17edo - Revision history

Yourmusic Productions: /* Instruments */ add new entry, consolidate existing ones.

2026-05-21T09:14:43Z

Instruments: add new entry, consolidate existing ones.

← Older revision		Revision as of 09:14, 21 May 2026
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	[[File:17edo soprano ukulele with 3D printed fretboard.jpg\|frameless\|640x640px]]		[[File:17edo soprano ukulele with 3D printed fretboard.jpg\|frameless\|640x640px]]

	~~Keyboards have also been built for 17edo — see [[Stephen Weigel]]'s [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025).~~

	=== Keyboards ===		=== Keyboards ===
	[[Lumatone mapping for 17edo\|Lumatone mappings for 17edo]] are available.		[[Lumatone mapping for 17edo\|Lumatone mappings for 17edo]] are available.

	It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following ~~video~~ by [[Chris Vaisvil]]:		The Striso Board can be tuned in many ways, but as it has 17 notes per octave and is organised in a circle of fifths based layout, it works particularly well with 17edo, letting you play far wider stretches of notes than a standard keyboard.

			[[File:Strisoboard_piano2a_s.jpg\|frameless]]

			It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following videos by [[Stephen Weigel]] and [[Chris Vaisvil]]:

			* [https://www.youtube.com/watch?v=2B14mttkavA ''Take This Stone (17-TET microtonal cover)''] (2025)
	* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)		* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)

Lucius Chiaraviglio: /* Keyboards */ Add demo video of a MIDI keyboard rebuilt for 17EDO

2026-05-04T03:32:10Z

Keyboards: Add demo video of a MIDI keyboard rebuilt for 17EDO

← Older revision		Revision as of 03:32, 4 May 2026
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	=== Keyboards ===		=== Keyboards ===
	[[Lumatone mapping for 17edo\|Lumatone mappings for 17edo]] are available.		[[Lumatone mapping for 17edo\|Lumatone mappings for 17edo]] are available.

			It is possible to rebuild some standard MIDI keyboards to have 17 note per octave by combining parts from multiple keyboards, as with the finished product shown in the following video by [[Chris Vaisvil]]:

			* [https://www.youtube.com/watch?v=nboggmtayk0 ''DIY microtonal piano - 17 notes per octave''] (2026)

	== Music ==		== Music ==

BudjarnLambeth: /* MOS scales */ add link

2026-03-28T05:54:20Z

MOS scales: add link

← Older revision		Revision as of 05:54, 28 March 2026
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	* diatonic ([[leapfrog]]/[[archy]]) [[5L 2s]] 3 3 3 1 3 3 1 (10\17, 1\1)		* diatonic ([[leapfrog]]/[[archy]]) [[5L 2s]] 3 3 3 1 3 3 1 (10\17, 1\1)
	* [[neutrominant]] [[3L 4s]] 3 2 3 2 3 2 2 (5\17, 1\1)		* [[neutrominant]] [[3L 4s]] 3 2 3 2 3 2 2 (5\17, 1\1) (''dedicated article: [[17edo neutral scale]]'')
	* [[neutrominant]] [[7L 3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)		* [[neutrominant]] [[7L 3s]] 2 2 2 1 2 2 1 2 2 1 (5\17, 1\1)
	* [[squares]] [[3L 5s]] 1 1 4 1 4 1 4 (6\17, 1\1)		* [[squares]] [[3L 5s]] 1 1 4 1 4 1 4 (6\17, 1\1)

Overthink: /* Commas */ - unneeded precision

2026-03-12T22:39:06Z

Commas: - unneeded precision

Show changes

Overthink: /* Commas */ add more

2026-03-12T22:35:53Z

Commas: add more

@@ Line 614: / Line 614: @@
 | Triru-agu
 | Orwellisma
 |-
 | 7
@@ Line 656: / Line 670: @@
 | Lozoyo
 | Keenanisma
 |-
 | 13
@@ Line 712: / Line 740: @@
 | Satritho
 | Threedie
 |-
 | 23
 | [[208/207]]
-| [4 -2 0 0 0 1 0 0 -1⟩
+| {{Monzo| 4 -2 0 0 0 1 0 0 -1 }}
-| 8.343
+| 8.3433
-| Twethutho 2nd
+| Twethutho
 | Vicetone comma
 |}
 <references group="note" />
-Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the patent val, the latter two due to 17edo's inaccurate prime 5.
+Note that due to the inaccurate prime 5, the rather large commas [[25/24]], [[525/512]], [[45/44]], and [[40/39]] are all tempered out by 17edo's patent val.
 === Rank-2 temperaments ===

