69edo - Revision history

FloraC: /* Notation */ SZG notation

2026-05-12T14:04:06Z

Notation: SZG notation

← Older revision		Revision as of 14:04, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	69edo can be notated with [[ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.		[[Stein–Zimmermann–Gould notation]] uses sharps and flats along with quartertone accidentals and arrows:
			{{Sharpness-sharp4-szg}}

			=== Kite's ups and downs notation ===
			69edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, downsharp, sharp, upsharp etc. and down, dud, upflat etc. Note that dup is equivalent to dudsharp and dud is equivalent to dupflat.
	{{Sharpness-sharp4a}}		{{Sharpness-sharp4a}}
	[[Alternative symbols for ups and downs notation]] uses sharps and flats along with Stein–Zimmerman [[24edo#Notation\|quarter-tone]] accidentals, combined with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
	~~{{Sharpness-sharp4}}~~
	=== Sagittal notation ===		=== Sagittal notation ===
	This notation uses the same sagittal sequence as ~~EDOs~~ [[62edo#Sagittal notation\|62]] and [[76edo#Sagittal notation\|76]].		This notation uses the same sagittal sequence as edos [[62edo #Sagittal notation\|62]] and [[76edo #Sagittal notation\|76]].

	==== Evo flavor ====		==== Evo flavor ====
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	</imagemap>		</imagemap>

	In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation#Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this ~~EDO~~.		In the diagrams above, a sagittal symbol followed by an equals sign (=) means that the following comma is the symbol's [[Sagittal notation #Primary comma\|primary comma]] (the comma it ''exactly'' represents in JI), while an approximately equals sign (≈) means it is a secondary comma (a comma it ''approximately'' represents in JI). In both cases the symbol exactly represents the tempered version of the comma in this edo.

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

Overthink: /* Theory */ Note 69b fifth

2026-02-27T05:05:19Z

Theory: Note 69b fifth

← Older revision		Revision as of 05:05, 27 February 2026
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	{{ED intro}}		{{ED intro}}
	== Theory ==		== Theory ==
	69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652{{c}}. Such a fifth is closer to [[2/7-comma meantone]] than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, ~~wherein~~ the ~~perfect~~ fifth ~~and~~ the ~~major third beat at equal rates~~. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.		69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652{{C}}. Such a fifth is closer to [[2/7-comma meantone]] than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, where the frequencies of the root, third, and fifth of a major triad are equidistant (in a linear scale); in other words, where the [[4:5:6]] triad is [[delta-rational]] (sometimes abbreviated DR). Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.

			The alternative sharp fifth of 713.043{{C}} in the 69b [[val]] supports a tuning of [[archy]] where the [[6:7:8]] triad, which divides the fourth instead of the fifth, is tuned close to DR.

	69edo offers two kinds of meantone 12-tone scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium\|lithium]] scale, which has a 6:5 step ratio and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s\|tcherepnin]] scale instead of traditional diatonic.		69edo offers two kinds of meantone 12-tone scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium\|lithium]] scale, which has a 6:5 step ratio and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s\|tcherepnin]] scale instead of traditional diatonic.

Lucius Chiaraviglio: /* Rank 2 temperaments */ More Devicromic Octacot information

2025-12-20T09:08:40Z

Rank 2 temperaments: More Devicromic Octacot information

← Older revision		Revision as of 09:08, 20 December 2025
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	\|1		\|1
	\|5\69		\|5\69
	\|[[Devichromic chords\|Devichromic Octacot]]<ref group="note" name="tempname">Placeholder name, with link to [[Devichromic chords]] article — no general article currently exists for Devichromic temperament, and this particular incarnation of Devichromic temperament is likely to receive a different permanent name.</ref>		\|[[Devichromic chords\|Devichromic Octacot]]<ref group="note" name="tempname">Placeholder name, with link to [[Devichromic chords]] article — no general article currently exists for Devichromic temperament, and this particular incarnation of Devichromic temperament is likely to receive a different permanent name. The temperament is [https://x31eq.com/pyscript/uv.html?uvs=81%3A80+400%3A399+%5B17%2C-1%2C8%2C0%2C-8%3E&page=0&limit=2_3_5_7_19 14c & 55d], specified by the 2.3.5.7.19 subgroup unison vector list [-4, 4, -1, 0, 0⟩ ([[81/80]]), [4, -1, 2, -1, -1⟩ ([[400/399]]), [17, -1, 8, 0, -8⟩ (51200000000/50950689123), the last of which currently has no article, but equates a stack of eight [[20/19]]s to [[3/2]].</ref>
	\|-		\|-
	\| 1		\| 1

Lucius Chiaraviglio: /* Proposed names */ Mapping seems to be by direct approximation rather than patent val

2025-12-20T08:46:46Z

Proposed names: Mapping seems to be by direct approximation rather than patent val

← Older revision		Revision as of 08:46, 20 December 2025
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	\| 0.000		\| 0.000
	\|}		\|}
	<nowiki />* Some simpler ratios listed		<nowiki />* Some simpler ratios listed and mapped by direct approximation (even if inconsistent).

