39edo - Revision history

VectorGraphics: added more patent val discussion

2026-06-03T09:10:56Z

added more patent val discussion

← Older revision		Revision as of 09:10, 3 June 2026
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	39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it does not do as good of a job at approximating [[JI]] as some other systems do. Because it can also approximate [[mavila]] as well as "anti-mavila" ([[oneirotonic]]), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).		39edo offers not one, but many, possible ways of extending tonality beyond the diatonic scale, even if it does not do as good of a job at approximating [[JI]] as some other systems do. Because it can also approximate [[mavila]] as well as "anti-mavila" ([[oneirotonic]]), the latter of which it inherits from [[13edo]], this makes 39edo an extremely versatile temperament usable in a wide range of situations (both harmonic and inharmonic).

			39edo is a reasonable tuning of [[triforce]] beyond 15edo, and optimizes both its semaphore and augmented components by tuning the fifth sharp.

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

Overthink: /* Intervals */ - obsolete note

2026-05-30T22:00:18Z

Intervals: - obsolete note

← Older revision		Revision as of 22:00, 30 May 2026
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	\| D		\| D
	\|}		\|}
	~~<nowiki/>* 11-limit in the 39d val, inconsistent intervals in ''italic''~~

	Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].		Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].

Overthink: /* Intervals */ left align those

2026-05-30T21:59:50Z

Intervals: left align those

← Older revision		Revision as of 21:59, 30 May 2026
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	== Intervals ==		== Intervals ==
	{\| class="wikitable center-all right-2 left-3 right-9 right-10"		{\| class="wikitable center-all right-2 left-3 left-4 left-5 right-9 right-10"
	\|-		\|-
	! rowspan="2" \| Steps		! rowspan="2" \| Steps
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	Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].		Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and downs notation #Chords and chord progressions]].


	== Notation ==		== Notation ==

Overthink: /* Intervals */ cleanup and links (minor note: don't italicize ","); Remove "nearest just interval" (generally not preferred).

2026-05-30T21:59:01Z

Intervals: cleanup and links (minor note: don't italicize ","); Remove "nearest just interval" (generally not preferred).

Show changes

VectorGraphics: added the patent val

2026-05-29T19:47:55Z

added the patent val

Show changes

VectorGraphics at 19:20, 29 May 2026

2026-05-29T19:20:09Z

← Older revision		Revision as of 19:20, 29 May 2026
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	== Theory ==		== Theory ==
	39edo's [[3/2\|perfect fifth]] is 5.8{{c}} sharp. Together with its best [[5/4\|classical major third]] which is the familiar 400{{c}} of [[12edo]]. We have two choices for a [[map]] for [[7/1\|7]], but the sharp one works better with the [[3/1\|3]] and [[5/1\|5]]. It also has a fine [[11/1\|11]], and adding it to consideration ~~the~~ choice for 39et is the sharp-tending 39df [[val]] {{val\| 39 62 91 '''110''' 135 '''145'''}}.		39edo's [[3/2\|perfect fifth]] is 5.8{{c}} sharp. Together with its best [[5/4\|classical major third]] which is the familiar 400{{c}} of [[12edo]]. We have two choices for a [[map]] for [[7/1\|7]], but the sharp one works better with the [[3/1\|3]] and [[5/1\|5]]. It also has a fine [[11/1\|11]], and adding it to consideration one possible choice for 39et is the sharp-tending 39df [[val]] {{val\| 39 62 91 '''110''' 135 '''145'''}}.

	As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap\|(39 {{=}} 17 + 22)}}; its fifth thus falls in the "shrub region" where the diatonic thirds are between standard neogothic thirds and septimal thirds. The specific 7-limit variant supported by 39et is [[quasisuper]]. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s\|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.		As a [[superpyth]] system, 39edo is intermediate between [[17edo]] and [[22edo]] {{nowrap\|(39 {{=}} 17 + 22)}}; its fifth thus falls in the "shrub region" where the diatonic thirds are between standard neogothic thirds and septimal thirds. The specific 7-limit variant supported by 39et is [[quasisuper]]. Alternatively, it can be seen as a [[hemifamity]] semaphore (that is, immunity) system in the patent val. While 17edo is superb for melody (as documented by [[George Secor]]), it does not approximate the 5th harmonic at all and only poorly approximates the 7th. 22edo is much better for 5-limit and 7-limit harmony but is less effective for melody because the [[diatonic semitone]] is [[quartertone]]-sized, which results in a very strange-sounding [[5L 2s\|diatonic scale]]. 39edo offers a compromise, since it still supports good 5- and 7-limit harmonies (though less close than 22edo), while at the same time having a diatonic semitone of 61.5 cents, as the ideal diatonic semitone for melody is somewhere in between 60 and 80 cents, i.e. a third tone, by Secor's estimates.

