18edo - Revision history

FloraC: /* Music */ +1

2026-05-07T15:04:46Z

Music: +1

← Older revision		Revision as of 15:04, 7 May 2026
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	; [[Francium]]		; [[Francium]]
	* "excucumber" from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/2uSQv7MbMOKMLue2FMVU9y Spotify] \| [https://francium223.bandcamp.com/track/excucumber Bandcamp] \| [https://www.youtube.com/watch?v=dcOsIrQEsg4 YouTube]		* "excucumber", from ''The Decatonic Album'' (2024) – [https://open.spotify.com/track/2uSQv7MbMOKMLue2FMVU9y Spotify] \| [https://francium223.bandcamp.com/track/excucumber Bandcamp] \| [https://www.youtube.com/watch?v=dcOsIrQEsg4 YouTube]

			; [[groundfault]]
			* "Life and Limb", from ''Souvenirs of the Affliction'' (2025) – [https://groundfco.bandcamp.com/track/life-and-limb-18edo-2 Bandcamp] \| [https://www.youtube.com/watch?v=rrjuGmmodn0&t=1751 YouTube (29:11–33:47)]

	; [[Aaron Andrew Hunt]]		; [[Aaron Andrew Hunt]]

FloraC: /* Music */ cleanup

2026-05-07T15:02:12Z

Music: cleanup

← Older revision		Revision as of 15:02, 7 May 2026
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	=== 20th century ===		=== 20th century ===
	; [[Ivan Wyschnegradsky]]		; [[Ivan Wyschnegradsky]]
	* [https://www.youtube.com/watch?v=gbPPYOygNJc] ''Prélude et Etude, Op.48''], for third-tone piano of [[Julián Carrillo]] (1966)		* [https://www.youtube.com/watch?v=gbPPYOygNJc ''Prélude et Etude'', Op. 48], for third-tone piano of [[Julián Carrillo]] (1966)

	=== 21st century ===		=== 21st century ===
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	; [[Beheld]]		; [[Beheld]]
	* [https://www.youtube.com/watch?v=Nog2LROg8Ss Overstrung vibe]		* [https://www.youtube.com/watch?v=Nog2LROg8Ss ''Overstrung vibe''] (2022)

	; [[Bryan Deister]]		; [[Bryan Deister]]
	* [https://www.youtube.com/shorts/-oi5eJA65Zc ''Waltz in 18edo''] (2025)		* [https://www.youtube.com/shorts/-oi5eJA65Zc ''Waltz in 18edo''] (2025)
	* ''Lament in 18edo'' (2025)		* [https://www.youtube.com/watch?v=r3FypUx_iIk ''Lament in 18edo''] (2025)
	** [https://www.youtube.com/shorts/c26Yp_aMgDw Short version with demo of Lumatone layout)]
	** [https://www.youtube.com/watch?v=r3FypUx_iIk ~~Full version~~]
	* [https://www.youtube.com/shorts/hNmse4IUWL0 ''18edo improv''] (2025)		* [https://www.youtube.com/shorts/hNmse4IUWL0 ''18edo improv''] (2025)

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	; [[Aaron Andrew Hunt]]		; [[Aaron Andrew Hunt]]
	* [https://soundcloud.com/uz1kt3k/fuga-a3-in-18et Fuga a3 in 18ET]		* [https://soundcloud.com/uz1kt3k/fuga-a3-in-18et ''Fuga a3 in 18ET'']{{dead link}}

	; [[Noah Jordan]]		; [[Noah Jordan]]
	* ''The Moon'' (~~18edo album recorded in~~ 2016 ~~on the 1/3 tone piano of Sonido 13 / Julian Carrillo~~) – [https://noahdeanjordan.bandcamp.com/album/the-moon BandCamp] \| [https://www.youtube.com/watch?v=TunyA3gwEJw YouTube]		* ''The Moon'' (2016) – [https://noahdeanjordan.bandcamp.com/album/the-moon BandCamp] \| [https://www.youtube.com/watch?v=TunyA3gwEJw YouTube] – 7-piece album recorded on the 1/3-tone piano of Sonido 13 / Julian Carrillo
	* [https://www.youtube.com/watch?v=O36ZQyq6oR8 ~~There and Back Again~~] ~~(a 20~~-~~minute microtonal journey)~~		* ''There and Back Again'' (2025) – [https://noahdeanjordan.bandcamp.com/album/there-and-back-again Bandcamp] \| [https://www.youtube.com/watch?v=O36ZQyq6oR8 YouTube] – 3-piece album recorded on the 1/3-tone piano of Sonido 13 / Julian Carrillo