Overthink: /* Commas */ expand val; - redundant limit

2026-03-12T22:04:12Z

Commas: expand val; - redundant limit

← Older revision		Revision as of 22:04, 12 March 2026
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	=== Commas ===		=== Commas ===
	17et [[tempering out\|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val\| 17 27 39 48 59 63 69 }}, cent values rounded to 5 digits.)		17et [[tempering out\|tempers out]] the following [[comma]]s. (Note: This assumes [[patent val]] {{val\| 17 27 39 48 59 63 69 72 77}}, cent values rounded to 5 digits.)

	{\| class="commatable wikitable center-all left-3 right-4 left-6"		{\| class="commatable wikitable center-all left-3 right-4 left-6"
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	\|}		\|}
	<references group="note" />		<references group="note" />
	Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the ~~13-limit~~ patent val, the latter two due to 17edo's inaccurate prime 5.		Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the patent val, the latter two due to 17edo's inaccurate prime 5.

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

Overthink: /* Commas */ add more

2026-03-12T22:02:57Z

Commas: add more

← Older revision		Revision as of 22:02, 12 March 2026
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	\|-		\|-
	! [[Harmonic limit\|Prime<br>limit]]		! [[Harmonic limit\|Prime<br>limit]]
	! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints</ref>		! [[Ratio]]<ref group="note">Ratios longer than 10 digits are presented by placeholders with informative hints.</ref>
	! [[Monzo]]		! [[Monzo]]
	! [[Cent]]s		! [[Cent]]s
Line 567:		Line 567:
	\|-		\|-
	\| 3		\| 3
	\| [[134217728/129140163\|(18 digits)]]		\| <abbr title="134217728/129140163">(18 digits)</abbr>
	\| {{Monzo\| 27 -17 }}		\| {{Monzo\| 27 -17 }}
	\| 66.765		\| 66.765
Line 586:		Line 586:
	\| Layo		\| Layo
	\| Schisma		\| Schisma
			\|-
			\| 7
			\| [[64/63]]
			\| {{Monzo\| 6 -2 0 -1 }}
			\| 27.264
			\| Ru
			\| Septimal comma
	\|-		\|-
	\| 7		\| 7
Line 593:		Line 600:
	\| Lazoyoyo		\| Lazoyoyo
	\| Avicennma		\| Avicennma
	\|-
	~~\| 7~~
	~~\| [[64/63]]~~
	~~\| {{Monzo\| 6 -2 0 -1 }}~~
	~~\| 27.264~~
	~~\| Ru~~
	~~\| Septimal comma~~
	\|-		\|-
	\| 7		\| 7
Line 621:		Line 621:
	\| Quinzo-ayoyo		\| Quinzo-ayoyo
	\| [[Wizma]]		\| [[Wizma]]
			\|-
			\| 11
			\| [[45/44]]
			\| {{Monzo\| -2 2 1 0 -1 }}
			\| 38.906
			\| Luyo
			\| Cake comma
	\|-		\|-
	\| 11		\| 11
Line 641:		Line 648:
	\| 7.1391		\| 7.1391
	\| Lulu		\| Lulu
	\| Rastma		\| Rastma, neutral thirds comma
	\|-		\|-
	\| 11		\| 11
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	\|-		\|-
	\| 13		\| 13
	\| [[~~1352~~/~~1331~~]]		\| [[78/77]]
	\| {{Monzo\| 3 0 0 0 -3 2 }}		\| {{Monzo\| 1 1 0 -1 -1 1 }}
	\| 27.~~101~~		\| 22.339
	\| ~~Bithotrilu~~		\| Tholuru
	\| ~~Lovecraft comma~~		\| Negustma
			\|-
			\| 13
			\| [[144/143]]
			\| {{Monzo\| 4 2 0 0 -1 -1 }}
			\| 12.064
			\| Thulu
			\| Grossma
			\|-
			\| 13
			\| [[169/168]]
			\| {{Monzo\| -3 -1 0 -1 0 2 }}
			\| 10.274
			\| Thothoru
			\| Buzurgisma, dhanvantarisma
	\|-		\|-
	\| 13		\| 13
	\| [[352/351]]		\| [[352/351]]
	\| [5 -3 0 0 1 -1⟩		\| [5 -3 0 0 1 -1⟩
	\| 4.~~925~~		\| 4.9253
	\| Thulo		\| Thulo
	\| Major minthma		\| Major minthma
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	\| [[364/363]]		\| [[364/363]]
	\| {{Monzo\| 2 -1 0 1 -2 1 }}		\| {{Monzo\| 2 -1 0 1 -2 1 }}
	\| 4.~~763~~		\| 4.7627
	\| Tholuluzo		\| Tholuluzo
	\| Minor minthma		\| Minor minthma
	\|-		\|-
	\| 17		\| 13
	\| [[~~136~~/~~135~~]]		\| [[512/507]]
	\| {{Monzo\| 3 -3 -1 0 0 0 1 }}		\| {{Monzo\| 9 -1 0 0 0 -2 }}
	\| 12.~~776~~		\| 16.990
	\| ~~Sogu 2nd~~		\| Thuthu
	\| ~~Diatisma~~		\| Tridecimal neutral thirds comma
			\|-
			\| 13
			\| [[1352/1331]]
			\| {{Monzo\| 3 0 0 0 -3 2 }}
			\| 27.101
			\| Bithotrilu
			\| Lovecraft comma
			\|-
			\| 13
			\| [[2197/2187]]
			\| {{Monzo\| 0 -7 0 0 0 3 }}
			\| 7.8980
			\| Satritho
			\| Threedie
	\|-		\|-
	\| 23		\| 23
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	\| Twethutho 2nd		\| Twethutho 2nd
	\| Vicetone comma		\| Vicetone comma
	\|-
	~~\| 23~~
	~~\| [[460/459]]~~
	~~\| [2 -3 1 0 0 0 -1 0 1⟩~~
	~~\| 3.767~~
	~~\| Twethosuyo~~
	~~\| Scanisma~~
	\|}		\|}
	<references group="note" />		<references group="note" />
	Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, ~~as stated~~.		Note that despite their relatively large size, the 17-comma, the avicennma and the chromatic semitone are all tempered out by the 13-limit patent val, the latter two due to 17edo's inaccurate prime 5.

