6edo - Revision history

MisterShafXen: why did it say stretched-octave when talking about octave compression

2026-05-14T19:50:16Z

why did it say stretched-octave when talking about octave compression

← Older revision		Revision as of 19:50, 14 May 2026
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	== Octave stretch or compression ==		== Octave stretch or compression ==
	If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some ~~stretched~~-octave 6edo tunings (least to most compressed) include [[equal tuning\|19ed9]], [[equal tuning\|20ed10]], [[14ed5]], [[zpi\|12zpi]] or [[17ed7]].		If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some compressed-octave 6edo tunings (least to most compressed) include [[equal tuning\|19ed9]], [[equal tuning\|20ed10]], [[14ed5]], [[zpi\|12zpi]] or [[17ed7]].

	== Instruments ==		== Instruments ==

Overthink: /* Theory */ links

2025-12-19T03:24:59Z

Theory: links

← Older revision		Revision as of 03:24, 19 December 2025
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	== Theory ==		== Theory ==
	6edo is identical to the 12edo whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic\|7-form]] for 2.3.5 and the [[Pentatonic\|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as 7edo for [[meantone]] or 5edo for [[superpyth]]. The root chord in this harmonic system can be seen as:		6edo is identical to the [[12edo]] whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic\|7-form]] for 2.3.5 and the [[Pentatonic\|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as [[7edo]] for [[meantone]] or [[5edo]] for [[superpyth]]. The root chord in this harmonic system can be seen as:

	* [0 2 5] = 4:5:7, with the harmonic seventh as a bounding interval		* [0 2 5] = 4:5:7, with the harmonic seventh as a bounding interval
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	=== Odd harmonics ===		=== Odd harmonics ===
	{{Harmonics in equal\|6~~\|intervals=odd~~}}		{{Harmonics in equal\|6}}

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

BudjarnLambeth: /* Octave stretch or compression */ fix links

2025-09-19T08:45:16Z

Octave stretch or compression: fix links

← Older revision		Revision as of 08:45, 19 September 2025
Line 355:		Line 355:

	== Octave stretch or compression ==		== Octave stretch or compression ==
	If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some stretched-octave 6edo tunings (least to most compressed) include [[~~ed9~~\|19ed9]], [[~~ed10~~\|20ed10]], [[14ed5]], [[zpi\|12zpi]] or [[17ed7]].		If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some stretched-octave 6edo tunings (least to most compressed) include [[equal tuning\|19ed9]], [[equal tuning\|20ed10]], [[14ed5]], [[zpi\|12zpi]] or [[17ed7]].

	== Instruments ==		== Instruments ==

BudjarnLambeth: Temporary until full version is done

2025-09-16T08:10:52Z

Temporary until full version is done

← Older revision		Revision as of 08:10, 16 September 2025
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	\| Tridecimal neutral second		\| Tridecimal neutral second
	\|}		\|}

			== Octave stretch or compression ==
			If one wishes to use 6edo as a 2.9.5 or 2.9.5.7 [[subgroup]] tuning, then it benefits from [[octave shrinking]]. Some stretched-octave 6edo tunings (least to most compressed) include [[ed9\|19ed9]], [[ed10\|20ed10]], [[14ed5]], [[zpi\|12zpi]] or [[17ed7]].

	== Instruments ==		== Instruments ==

Yourmusic Productions: /* Instruments */ expansion.

2025-08-06T09:37:37Z

Instruments: expansion.

← Older revision		Revision as of 09:37, 6 August 2025
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	== Instruments ==		== Instruments ==
	A [[Lumatone mapping for 6edo]] is available.		Any instruments that can play the full gamut of 12edo (ie, not diatonic harmonicas, dulcimers or harps) can obviously also play 6edo as well, although it is significantly more ergonomic on some instruments than others.

			If you want a more specialist design making 6edo music easy to play without having to worry about hitting out of key 12edo notes, a [[Lumatone mapping for 6edo]] is available, or you could remove all the unwanted bars on a xylophone or marimba.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 6edo is now available

2025-08-06T09:09:37Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 6edo is now available

← Older revision		Revision as of 09:09, 6 August 2025
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	\| Tridecimal neutral second		\| Tridecimal neutral second
	\|}		\|}

			== Instruments ==
			A [[Lumatone mapping for 6edo]] is available.