	; [[Mandrake]]		; [[Mandrake]]
	* [https://www.youtube.com/watch?v=R1uz0ok4-Zs Such And Flowers]		* [https://www.youtube.com/watch?v=R1uz0ok4-Zs ''Such And Flowers''] (2022)
	* [https://www.youtube.com/watch?v=2AquW_cqUQc That Kinda Lo-Fi Feel]		* [https://www.youtube.com/watch?v=2AquW_cqUQc ''That Kinda Lo-Fi Feel''] (2022)

	; [[Leo Matarazzo]]		; [[Leo Matarazzo]]
	* [https://www.youtube.com/watch?v=G2vrqyE0ZX4 ''Eris ~~- Microtonal 18edo~~''] (2026)		* [https://www.youtube.com/watch?v=G2vrqyE0ZX4 ''Eris''] (2026)

	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]
	* [https://www.youtube.com/watch?v=vUTHZNzBwUo Air Triste]		* [https://www.youtube.com/watch?v=vUTHZNzBwUo ''Air Triste''] (2018)

	; [[Herman Miller]]		; [[Herman Miller]]
	* [https://soundcloud.com/morphosyntax-1/revealing-the-path Revealing the Path] (2018)		* [https://soundcloud.com/morphosyntax-1/revealing-the-path ''Revealing the Path''] (2018)

	; [[Mundoworld]]		; [[Mundoworld]]
	* [https://www.youtube.com/watch?v=iIaROmh7wD0 I Am the Monster I Fear]		* [https://www.youtube.com/watch?v=iIaROmh7wD0 ''I Am the Monster I Fear''] (2023)

	; [[No Clue Music]]		; [[No Clue Music]]
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	; [[norokusi]]		; [[norokusi]]
	* [https://www.youtube.com/watch?v=pEvT2oyWEuo 3 Bagatelles]		* [https://www.youtube.com/watch?v=pEvT2oyWEuo ''3 Bagatelles''] (2021)

	; [[NullPointerException Music]]		; [[NullPointerException Music]]
	* [https://www.youtube.com/watch?v=hNgI6oRYNHA ''Three Worlds Order''] (2020)		* [https://www.youtube.com/watch?v=hNgI6oRYNHA ''Three Worlds Order''] (2020)
	* [https://www.youtube.com/watch?v=FnYxYuukgrM ''Edolian ~~- Confusion~~''] (2020)		* [https://www.youtube.com/watch?v=FnYxYuukgrM "Confusion"], from [https://www.youtube.com/playlist?list=PLg1YtcJbLxnwTJkG4m0BWZWxIHj7ScdNn ''Edolian''] (2020)
	* [https://www.youtube.com/watch?v=1k4rNjyaZsE ''Purgatory''] (2021)		* [https://www.youtube.com/watch?v=1k4rNjyaZsE ''Purgatory''] (2021)
	* [https://www.youtube.com/watch?v=a7AtOuX1NAE ''The Hydrogen Atom''] (2023)		* [https://www.youtube.com/watch?v=a7AtOuX1NAE ''The Hydrogen Atom''] (2023)

	; [[Carlo Serafini]]		; [[Carlo Serafini]]
	* [http://www.seraph.it/~~dep~~/~~det/DoAndroidsDreamof18ED2~~.~~mp3.mp3 Do Androids Dream Of 18ED2?~~] ([http://www.seraph.it/~~blog_files~~/~~fb0306486b51c270607f90a0c795d531-202~~.~~html blog entry~~])		* ''Do Androids Dream Of 18ED2?'' (2015) – [http://www.seraph.it/blog_files/fb0306486b51c270607f90a0c795d531-202.html blog] \| [http://www.seraph.it/dep/det/DoAndroidsDreamof18ED2.mp3.mp3 play]{{dead link}}

	; [[TomPrice719]]		; [[TomPrice719]]
	* [https://soundcloud.com/tomprice719/composition-of-june-2015 Composition of June 2015]		* [https://soundcloud.com/tomprice719/composition-of-june-2015 ''Composition of June 2015''] (2015)

	; [[Chris Vaisvil]]		; [[Chris Vaisvil]]
	* [http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3 ~~Prelude in 18et], [http://chrisvaisvil.com/?p=3 composer notes~~]		* ''Prelude in 18et'' (2009) – [https://www.chrisvaisvil.com/prelude-in-18et/ blog] \| [http://micro.soonlabel.com/18-ET/prelude-in-18et.mp3 play]
	* [http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3 Flippertronics]		* [http://micro.soonlabel.com/18-ET/daily20110401-18c-flippertronics.mp3 ''Flippertronics'']
	* [http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3 Gerbils at the Wheel of Government] (in 9 and 18 edo simultaneously)		* [http://micro.soonlabel.com/9-edo/daily20111008b_gerbils_at_the_wheel_of_government.mp3 ''Gerbils at the Wheel of Government''] (in 9 and 18 edo simultaneously)