	=== Rank-2 temperaments ===		=== Rank-2 temperaments ===

Overthink: /* Commas */ formatting

2026-03-12T19:40:16Z

Commas: formatting

← Older revision		Revision as of 19:40, 12 March 2026
Line 657:		Line 657:
	\| Lovecraft comma		\| Lovecraft comma
	\|-		\|-
	\|13		\| 13
	\|[[352/351]]		\| [[352/351]]
	\|[5 -3 0 0 1 -1⟩		\| [5 -3 0 0 1 -1⟩
	\|4.925		\| 4.925
	\|Thulo		\| Thulo
	\|Major minthma		\| Major minthma
	\|-		\|-
	\| 13		\| 13
Line 678:		Line 678:
	\| Diatisma		\| Diatisma
	\|-		\|-
	\|23		\| 23
	\|[[208/207]]		\| [[208/207]]
	\|[4 -2 0 0 0 1 0 0 -1⟩		\| [4 -2 0 0 0 1 0 0 -1⟩
	\|8.343		\| 8.343
	\|Twethutho 2nd		\| Twethutho 2nd
	\|Vicetone comma		\| Vicetone comma
	\|-		\|-
	\|23		\| 23
	\|[[460/459]]		\| [[460/459]]
	\|[2 -3 1 0 0 0 -1 0 1⟩		\| [2 -3 1 0 0 0 -1 0 1⟩
	\|3.767		\| 3.767
	\|Twethosuyo		\| Twethosuyo
	\|Scanisma		\| Scanisma
	\|}		\|}
	<references group="note" />		<references group="note" />