	== Notation ==		== Notation ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''69edo waltz'' (2025)

2025-12-03T06:54:57Z

Music: Add Bryan Deister's ''69edo waltz'' (2025)

← Older revision		Revision as of 06:54, 3 December 2025
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	* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)		* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)
	* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)		* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)
			* [https://www.youtube.com/shorts/GOjgAm6uwOY ''69edo waltz''] (2025)

	; [[Eliora]]		; [[Eliora]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Compass - Mili (microtonal cover in 69edo)'' (2025)

2025-05-30T07:11:29Z

Music: Add Bryan Deister's ''Compass - Mili (microtonal cover in 69edo)'' (2025)

← Older revision		Revision as of 07:11, 30 May 2025
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	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)		* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)
			* [https://www.youtube.com/shorts/4XBELeySMPk ''Compass - Mili (microtonal cover in 69edo)''] (2025)

	; [[Eliora]]		; [[Eliora]]

Lucius Chiaraviglio: /* Theory */ Add links to some commas

2025-05-26T18:23:39Z

Theory: Add links to some commas

← Older revision		Revision as of 18:23, 26 May 2025
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	69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652{{c}}. Such a fifth is closer to [[2/7-comma meantone]] than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.		69edo has been called "the love-child of [[23edo]] and [[quarter-comma meantone]]". As a meantone system, it is on the flat side, with a fifth of 695.652{{c}}. Such a fifth is closer to [[2/7-comma meantone]] than 1/4-comma, and is nearly identical to that of "Synch-Meantone", or Wilson's equal beating meantone, wherein the perfect fifth and the major third beat at equal rates. Therefore 69edo can be treated as a closed system of Synch-Meantone for most purposes.

	69edo offers two kinds of meantone 12-tone scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium\|lithium]] scale, which has a 6:5 step ratio and stems from a temperament tempering out 3125/3087 along with 81/80. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s\|tcherepnin]] scale instead of traditional diatonic.		69edo offers two kinds of meantone 12-tone scales. One is the raw meantone scale, which has a 7:4 step ratio, and other is period-3 [[Meantone family#Lithium\|lithium]] scale, which has a 6:5 step ratio and stems from a temperament tempering out [[3125/3087]] along with [[81/80]]. It should be noted that while the lithium scale has a meantone fifth, it produces a [[3L 6s\|tcherepnin]] scale instead of traditional diatonic.

	In the [[7-limit]] it is a [[mohajira]] system, tempering out 6144/6125, but not a septimal meantone system, as [[126/125]] maps to one step. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap\|31 & 69}} variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.		In the [[7-limit]] it is a [[mohajira]] system, tempering out [[6144/6125]], but not a septimal meantone system, as [[126/125]] maps to one step. In the 11-limit it tempers out [[99/98]], and supports the {{nowrap\|31 & 69}} variant of mohajira, identical to the standard 11-limit mohajira in [[31edo]] but not in 69.

	The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is {{nowrap\|22 & 69}}, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.		The [[concoctic scale]] for 69edo is 22\69, and the corresponding rank two temperament is {{nowrap\|22 & 69}}, defined by tempering out the [-41, 1, 17⟩ comma in the 5-limit.

Lucius Chiaraviglio: /* Rank 2 temperaments */ Add 5\69 with placeholder name Devichromic Octacot (with link to Devichromic chords article), which is demonstrated in Lumatone mapping for 69edo

2025-05-26T07:46:20Z

Rank 2 temperaments: Add 5\69 with placeholder name Devichromic Octacot (with link to Devichromic chords article), which is demonstrated in Lumatone mapping for 69edo

← Older revision		Revision as of 07:46, 26 May 2025
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	\| 2\69		\| 2\69
	\| [[Gammy]] (69de)		\| [[Gammy]] (69de)
			\|-
			\|1
			\|5\69
			\|[[Devichromic chords\|Devichromic Octacot]]<ref group="note" name="tempname">Placeholder name, with link to [[Devichromic chords]] article — no general article currently exists for Devichromic temperament, and this particular incarnation of Devichromic temperament is likely to receive a different permanent name.</ref>
	\|-		\|-
	\| 1		\| 1
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	\| [[Nessafof]] (69e)		\| [[Nessafof]] (69e)
	\|}		\|}
			<references group="note" />

	== Scales ==		== Scales ==

Lucius Chiaraviglio: /* Music */ Insert Instruments section before this, now that a Lumatone mapping for 69edo is now available

2025-05-26T07:22:20Z

Music: Insert Instruments section before this, now that a Lumatone mapping for 69edo is now available

← Older revision		Revision as of 07:22, 26 May 2025
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	* Lithium[9], [[3L 6s]] – 11 6 6 11 6 6 11 6 6		* Lithium[9], [[3L 6s]] – 11 6 6 11 6 6 11 6 6
	* Lithium[12], [[9L 3s]] – 5 6 6 6 5 6 6 6 5 6 6 6		* Lithium[12], [[9L 3s]] – 5 6 6 6 5 6 6 6 5 6 6 6

			== Instruments ==

			A [[Lumatone mapping for 69edo]] is available.

	== Music ==		== Music ==

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''microtonal improvisation in 69edo'' (2025)

2025-05-24T07:52:01Z

Music: Add Bryan Deister's ''microtonal improvisation in 69edo'' (2025)

← Older revision		Revision as of 07:52, 24 May 2025
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	== Music ==		== Music ==
			; [[Bryan Deister]]
			* [https://www.youtube.com/watch?v=ZAqPonAHuUM ''microtonal improvisation in 69edo''] (2025)

	; [[Eliora]]		; [[Eliora]]
	* [https://www.youtube.com/watch?v=a4vNlDU6Vkw ''Hypergiant Sakura''] (2021)		* [https://www.youtube.com/watch?v=a4vNlDU6Vkw ''Hypergiant Sakura''] (2021)