108edo - Revision history

Yourmusic Productions: Add music.

2025-08-17T11:27:07Z

Add music.

← Older revision		Revision as of 11:27, 17 August 2025
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	{{Interval table}}		{{Interval table}}

			== Music ==
			; [[Billy Stiltner]]
			* [https://billystiltner.bandcamp.com/track/108-tone-equal 108 tone equal]
	[[Category:Valentine]]		[[Category:Valentine]]

ArrowHead294 at 16:47, 18 February 2025

2025-02-18T16:47:56Z

← Older revision		Revision as of 16:47, 18 February 2025
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	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|108~~}}		{{ED intro}}

	== Theory ==		== Theory ==

FloraC at 08:40, 8 June 2024

2024-06-08T08:40:19Z

← Older revision		Revision as of 08:40, 8 June 2024
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	== Theory ==		== Theory ==
	108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]], and 1344/1331 and the 108e val tempers out [[121/120]], [[176/175]], [[385/384]], and [[441/440]], supporting 11-limit valentine for which it is again a good tuning.		108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and 1344/1331, and the 108e val tempers out [[121/120]], [[176/175]], [[385/384]], and [[441/440]], supporting 11-limit valentine for which it is again a good tuning.

	108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.		108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.

FloraC: +more commas

2024-06-08T08:39:06Z

+more commas

← Older revision		Revision as of 08:39, 8 June 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and the 108e val tempers out [[121/120]] ~~and~~ [[176/175]], supporting 11-limit valentine for which it is again a good tuning.		108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]], and 1344/1331 and the 108e val tempers out [[121/120]], [[176/175]], [[385/384]], and [[441/440]], supporting 11-limit valentine for which it is again a good tuning.

	108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.		108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.

FloraC: +subsets and supersets

2024-06-08T08:33:27Z

+subsets and supersets

← Older revision		Revision as of 08:33, 8 June 2024
Line 3:		Line 3:

	== Theory ==		== Theory ==
	108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.		108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the [[patent val]] tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.

	108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.		108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.
Line 9:		Line 9:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|108}}		{{Harmonics in equal\|108}}

			=== Subsets and supersets ===
			Since 108 factors into {{factorization\|108}}, 108edo has subset edos {{EDOs\| 2, 3, 4, 6, 9, 12, 18, 27, 36, and 54 }}.

	== Intervals ==		== Intervals ==

FloraC: Cleanup

2024-06-08T08:31:28Z

Cleanup

← Older revision		Revision as of 08:31, 8 June 2024
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	{{EDO intro\|108}}		{{EDO intro\|108}}

	==Theory==		== Theory ==
	~~108edo~~ tempers out the Pythagorean comma~~, 531441/524288,~~ in the 3-limit and 1990656/1953125~~, the valensixthtone~~ comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, ~~supporting~~ [[~~Starling_temperaments#Valentine temperament\|~~valentine ~~temperament~~]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.		108et [[tempering out\|tempers out]] the [[Pythagorean comma]] in the 3-limit and 1990656/1953125 ([[valentine comma]]) in the 5-limit. In the 7-limit it tempers out [[126/125]] and [[1029/1024]], [[support]]ing [[valentine]], and making for a good tuning for it and for [[starling]] temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out [[540/539]] and the 108e val tempers out [[121/120]] and [[176/175]], supporting 11-limit valentine for which it is again a good tuning.

			108edo is the smallest 12''n''-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.

	~~108edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.~~
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|108}}		{{Harmonics in equal\|108}}
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	{{Interval table}}		{{Interval table}}

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Valentine]]		[[Category:Valentine]]

BudjarnLambeth: Added interval table

2024-01-21T07:03:24Z

Added interval table

← Older revision		Revision as of 07:03, 21 January 2024
Line 8:		Line 8:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|108}}		{{Harmonics in equal\|108}}

			== Intervals ==
			{{Interval table}}

	[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->		[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->
	[[Category:Valentine]]		[[Category:Valentine]]

Eliora: /* Miscellany */

2023-05-30T21:14:16Z

Miscellany

Show changes

CompactStar at 21:51, 2 May 2023

2023-05-02T21:51:08Z

← Older revision		Revision as of 21:51, 2 May 2023
Line 5:		Line 5:
	108edo tempers out the Pythagorean comma, 531441/524288, in the 3-limit and 1990656/1953125, the valensixthtone comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament\|valentine temperament]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.		108edo tempers out the Pythagorean comma, 531441/524288, in the 3-limit and 1990656/1953125, the valensixthtone comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament\|valentine temperament]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.

	108edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, ~~which~~ is [[27edo]]'s superpyth fifth.		108edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, that is [[27edo]]'s superpyth fifth.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|108}}		{{Harmonics in equal\|108}}

CompactStar at 21:51, 2 May 2023

2023-05-02T21:51:02Z

← Older revision		Revision as of 21:51, 2 May 2023
Line 5:		Line 5:
	108edo tempers out the Pythagorean comma, 531441/524288, in the 3-limit and 1990656/1953125, the valensixthtone comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament\|valentine temperament]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.		108edo tempers out the Pythagorean comma, 531441/524288, in the 3-limit and 1990656/1953125, the valensixthtone comma, in the 5-limit. In the 7-limit it tempers out 126/125 and 1029/1024, supporting [[Starling_temperaments#Valentine temperament\|valentine temperament]], and making for a good tuning for it and for starling temperament, the planar temperament tempering out 126/125. In the 11-limit the patent val tempers out 540/539 and the 108e val tempers out 121/120 and 176/175, supporting 11-limit valentine for which it is again a good tuning.

			108edo is the smallest 12n-edo which offers a decent alternative fifth to 12edo's fifth, which is [[27edo]]'s superpyth fifth.
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|108}}		{{Harmonics in equal\|108}}