	== Music ==		== Music ==

VectorGraphics at 04:30, 6 June 2025

2025-06-06T04:30:00Z

← Older revision		Revision as of 04:30, 6 June 2025
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	== Theory ==		== Theory ==
	As a ~~subset of~~ [[~~12edo~~]], ~~6edo can be notated on a five~~-~~line staff with standard notation~~. ~~It is~~ the ~~first~~ [[~~edo~~]] that ~~is not~~ a [[~~zeta peak edo\|zeta peak~~]], ~~has lower~~ [[~~Consistency limits of small EDOs\|consistency~~]] ~~than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator~~. ~~This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third~~ harmonic~~, but has still seen more use than most edos other than 12, since it~~ can be ~~played on any 12-tone instrument.~~		6edo is identical to the 12edo whole-tone scale, however, it does have xenharmonic theoretical appeal. The 6-form is a simple basis for harmony in the [[2.5.7 subgroup]], somewhat like the [[Heptatonic\|7-form]] for 2.3.5 and the [[Pentatonic\|5-form]] for 2.3.7. This means that 6edo itself can be seen as a particularly crude tuning of temperaments like [[didacus]], in the same way as 7edo for [[meantone]] or 5edo for [[superpyth]]. The root chord in this harmonic system can be seen as:

	~~While 6edo does not well approximate~~ the ~~3rd~~ harmonic, it ~~does contain~~ a ~~good approximation of~~ the 9th harmonic. ~~Therefore~~, 6edo ~~can be treated as a~~ 2.9.5.7-[[~~subgroup~~]] ~~temperament~~.		* [0 2 5] = 4:5:7, with the harmonic seventh as a bounding interval
			* [0 3 4] = 5:7:8, with the minor sixth as a bounding interval
			* [0 1 3] = 7:8:10, with the large septimal tritone as a bounding interval

			Whichever way, this is very different from standard functional harmony.

			If the prime 3 is added, it leads to absurd interpretations such as [[father]], as it is almost 100 cents sharp. However, in a composite subgroup, the 9th harmonic can be introduced, being directly approximated by 1 step of 6edo. In 2.9.5.7, the most salient fact about 6edo is that both [[64/63]] and [[81/80]] are tempered out, implying the restriction of both 2.3.7 [[superpyth]] and 2.3.5 [[meantone]] temperament (that is, [[Dominant (temperament)\|dominant]] temperament) to 2.9.5.7.

			6edo is the first edo to have lower [[Consistency limits of small EDOs\|consistency]] than the one that precedes it, and the highest edo that has no single period mode of symmetry scales other than using the single step as a generator. This means it is relatively poor for its size at creating traditional tonal music, with 5edo and 7edo both having much better representations of the third harmonic, but has still seen more use than most edos other than 12, since it can be played on any 12-tone instrument.

			=== Notation ===
			As a subset of [[12edo]], 6edo can be notated on a five-line staff with standard notation.

	=== Odd harmonics ===		=== Odd harmonics ===

Sintel: /* Uniform maps */ use new args

2025-03-29T17:07:37Z

Uniform maps: use new args

← Older revision		Revision as of 17:07, 29 March 2025
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	== Regular temperament properties ==		== Regular temperament properties ==
	=== Uniform maps ===		=== Uniform maps ===
	{{Uniform map\|~~13\|5.5\|~~6.5}}		{{Uniform map\|edo=6}}

	=== Commas ===		=== Commas ===

FloraC: -redundant category

2025-02-23T13:26:54Z

-redundant category

← Older revision		Revision as of 13:26, 23 February 2025
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	[[Category:6-tone scales]]		[[Category:6-tone scales]]
	[[Category:Listen]]		[[Category:Listen]]
	~~[[Category:Macrotonal]]~~

ArrowHead294 at 15:58, 20 February 2025

2025-02-20T15:58:31Z

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