986edo - Revision history

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"

2026-03-13T13:32:23Z

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 13:32, 13 March 2026
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	\| [[Gary]]		\| [[Gary]]
	\|}		\|}
	<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

ArrowHead294 at 12:35, 21 February 2025

2025-02-21T12:35:51Z

← Older revision		Revision as of 12:35, 21 February 2025
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	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===
	{\| class="wikitable center-all left-5"		{\| class="wikitable center-all left-5"
	\|+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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	\| [[Gary]]		\| [[Gary]]
	\|}		\|}
			<nowiki />* [[Normal lists\|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists\|minimal form]] in parentheses if distinct

Francium: changed EDO intro to ED intro

2025-02-21T06:09:08Z

changed EDO intro to ED intro

← Older revision		Revision as of 06:09, 21 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|986~~}}		{{ED intro}}

	== Theory ==		== Theory ==
	986edo is a good 2.3.7.11 subgroup tuning, but it is in[[consistent]] to the 5-odd-limit and larger due to a high error on the [[5/4\|5th harmonic]]. 986edo has an excellent [[11/8\|11th harmonic]], being the denominator of a [[convergent]] to log<sub>2</sub>11, after [[949edo\|949]] and before [[1935edo\|1935]]. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either [[17/16\|17]], [[23/16\|23]], [[29/16\|29]], or [[31/16\|31]].		986edo is a good 2.3.7.11 subgroup tuning, but it is in[[consistent]] to the 5-odd-limit and larger due to a high error on the [[5/4\|5th harmonic]]. 986edo has an excellent [[11/8\|11th harmonic]], being the denominator of a [[convergent]] to log<sub>2</sub>11, after [[949edo\|949]] and before [[1935edo\|1935]]. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either [[17/16\|17]], [[23/16\|23]], [[29/16\|29]], or [[31/16\|31]].

	In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out, 131072/130977, 3195731/3188646, 33554432/33480783, 67110351/67108864, and {{monzo\|5 4 0 28 -26}} in the 2.3.7.11 subgroup.		In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out, 131072/130977, 3195731/3188646, 33554432/33480783, 67110351/67108864, and {{monzo\|5 4 0 28 -26}} in the 2.3.7.11 subgroup.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|986}}		{{harmonics in equal\|986}}

	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 986 factors as {{Factorization\|986}}, 986edo has subset edos {{EDOs\|1, 2, 17, 29, 34, 58, 493}}.		Since 986 factors as {{Factorization\|986}}, 986edo has subset edos {{EDOs\|1, 2, 17, 29, 34, 58, 493}}.

Eliora: /* Theory */

2024-02-18T17:20:52Z

Theory

← Older revision		Revision as of 17:20, 18 February 2024
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	986edo is a good 2.3.7.11 subgroup tuning, but it is in[[consistent]] to the 5-odd-limit and larger due to a high error on the [[5/4\|5th harmonic]]. 986edo has an excellent [[11/8\|11th harmonic]], being the denominator of a [[convergent]] to log<sub>2</sub>11, after [[949edo\|949]] and before [[1935edo\|1935]]. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either [[17/16\|17]], [[23/16\|23]], [[29/16\|29]], or [[31/16\|31]].		986edo is a good 2.3.7.11 subgroup tuning, but it is in[[consistent]] to the 5-odd-limit and larger due to a high error on the [[5/4\|5th harmonic]]. 986edo has an excellent [[11/8\|11th harmonic]], being the denominator of a [[convergent]] to log<sub>2</sub>11, after [[949edo\|949]] and before [[1935edo\|1935]]. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either [[17/16\|17]], [[23/16\|23]], [[29/16\|29]], or [[31/16\|31]].

	In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out ~~19712~~/~~19683~~, ~~41503~~/~~41472~~ in the 2.3.7.11 subgroup.		In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out, 131072/130977, 3195731/3188646, 33554432/33480783, 67110351/67108864, and {{monzo\|5 4 0 28 -26}} in the 2.3.7.11 subgroup.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{harmonics in equal\|986}}		{{harmonics in equal\|986}}

Eliora: /* Theory */

2024-02-07T22:15:28Z

Theory

← Older revision		Revision as of 22:15, 7 February 2024
Line 5:		Line 5:

	In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out 19712/19683, 41503/41472 in the 2.3.7.11 subgroup.		In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out 19712/19683, 41503/41472 in the 2.3.7.11 subgroup.
			=== Prime harmonics ===
	{{harmonics in equal\|986}}		{{harmonics in equal\|986}}
			=== Subsets and supersets ===
			Since 986 factors as {{Factorization\|986}}, 986edo has subset edos {{EDOs\|1, 2, 17, 29, 34, 58, 493}}.

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

Eliora: create page, also octave-reduced links per discussion in #wiki, - 17 not 17 as an octave-reduced harmonic is more helpful to the reader.

2024-02-07T22:13:59Z

create page, also octave-reduced links per discussion in #wiki, - 17 not 17 as an octave-reduced harmonic is more helpful to the reader.

New page

{{Infobox ET}}
{{EDO intro|986}}
== Theory ==
986edo is a good 2.3.7.11 subgroup tuning, but it is in[[consistent]] to the 5-odd-limit and larger due to a high error on the [[5/4|5th harmonic]]. 986edo has an excellent [[11/8|11th harmonic]], being the denominator of a [[convergent]] to log<sub>2</sub>11, after [[949edo|949]] and before [[1935edo|1935]]. In the 2.3.7.11 subgroup, 986edo can be used with optional additions of either [[17/16|17]], [[23/16|23]], [[29/16|29]], or [[31/16|31]].

In the 2.3.7 subgroup, 986edo tempers out the [[garischisma]], and is a strong tuning for 2.3.7.11-subgroup [[gary]]. It also tempers out 19712/19683, 41503/41472 in the 2.3.7.11 subgroup.

{{harmonics in equal|986}}

== Regular temperament properties ==
=== Rank-2 temperaments ===
{| class="wikitable center-all left-5"
|+Table of rank-2 temperaments by generator
! Periods<br>per 8ve
! Generator*
! Cents*
! Associated<br>Ratio*
! Temperaments
|-
| 1
| 409\986
| 497.769
| 4/3
| [[Gary]]
|}