82edo - Revision history

BudjarnLambeth: /* Approximation to JI */ Remove the zeta peak table that had no explanation or context

2025-09-17T02:00:32Z

Approximation to JI: Remove the zeta peak table that had no explanation or context

← Older revision		Revision as of 02:00, 17 September 2025
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	{{Sharpness-sharp8}}		{{Sharpness-sharp8}}

	~~== Approximation to JI ==~~
	~~=== Zeta peak index ===~~
	~~{{ZPI~~
	~~\| zpi = 448~~
	~~\| steps = 81.9541455954050~~
	~~\| step size = 14.6423343356444~~
	~~\| tempered height = 6.653983~~
	~~\| pure height = 5.154524~~
	~~\| integral = 0.941321~~
	~~\| gap = 14.718732~~
	~~\| octave = 1200.67141552284~~
	~~\| consistent = 8~~
	~~\| distinct = 8~~
	}}

	== Instruments ==		== Instruments ==

Lucius Chiaraviglio: /* Instruments */ Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 82edo'' (2025)

2025-07-14T21:30:46Z

Instruments: Insert music section after this, starting with Bryan Deister's ''microtonal improvisation in 82edo'' (2025)

← Older revision		Revision as of 21:30, 14 July 2025
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	== Instruments ==		== Instruments ==
	* [[Lumatone mapping for 82edo]]		* [[Lumatone mapping for 82edo]]

			== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/p9xUY8EU7Zg ''microtonal improvisation in 82edo''] (2025)

Yourmusic Productions: Add lumatone mapping link.

2025-07-12T08:15:20Z

Add lumatone mapping link.

← Older revision		Revision as of 08:15, 12 July 2025
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	\| distinct = 8		\| distinct = 8
	}}		}}

			== Instruments ==
			* [[Lumatone mapping for 82edo]]

FloraC: No need to remind readers of what a regular temperament is everywhere

2025-04-11T11:01:20Z

No need to remind readers of what a regular temperament is everywhere

← Older revision		Revision as of 11:01, 11 April 2025
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	== Theory ==		== Theory ==
	82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap\|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead. ~~(''See [[regular temperament]] for more about what all this means and how to use it.'')~~		82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap\|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.

	=== Prime harmonics ===		=== Prime harmonics ===

BudjarnLambeth: /* Theory */ (''See regular temperament for more about what all this means and how to use it.'')

2025-04-11T07:21:34Z

Theory: (''See regular temperament for more about what all this means and how to use it.'')

← Older revision		Revision as of 07:21, 11 April 2025
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	== Theory ==		== Theory ==
	82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap\|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.		82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap\|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead. (''See [[regular temperament]] for more about what all this means and how to use it.'')

	=== Prime harmonics ===		=== Prime harmonics ===

ArrowHead294: /* Zeta peak index */

2025-03-20T15:11:23Z

Zeta peak index

← Older revision		Revision as of 15:11, 20 March 2025
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	== Approximation to JI ==		== Approximation to JI ==
	=== Zeta peak index ===		=== Zeta peak index ===
	{~~\| class="wikitable center-all"~~		{{ZPI
	\|-		\| zpi = 448
	~~! colspan="3"~~ \| ~~Tuning~~		\| steps = 81.9541455954050
	~~! colspan~~=~~"3" \| Strength~~		\| step size = 14.6423343356444
	~~! colspan="2"~~ \| ~~Closest edo~~		\| tempered height = 6.653983
	~~! colspan~~=~~"2" \| Integer limit~~		\| pure height = 5.154524
	\|-		\| integral = 0.941321
	~~! ZPI~~		\| gap = 14.718732
	~~! Steps per octave~~		\| octave = 1200.67141552284
	~~! Step size (cents)~~		\| consistent = 8
	~~! Height~~		\| distinct = 8
	~~! Integral~~		}}
	~~! Gap~~
	~~! Edo~~
	~~! Octave (cents)~~
	~~! Consistent~~
	~~! Distinct~~
	\|-
	~~\| [[448zpi]]~~
	\| 81.9541455954050
	\| 14.6423343356444
	\| 6.653983
	\| 0.941321
	\| 14.718732
	\| ~~82edo~~
	\| 1200.67141552284
	\| 8
	\| 8
	\|}