	; [[Julia Werntz]], [[Eric Moe]] & the [[Pandelis Karayorgis Trio]]		; [[Julia Werntz]], [[Eric Moe]] & the [[Pandelis Karayorgis Trio]]
	* ''[https://driffrecords.bandcamp.com/album/climbing-to-sleep Climbing to Sleep]'' ~~- jazz album~~ (2025)		* [https://driffrecords.bandcamp.com/album/climbing-to-sleep ''Climbing to Sleep''] (2025) – jazz album

	; [[Xenon]]		; [[Xenon]]
	* [https://www.youtube.com/watch?v=fj_AISfnFnY Deranged Anger]		* [https://www.youtube.com/watch?v=fj_AISfnFnY ''Deranged Anger''] (2021)

	; [[David Zaydullin]]		; [[David Zaydullin]]

Lucius Chiaraviglio: /* 21st century */ Add Leo Matarazzo's ''Eris - Microtonal 18edo'' (2026)

2026-05-04T03:27:03Z

21st century: Add Leo Matarazzo's ''Eris - Microtonal 18edo'' (2026)

← Older revision		Revision as of 03:27, 4 May 2026
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	* [https://www.youtube.com/watch?v=R1uz0ok4-Zs Such And Flowers]		* [https://www.youtube.com/watch?v=R1uz0ok4-Zs Such And Flowers]
	* [https://www.youtube.com/watch?v=2AquW_cqUQc That Kinda Lo-Fi Feel]		* [https://www.youtube.com/watch?v=2AquW_cqUQc That Kinda Lo-Fi Feel]

			; [[Leo Matarazzo]]
			* [https://www.youtube.com/watch?v=G2vrqyE0ZX4 ''Eris - Microtonal 18edo''] (2026)

	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]

Lucius Chiaraviglio: Undo revision 223859 by Lucius Chiaraviglio (talk) Got more information — Bryan Deister's ''18 tone unequal improv'' (2026) actually belongs under 36edo

2026-02-13T01:00:29Z

Undo revision 223859 by Lucius Chiaraviglio (talk) Got more information — Bryan Deister's ''18 tone unequal improv'' (2026) actually belongs under 36edo

← Older revision		Revision as of 01:00, 13 February 2026
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	=== 21st century ===		=== 21st century ===
	~~==== 18 equal divisions of the octave (18edo proper) ====~~
	; [[Ambient Esoterica]]		; [[Ambient Esoterica]]
	* [https://www.youtube.com/watch?v=Cp_lTUNmtd8 ''XVIII-TET Tribute to Full Moon in Virgo''] (2024)		* [https://www.youtube.com/watch?v=Cp_lTUNmtd8 ''XVIII-TET Tribute to Full Moon in Virgo''] (2024)
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	; [[David Zaydullin]]		; [[David Zaydullin]]
	* [https://www.youtube.com/watch?v=QzKNP-NwHu0 ''Phaserun''] (2024)		* [https://www.youtube.com/watch?v=QzKNP-NwHu0 ''Phaserun''] (2024)

	~~==== Unequal Derivatives of 18edo ====~~
	~~; [[Bryan Deister]]~~
	* [https://www.youtube.com/shorts/MjUdMnUA-2k ''18 tone unequal improv''] (2026)

	== See also ==		== See also ==

Yourmusic Productions: /* Keyboards */ remove duplicated sentence.

2026-02-12T22:17:51Z

Keyboards: remove duplicated sentence.

← Older revision		Revision as of 22:17, 12 February 2026
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	=== Keyboards ===		=== Keyboards ===
	~~[[Julián Carrillo]] built at least one third-tone piano in~~ [[Julián Carrillo]] built at least one third-tone piano in 18edo.		[[Julián Carrillo]] built at least one third-tone piano in 18edo.

	[[Lumatone mapping for 18edo\|Lumatone mappings for 18edo]] are available.		[[Lumatone mapping for 18edo\|Lumatone mappings for 18edo]] are available.

