colspan~~=~~"3" \| Tuning~~		\| steps = 152.052848107925
	~~! colspan="3"~~ \| ~~Strength~~		\| step size = 7.89199291517551
	~~! colspan~~=~~"2" \| Closest edo~~		\| tempered height = 10.468420
	~~! colspan="2" \| Integer limit~~		\| pure height = 7.617532
	\|-		\| integral = 1.593855
	~~! ZPI~~		\| gap = 19.487224
	~~! Steps per octave~~		\| octave = 1199.58292310668
	~~! Step size (cents)~~		\| consistent = 15
	~~! Height~~		\| distinct = 15
	~~! Integral~~		}}
	~~! Gap~~
	~~! Edo~~
	~~! Octave (cents)~~
	~~! Consistent~~
	~~! Distinct~~
	\|-
	~~\| [[965zpi]]~~
	\| 152.052848107925
	\| 7.89199291517551
	\| 10.468420
	\| 1.593855
	\| 19.487224
	\| ~~152edo~~
	\| 1199.58292310668
	\| 15
	\| 15
	\|}

	== Regular temperament properties ==		== Regular temperament properties ==

ArrowHead294 at 17:07, 18 February 2025

2025-02-18T17:07:42Z

← Older revision		Revision as of 17:07, 18 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|152~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC: Consolidate sections

2025-01-19T10:18:02Z

Consolidate sections

← Older revision		Revision as of 10:18, 19 January 2025
Line 14:		Line 14:
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs\| 2, 4, 8, 19, 38, 76 }}.		Since 152 factors into 2<sup>3</sup> × 19, 152edo has subset edos {{EDOs\| 2, 4, 8, 19, 38, 76 }}.

			== Approximation to JI ==
			=== Zeta peak index ===
			{\| class="wikitable center-all"
			\|-
			! colspan="3" \| Tuning
			! colspan="3" \| Strength
			! colspan="2" \| Closest edo
			! colspan="2" \| Integer limit
			\|-
			! ZPI
			! Steps per octave
			! Step size (cents)
			! Height
			! Integral
			! Gap
			! Edo
			! Octave (cents)
			! Consistent
			! Distinct
			\|-
			\| [[965zpi]]
			\| 152.052848107925
			\| 7.89199291517551
			\| 10.468420
			\| 1.593855
			\| 19.487224
			\| 152edo
			\| 1199.58292310668
			\| 15
			\| 15
			\|}

	== Regular temperament properties ==		== Regular temperament properties ==
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	\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator		\|+ style="font-size: 105%;" \| Table of rank-2 temperaments by generator
	\|-		\|-
	! Periods<br />per 8ve		! Periods<br>per 8ve
	! Generator*		! Generator*
	! Cents*		! Cents*
	! Associated<br />ratio*		! Associated<br>ratio*
	! Temperaments		! Temperaments
	\|-		\|-
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	\|-		\|-
	\| 2		\| 2
	\| 43\152<br />(33\152)		\| 43\152<br>(33\152)
	\| 339.47<br />(260.53)		\| 339.47<br>(260.53)
	\| 243/200<br />(64/55)		\| 243/200<br>(64/55)
	\| [[Hemiamity]]		\| [[Hemiamity]]
	\|-		\|-
	\| 2		\| 2
	\| 55\152<br />(21\152)		\| 55\152<br>(21\152)
	\| 434.21<br />(165.79)		\| 434.21<br>(165.79)
	\| 9/7<br />(11/10)		\| 9/7<br>(11/10)
	\| [[Supers]]		\| [[Supers]]
	\|-		\|-
	\| 4		\| 4
	\| 63\152<br />(13\152)		\| 63\152<br>(13\152)
	\| 497.37<br />(102.63)		\| 497.37<br>(102.63)
	\| 4/3<br />(35/33)		\| 4/3<br>(35/33)
	\| [[Undim]] / [[unlit]]		\| [[Undim]] / [[unlit]]
	\|-		\|-
	\| 8		\| 8
	\| 63\152<br />(6\152)		\| 63\152<br>(6\152)
	\| 497.37<br />(47.37)		\| 497.37<br>(47.37)
	\| 4/3<br />(36/35)		\| 4/3<br>(36/35)
	\| [[Twilight]]		\| [[Twilight]]
	\|-		\|-
	\| 8		\| 8
	\| 74\152<br />(2\152)		\| 74\152<br>(2\152)
	\| 584.21<br />(15.79)		\| 584.21<br>(15.79)
	\| 7/5<br />(126/125)		\| 7/5<br>(126/125)
	\| [[Octoid]] (152f) / [[octopus]] (152)		\| [[Octoid]] (152f) / [[octopus]] (152)
	\|-		\|-
	\| 19		\| 19
	\| 63\152<br />(1\152)		\| 63\152<br>(1\152)
	\| 497.37<br />(7.89)		\| 497.37<br>(7.89)
	\| 4/3<br />(225/224)		\| 4/3<br>(225/224)
	\| [[Enneadecal]]		\| [[Enneadecal]]
	\|-		\|-
	\| 38		\| 38
	\| 63\152<br />(1\152)		\| 63\152<br>(1\152)
	\| 497.37<br />(7.89)		\| 497.37<br>(7.89)
	\| 4/3<br />(225/224)		\| 4/3<br>(225/224)
	\| [[Hemienneadecal]]		\| [[Hemienneadecal]]
	\|}		\|}
	<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