	Alternatively, if we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]], and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s\|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]], and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.		Alternatively, if we take 22\39 as a fifth, 39edo can be used as a tuning of [[mavila]], and from that point of view it seems to have attracted the attention of the [[Armodue]] school, an Italian group that use the scheme of [[7L 2s\|superdiatonic]] LLLsLLLLs like a base scale for notation and theory, suited in [[16edo]], and allied systems: [[25edo]] [1/3-tone 3;2]; [[41edo]] [1/5-tone 5;3]; and [[57edo]] [1/7-tone 7;4]. The [[hornbostel]] temperament is included too with: [[23edo]] [1/3-tone 3;1]; 39edo [1/5-tone 5;2] & [[62edo]] [1/8-tone 8;3]. The mavila fifth in 39edo like all mavila fifths is very, very flat, in this case, 25{{c}} flat.

FloraC: /* Notation */ SZG notation

2026-05-12T13:01:40Z

Notation: SZG notation

← Older revision		Revision as of 13:01, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	39edo can be notated with [[ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).		[[Stein–Zimmermann–Gould notation]] uses sharps and flats with arrows:
			{{Sharpness-sharp5-szg}}

			=== Kite's ups and downs notation ===
			39edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, dupflat etc. Note that dudsharp is equivalent to trup (triple-up) and dupflat is equivalent to trud (triple-down).
	{{Ups and downs sharpness}}		{{Ups and downs sharpness}}

	Another notation uses [[Alternative symbols for ups and downs notation #Sharp-5\|alternative ups and downs]]. Here, this can be done using sharps and flats with arrows, borrowed from extended [[Helmholtz–Ellis notation]]:
	~~{{Sharpness-sharp5}}~~

	=== Sagittal notation ===		=== Sagittal notation ===
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	\| 2/1		\| 2/1
	\|}		\|}

	== Approximation to JI ==		== Approximation to JI ==
	=== Interval mappings ===		=== Interval mappings ===

FloraC: /* Music */ ++

2026-05-07T13:42:15Z

Music: ++

← Older revision		Revision as of 13:42, 7 May 2026
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	* [https://www.youtube.com/watch?v=kYQyRY7xFJs ''Waltz in 39edo''] (2025)		* [https://www.youtube.com/watch?v=kYQyRY7xFJs ''Waltz in 39edo''] (2025)
	* [https://www.youtube.com/watch?v=Vzife15uUU4 ''Tilt Your Head Down''] (2026)		* [https://www.youtube.com/watch?v=Vzife15uUU4 ''Tilt Your Head Down''] (2026)

			; [[groundfault]]
			* From ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/album/souvenirs-of-the-affliction Bandcamp] \| [https://www.youtube.com/watch?v=rrjuGmmodn0 YouTube]
			** "Resolute Prelude"
			** "Residual Soliloquy"

	; [[Randy Wells]]		; [[Randy Wells]]

FloraC: /* Music */ cleanup and sectioning

2026-05-07T13:40:31Z

Music: cleanup and sectioning

← Older revision		Revision as of 13:40, 7 May 2026
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	== Music ==		== Music ==
			=== Modern renderings ===
			; {{W\|HOYO-MiX}}
			* [https://www.youtube.com/shorts/4y11CWLIHNA "Sinner's Finale" from ''Genshin Impact OST''] (2023) – covered by [[Bryan Deister]] (2025)

			=== 21st century ===
	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023)		* [https://www.youtube.com/shorts/oeFI957W-xg ''39edo''] (2023)
	* [https://www.youtube.com/watch?v=XLRaG_pBN7k ''39edo jam''] (2025)		* [https://www.youtube.com/watch?v=XLRaG_pBN7k ''39edo jam''] (2025)
	* [https://www.youtube.com/shorts/4y11CWLIHNA ''Sinner's Finale - Genshin Impact (microtonal cover in 39edo)''] (2025)
	* [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025)		* [https://www.youtube.com/shorts/1T_xrZpUslQ ''39edo improv''] (2025)
	* [https://www.youtube.com/watch?v=kYQyRY7xFJs ''Waltz in 39edo''] (2025)		* [https://www.youtube.com/watch?v=kYQyRY7xFJs ''Waltz in 39edo''] (2025)
	* ~~''Tilt Your Head Down - 39edo '' (2026) [https://www.youtube.com/shorts/Tf812DJzoEA <nowiki>[short]</nowiki>],~~ [https://www.youtube.com/watch?v=Vzife15uUU4 ~~<nowiki>[full song]</nowiki>~~]		* [https://www.youtube.com/watch?v=Vzife15uUU4 ''Tilt Your Head Down''] (2026)

	; [[Randy Wells]]		; [[Randy Wells]]

Fitzgerald Lee: /* Notation */

2026-04-17T10:49:28Z

Notation

← Older revision		Revision as of 10:49, 17 April 2026
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	\| 2/1		\| 2/1
	\|}		\|}
			== Approximation to JI ==
			=== Interval mappings ===
			{{Q-odd-limit intervals}}
			{{Q-odd-limit intervals\|39.1\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 39df val mapping}}

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