Lucius Chiaraviglio: /* 21st century */ Split into 18 equal divisions of the octave (18edo proper) and Unequal Derivatives of 18edo, the latter starting with Bryan Deister's 18 tone unequal improv (2026); may have to move this, pending more information

2026-02-12T08:58:17Z

21st century: Split into 18 equal divisions of the octave (18edo proper) and Unequal Derivatives of 18edo, the latter starting with Bryan Deister's 18 tone unequal improv (2026); may have to move this, pending more information

← Older revision		Revision as of 08:58, 12 February 2026
Line 585:		Line 585:

	=== 21st century ===		=== 21st century ===
			==== 18 equal divisions of the octave (18edo proper) ====
	; [[Ambient Esoterica]]		; [[Ambient Esoterica]]
	* [https://www.youtube.com/watch?v=Cp_lTUNmtd8 ''XVIII-TET Tribute to Full Moon in Virgo''] (2024)		* [https://www.youtube.com/watch?v=Cp_lTUNmtd8 ''XVIII-TET Tribute to Full Moon in Virgo''] (2024)
Line 652:		Line 653:
	; [[David Zaydullin]]		; [[David Zaydullin]]
	* [https://www.youtube.com/watch?v=QzKNP-NwHu0 ''Phaserun''] (2024)		* [https://www.youtube.com/watch?v=QzKNP-NwHu0 ''Phaserun''] (2024)

			==== Unequal Derivatives of 18edo ====
			; [[Bryan Deister]]
			* [https://www.youtube.com/shorts/MjUdMnUA-2k ''18 tone unequal improv''] (2026)

	== See also ==		== See also ==

Lucius Chiaraviglio: Update ¢ symbol to {{c}}; /* Theory */ Improve wording

2026-02-12T06:42:01Z

Update ¢ symbol to {{c}}; Theory: Improve wording

← Older revision		Revision as of 06:42, 12 February 2026
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	In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.		In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.

	However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.~~33¢~~, 5/4 to ~~400¢~~ and 7/4 to ~~1000¢~~; as a result, 28/27 is tempered out, and ~~weird~~ things happen: 9/8 and 7/6 are both mapped to 266.~~67¢~~, while 8/7 gets mapped below both of them to ~~200¢~~, making for a rather disordered [[9-odd-limit]] [[tonality diamond]], ~~but hey, whatever floats your boat!~~ This 7-limit mapping [[support]]s 7-limit [[sixix]] thus is strongly associated with 18edo's [[4L 3s]] [[mos]].		However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.33{{c}}, 5/4 to 400{{c}} and 7/4 to 1000{{c}}; as a result, 28/27 is tempered out, and unintuitive things happen: 9/8 and 7/6 are both mapped to 266.67{{c}}, while 8/7 gets mapped below both of them to 200{{c}}, making for a rather disordered [[9-odd-limit]] [[tonality diamond]], although this may be serviceable for the more exotemperamental music. This 7-limit mapping [[support]]s 7-limit [[sixix]], and thus is strongly associated with 18edo's [[4L 3s]] [[mos]].

	18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.		18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.
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	== Notation ==		== Notation ==
	=== Ups and downs notation ===		=== Ups and downs notation ===
	18edo can be notated with [[ups and downs]]. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4¢ worse that the best approximation, which becomes the up-fifth.		18edo can be notated with [[ups and downs]]. The notational 5th is the 2nd-best approximation of 3/2, 10\18. This is only 4{{c}} worse that the best approximation, which becomes the up-fifth.
	{{Mavila}}		{{Mavila}}
	{\| class="wikitable center-all right-2"		{\| class="wikitable center-all right-2"
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	18edo is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you!		18edo is an ideal scale for the first-time refretter, because you can retain all the even-number frets from 12-tET--essentially 1/3 of your work is done for you!

	The 8-note oneirotonic scale maps very simply to a 6-string guitar tuned in "reverse-standard" tuning (tune using four 466.~~667¢~~ intervals, with one 533.~~333¢~~ interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand).		The 8-note oneirotonic scale maps very simply to a 6-string guitar tuned in "reverse-standard" tuning (tune using four 466.667{{c}} intervals, with one 533.333{{c}} interval between the 2nd and 3rd strings), making for a softer learning-curve than EDOs like 14, 16, or 21 (all of which are most evenly open-tuned using a series of sharpened 4ths and a minor or neutral 3rd, and whose scales thus often require position-shifting and/or larger stretches of the hand).

	=== Keyboards ===		=== Keyboards ===

Overthink: /* Theory */ fix this

2026-02-11T23:11:33Z

Theory: fix this

← Older revision		Revision as of 23:11, 11 February 2026
Line 15:		Line 15:
	In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.		In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.