	~~== Zeta properties ==~~
	~~=== Zeta peak index ===~~
	~~{\| class="wikitable"~~
	\|-
	~~! colspan="3" \| Tuning~~
	~~! colspan="3" \| Strength~~
	~~! colspan="2" \| Closest EDO~~
	~~! colspan="2" \| Integer limit~~
	\|-
	~~! ZPI~~
	~~! Steps per octave~~
	~~! Step size (cents)~~
	~~! Height~~
	~~! Integral~~
	~~! Gap~~
	~~! EDO~~
	~~! Octave (cents)~~
	~~! Consistent~~
	~~! Distinct~~
	\|-
	~~\| [[965zpi]]~~
	~~\| 152.052848107925~~
	~~\| 7.89199291517551~~
	~~\| 10.468420~~
	~~\| 1.593855~~
	~~\| 19.487224~~
	~~\| 152edo~~
	~~\| 1199.58292310668~~
	~~\| 15~~
	~~\| 15~~
	\|}

	== Music ==		== Music ==

ArrowHead294: Formatting

2025-01-19T02:46:40Z

Formatting

← Older revision		Revision as of 02:46, 19 January 2025
Line 174:		Line 174:

	== Zeta properties ==		== Zeta properties ==
	===Zeta peak index===		=== Zeta peak index ===
	{\| class="wikitable"		{\| class="wikitable"
	~~! colspan="3" \|Tuning~~
	~~! colspan="3" \|Strength~~
	~~! colspan="2" \|Closest EDO~~
	~~! colspan="2" \|Integer limit~~
	\|-		\|-
	!~~ZPI~~		! colspan="3" \| Tuning
	!~~Steps per octave~~		! colspan="3" \| Strength
	~~!Step size (cents)~~		! colspan="2" \| Closest EDO
	~~!Height~~		! colspan="2" \| Integer limit
	~~!Integral~~
	~~!Gap~~
	!EDO
	!~~Octave (cents)~~
	~~!Consistent~~
	~~!Distinct~~
	\|-		\|-
	\|[[965zpi]]		! ZPI
	\|152.052848107925		! Steps per octave
	\|7.89199291517551		! Step size (cents)
	\|10.468420		! Height
	\|1.593855		! Integral
	\|19.487224		! Gap
	\|152edo		! EDO
	\|1199.58292310668		! Octave (cents)
	\|15		! Consistent
	\|15		! Distinct
			\|-
			\| [[965zpi]]
			\| 152.052848107925
			\| 7.89199291517551
			\| 10.468420
			\| 1.593855
			\| 19.487224
			\| 152edo
			\| 1199.58292310668
			\| 15
			\| 15
	\|}		\|}

	== Music ==		== Music ==
	; [[birdshite stalactite]]		; [[birdshite stalactite]]