ArrowHead294 at 16:32, 20 February 2025

2025-02-20T16:32:45Z

← Older revision		Revision as of 16:32, 20 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|82~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	82edo's [[patent val]] is [[contorted]] in the [[11-limit]], ~~from~~ 82 = 2 × 41. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] & [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.		82edo's [[patent val]] is [[contorted]] in the [[11-limit]], since {{nowrap\|82 {{=}} 2 × 41}}. In the [[13-limit]] the patent val tempers out [[169/168]] and [[676/675]], and in the [[17-limit]] tempers out [[273/272]]. It provides the optimal patent val for [[soothsaying]] temperament and [[support]]s [[baladic]] temperament. The 82d val tempers out [[50/49]] and is an excellent tuning for [[astrology]] and [[byhearted]], surpassing their optimal patent vals. The alternative 82e val tempers out [[121/120]] instead.

	=== Prime harmonics ===		=== Prime harmonics ===

FloraC: Consolidate sections

2025-01-19T09:58:51Z

Consolidate sections

← Older revision		Revision as of 09:58, 19 January 2025
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	{{Sharpness-sharp8}}		{{Sharpness-sharp8}}

	== ~~Zeta properties~~ ==		== Approximation to JI ==
	=== Zeta peak index ===		=== Zeta peak index ===
	{\| class="wikitable"		{\| class="wikitable center-all"
	\|-		\|-
	! colspan="3" \| Tuning		! colspan="3" \| Tuning
	! colspan="3" \| Strength		! colspan="3" \| Strength
	! colspan="2" \| Closest ~~EDO~~		! colspan="2" \| Closest edo
	! colspan="2" \| Integer limit		! colspan="2" \| Integer limit
	\|-		\|-
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	! Integral		! Integral
	! Gap		! Gap
	! ~~EDO~~		! Edo
	! Octave (cents)		! Octave (cents)
	! Consistent		! Consistent

ArrowHead294: Formatting + notation

2025-01-19T02:35:53Z

Formatting + notation

← Older revision		Revision as of 02:35, 19 January 2025
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	== Intervals ==		== Intervals ==
	{\| class="wikitable right-1 right-2 left-3 left-4 left-5"		{\| class="wikitable right-1 right-2 left-3 left-4 left-5"
	\|+		\|-
	! #		! rowspan="2" \| #
	! Cents		! rowspan="2" \| Cents
	! Approximate ~~Ratios~~*		! rowspan="2" \| Approximate ratios*
	! Additional ~~Ratios<br>with 11's (~~82e ~~Val)~~		! colspan="2" \| Additional ratios
	! ~~Additional Ratios<br>with 11's (Patent Val)~~		\|-
			! Using the 82e val
			! Using the patent val
	\|-		\|-
	\| 0		\| 0
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	\|		\|
	\|}		\|}
	<nowiki>*~~</nowiki> as~~ a no-11 19-limit temperament		<nowiki />* As a no-11 19-limit temperament
	==Zeta properties==
	===Zeta peak index===		== Notation ==
			=== Ups and downs notation ===
			60edo can be notated using [[ups and downs notation]] using [[Helmholtz–Ellis]] accidentals:

			{{Sharpness-sharp8}}

			== Zeta properties ==
			=== 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~~
	\|-		\|-
	\|[[448zpi]]		! ZPI
	\|81.9541455954050		! Steps per octave
	\|14.6423343356444		! Step size (cents)
	\|6.653983		! Height
	\|0.941321		! Integral
	\|14.718732		! Gap
	\|82edo		! EDO
	\|1200.67141552284		! Octave (cents)
	\|8		! Consistent
	\|8		! Distinct
			\|-
			\| [[448zpi]]
			\| 81.9541455954050
			\| 14.6423343356444
			\| 6.653983
			\| 0.941321
			\| 14.718732
			\| 82edo
			\| 1200.67141552284
			\| 8
			\| 8
	\|}		\|}

Contribution: /* Zeta peak index */

2025-01-18T23:06:16Z

Zeta peak index

← Older revision		Revision as of 23:06, 18 January 2025
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	\|0.941321		\|0.941321
	\|14.718732		\|14.718732
	\|[[82edo]]		\|82edo
	\|1200.67141552284		\|1200.67141552284
	\|8		\|8
	\|8		\|8
	\|}		\|}