Overthink: /* Theory */ link wart notation; commas section

2026-03-12T19:38:09Z

Theory: link wart notation; commas section

← Older revision		Revision as of 19:38, 12 March 2026
Line 12:		Line 12:
	17edo is the next smallest edo to have a [[5L 2s\|diatonic]] [[3/2\|perfect fifth]] after [[12edo]], and is quite popular for that reason. The perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the [[hard]]ness of [[Pythagorean tuning]] rather than mellowing it out as in [[meantone]]. It completely misses [[harmonic]] [[5/1\|5]], with [[5/4]] and [[6/5]] both being about halfway between its steps, but it approximates harmonics [[7/1\|7]], [[11/1\|11]], [[13/1\|13]], and [[23/1\|23]] acceptably, with a sharp tuning for all of them. It can thus be treated as a temperament of the 2.3.25.7.11.13.23 [[subgroup]] or any of its subsets, where it is quite accurate for its size.		17edo is the next smallest edo to have a [[5L 2s\|diatonic]] [[3/2\|perfect fifth]] after [[12edo]], and is quite popular for that reason. The perfect fifth is around 4 cents sharp of just, and around 6 cents sharp of 12edo's, lending itself to a diatonic scale with more constrasting large and small steps, so it can be seen as a tuning that emphasizes the [[hard]]ness of [[Pythagorean tuning]] rather than mellowing it out as in [[meantone]]. It completely misses [[harmonic]] [[5/1\|5]], with [[5/4]] and [[6/5]] both being about halfway between its steps, but it approximates harmonics [[7/1\|7]], [[11/1\|11]], [[13/1\|13]], and [[23/1\|23]] acceptably, with a sharp tuning for all of them. It can thus be treated as a temperament of the 2.3.25.7.11.13.23 [[subgroup]] or any of its subsets, where it is quite accurate for its size.

	A notable [[comma]] it [[tempering out\|tempers out]] is [[64/63]], which equates the harmonic seventh [[7/4]] with the pythagorean minor seventh [[16/9]], while its patent val does not temper out [[81/80]]. This makes 17edo by default a [[superpyth]]agorean system rather than a [[meantone]] one, being very close to 1/7-comma superpyth. Other commas it tempers out ~~include [[78/77]], [[99/98]], [[144/143]], [[169/168]],~~ [[~~243/242~~]]~~, and many more~~, each of which has its own effect on the structure of 17edo. If one wants to approximate JI with prime 5, then 17edo would not be the best option, and it would be better to use other systems like [[19edo]], [[22edo]], [[27edo]], or [[31edo]] instead. That said, the 17[[~~wart\|c~~]] [[~~val~~]] does temper out 81/80 (while improving consistency as shown below in [[#Approximation to JI]]), while still tempering out 64/63, thus placing it on the meantone spectrum with the [[dominant (temperament)\|dominant]] [[extension]].		A notable [[comma]] it [[tempering out\|tempers out]] is [[64/63]], which equates the harmonic seventh [[7/4]] with the pythagorean minor seventh [[16/9]], while its patent val does not temper out [[81/80]]. This makes 17edo by default a [[superpyth]]agorean system rather than a [[meantone]] one, being very close to 1/7-comma superpyth. Other commas it tempers out can be found in the [[#Commas]] section, each of which has its own effect on the structure of 17edo. If one wants to approximate JI with prime 5, then 17edo would not be the best option, and it would be better to use other systems like [[19edo]], [[22edo]], [[27edo]], or [[31edo]] instead. That said, the 17c [[val]] (written using [[wart notation]]) does temper out 81/80 (while improving consistency as shown below in [[#Approximation to JI]]), while still tempering out 64/63, thus placing it on the meantone spectrum with the [[dominant (temperament)\|dominant]] [[extension]].

	=== As a means of extending harmony ===		=== As a means of extending harmony ===

Lucius Chiaraviglio: /* Commas */ Add scanisma

2026-03-09T09:28:05Z

Commas: Add scanisma

← Older revision		Revision as of 09:28, 9 March 2026
Line 684:		Line 684:
	\|Twethutho 2nd		\|Twethutho 2nd
	\|Vicetone comma		\|Vicetone comma
			\|-
			\|23
			\|[[460/459]]
			\|[2 -3 1 0 0 0 -1 0 1⟩
			\|3.767
			\|Twethosuyo
			\|Scanisma
	\|}		\|}
	<references group="note" />		<references group="note" />