	However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.33¢, 5/4 to 400¢ and 7/4 to 1000¢; as a result, 28/27 is tempered out, and weird things happen: 9/8 and 7/6 are both mapped to 266.67¢, while 8/7 gets mapped below both of them to 200¢, making for a rather disordered 7-odd-limit tonality diamond, but hey, whatever floats your boat! This 7-limit mapping [[support]]s 7-limit [[sixix]] thus is strongly associated with 18edo's [[4L 3s]] [[mos]].		However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.33¢, 5/4 to 400¢ and 7/4 to 1000¢; as a result, 28/27 is tempered out, and weird things happen: 9/8 and 7/6 are both mapped to 266.67¢, while 8/7 gets mapped below both of them to 200¢, making for a rather disordered [[9-odd-limit]] [[tonality diamond]], but hey, whatever floats your boat! This 7-limit mapping [[support]]s 7-limit [[sixix]] thus is strongly associated with 18edo's [[4L 3s]] [[mos]].

	18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.		18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.

Overthink: standardize order, minor fixes

2026-01-22T04:27:35Z

standardize order, minor fixes

Show changes

Lucius Chiaraviglio: /* Keyboards */ Julián Carrillo built at least one third-tone piano in 18edo, which can be heard in a few of the recordings in the music section below.

2026-01-05T02:35:59Z

Keyboards: Julián Carrillo built at least one third-tone piano in 18edo, which can be heard in a few of the recordings in the music section below.

← Older revision		Revision as of 02:35, 5 January 2026
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	=== Keyboards ===		=== Keyboards ===
			[[Julián Carrillo]] built at least one third-tone piano in [[Julián Carrillo]] built at least one third-tone piano in 18edo.

	[[Lumatone mapping for 18edo\|Lumatone mappings for 18edo]] are available.		[[Lumatone mapping for 18edo\|Lumatone mappings for 18edo]] are available.

← Older revision		Revision as of 23:11, 11 February 2026
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	In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.		In order to access the excellent consonances actually available, one must take a considerably "non-common-practice" approach, meaning to avoid the usual closed-voice "root-3rd-5th" type of chord and instead use chords which are either more compressed or more stretched out. 18edo may be treated as a temperament of the 17-limit [[kN_subgroups\|418 subgroup]] [[just intonation subgroup]] 2.9.75.21.55.39.51. On this subgroup it tempers out exactly the same commas as [[72edo]] does on the full [[17-limit]], and gives precisely the same tunings. The subgroup can be put into a single chord, for example 32:36:39:42:51:55:64:75 (in terms of 18edo, 0-3-5-7-12-14-18-22), and transpositions and inversions of this chord or its subchords provide plenty of harmonic resources. 18edo also approximates 12:13:14:17:23:27:29 quite well, with the least maximum relative error out of any edos ≤ 100 (the worst-approximated interval is [[23/13]], with relative error 18.36%). Hence it can be viewed as an "/3 temperament" (/3 used in the [[primodality]] sense), specifically in the 2.9.13/12.7/6.17/12.23/12.29/24 subgroup. As for more simple subgroups, 18edo can be treated as a 2.9.5.11 subgroup temperament.

	However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.33¢, 5/4 to 400¢ and 7/4 to 1000¢; as a result, 28/27 is tempered out, and weird things happen: 9/8 and 7/6 are both mapped to 266.67¢, while 8/7 gets mapped below both of them to 200¢, making for a rather disordered 7-odd-limit tonality diamond, but hey, whatever floats your boat! This 7-limit mapping [[support]]s 7-limit [[sixix]] thus is strongly associated with 18edo's [[4L 3s]] [[mos]].		However, less accurate approximations can be used, and 18edo can be treated as a 7-limit (with 3s) exotemperament with the mapping {{val\| 18 29 42 51 }}. This maps 3/2 to 733.33¢, 5/4 to 400¢ and 7/4 to 1000¢; as a result, 28/27 is tempered out, and weird things happen: 9/8 and 7/6 are both mapped to 266.67¢, while 8/7 gets mapped below both of them to 200¢, making for a rather disordered [[9-odd-limit]] [[tonality diamond]], but hey, whatever floats your boat! This 7-limit mapping [[support]]s 7-limit [[sixix]] thus is strongly associated with 18edo's [[4L 3s]] [[mos]].

	18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.		18edo contains sub-edos [[2edo\|2]], [[3edo\|3]], [[6edo\|6]], and [[9edo\|9]], and itself is half of [[36edo]] and one-fourth of 72edo. It bears some similarities to [[13edo]] (with its very flat 4ths and nice subminor 3rds), [[11edo]] (with its very sharp minor 3rds, two of which span a very flat 5th), [[16edo]] (with its sharp 4ths and flat 5ths), and [[17edo]] and [[19edo]] (with its narrow semitone, three of which comprise a whole-tone). It is an excellent tuning for those seeking a forceful deviation from the common practice.