21edo - Revision history

Overthink: /* Intervals */ some note names in table; more notation is later

2026-05-25T04:58:58Z

Intervals: some note names in table; more notation is later

← Older revision		Revision as of 04:58, 25 May 2026
Line 24:		Line 24:

	== Intervals ==		== Intervals ==
	Inconsistent intervals are in ''italics''.		Note names are given with 7edo as the naturals and arrows (written as ^ and v) for inflections up/down by one edostep. Inconsistent intervals are in ''italics''.
	{\| class="wikitable center-1 right-2"
			{\| class="wikitable center-1 right-2 right-3"
	\|-		\|-
	! #		! #
			! Name
	! Cents		! Cents
	! Approximate Ratios*		! Approximate Ratios*
	\|-		\|-
	\| 0		\| 0
			\| C
	\| 0.00		\| 0.00
	\| [[1/1]]		\| [[1/1]]
	\|-		\|-
	\| 1		\| 1
			\| ^C
	\| 57.14		\| 57.14
	\| [[21/20]]		\| [[21/20]]
	\|-		\|-
	\| 2		\| 2
			\| vD
	\| 114.29		\| 114.29
	\| [[14/13]], [[15/14]], [[16/15]]		\| [[14/13]], [[15/14]], [[16/15]]
	\|-		\|-
	\| 3		\| 3
			\| D
	\| 171.43		\| 171.43
	\| ''[[9/8]]'', ''[[13/12]]'', [[35/32]]		\| ''[[9/8]]'', ''[[13/12]]'', [[35/32]]
	\|-		\|-
	\| 4		\| 4
			\| ^D
	\| 228.57		\| 228.57
	\| [[8/7]], ''[[10/9]]''		\| [[8/7]], ''[[10/9]]''
	\|-		\|-
	\| 5		\| 5
			\| vE
	\| 285.71		\| 285.71
	\|''[[6/5]]'', [[7/6]]		\|''[[6/5]]'', [[7/6]]
	\|-		\|-
	\| 6		\| 6
			\| E
	\| 342.86		\| 342.86
	\| [[39/32]], [[128/105]], [[16/13]]		\| [[39/32]], [[128/105]], [[16/13]]
	\|-		\|-
	\| 7		\| 7
			\| ^E
	\| 400.00		\| 400.00
	\| [[5/4]], ''[[9/7]]''		\| [[5/4]], ''[[9/7]]''
	\|-		\|-
	\| 8		\| 8
			\| vF
	\| 457.14		\| 457.14
	\| [[13/10]], [[21/16]]		\| [[13/10]], [[21/16]]
	\|-		\|-
	\| 9		\| 9
			\| F
	\| 514.29		\| 514.29
	\| [[4/3]]		\| [[4/3]]
	\|-		\|-
	\| 10		\| 10
			\| ^F
	\| 571.43		\| 571.43
	\| [[7/5]]		\| [[7/5]]
	\|-		\|-
	\| 11		\| 11
			\| vG
	\| 628.57		\| 628.57
	\| [[10/7]]		\| [[10/7]]
	\|-		\|-
	\| 12		\| 12
			\| G
	\| 685.71		\| 685.71
	\| [[3/2]]		\| [[3/2]]
	\|-		\|-
	\| 13		\| 13
			\| ^G
	\| 742.86		\| 742.86
	\| [[20/13]], [[32/21]]		\| [[20/13]], [[32/21]]
	\|-		\|-
	\| 14		\| 14
			\| vA
	\| 800.00		\| 800.00
	\| [[8/5]], ''[[14/9]]''		\| [[8/5]], ''[[14/9]]''
	\|-		\|-
	\| 15		\| 15
			\| A
	\| 857.14		\| 857.14
	\| [[64/39]], [[105/64]], [[13/8]]		\| [[64/39]], [[105/64]], [[13/8]]
	\|-		\|-
	\| 16		\| 16
			\| ^A
	\| 914.29		\| 914.29
	\|''[[5/3]]'', [[12/7]]		\|''[[5/3]]'', [[12/7]]
	\|-		\|-
	\| 17		\| 17
			\| vB
	\| 971.43		\| 971.43
	\| [[7/4]], ''[[9/5]]''		\| [[7/4]], ''[[9/5]]''
	\|-		\|-
	\| 18		\| 18
			\| B
	\| 1028.57		\| 1028.57
	\| ''[[16/9]]'', ''[[24/13]]'', [[64/35]]		\| ''[[16/9]]'', ''[[24/13]]'', [[64/35]]
	\|-		\|-
	\| 19		\| 19
			\| ^B
	\| 1085.71		\| 1085.71
	\| [[13/7]], [[28/15]], [[15/8]]		\| [[13/7]], [[28/15]], [[15/8]]
	\|-		\|-
	\| 20		\| 20
			\| vC
	\| 1142.86		\| 1142.86
	\| [[40/21]]		\| [[40/21]]
	\|-		\|-
	\| 21		\| 21
			\| C
	\| 1200.00		\| 1200.00
	\| [[2/1]]		\| [[2/1]]

Overthink: /* Notation */ some text

2026-05-25T04:53:00Z

Notation: some text

← Older revision		Revision as of 04:53, 25 May 2026
Line 122:		Line 122:

	== Notation ==		== Notation ==
			The following table gives a comparison of some notation systems for 21edo.
	{\| class="wikitable center-all right-3 right-5"		{\| class="wikitable center-all right-3 right-5"
	\|-		\|-
Line 130:		Line 130:
	! [[5L 3s]] octatonic<br>notation		! [[5L 3s]] octatonic<br>notation
	! [[Extended-diatonic interval names\|Extended-diatonic <br> interval name]]		! [[Extended-diatonic interval names\|Extended-diatonic <br> interval name]]
	\|+ ~~style="font-size: 105%; white-space: nowrap;" \| Notation systems for 21edo~~		\|+
	\|-		\|-
	\| 0		\| 0

Overthink: /* Intervals */ center-align first column; shorter header

2026-05-25T03:33:22Z

Intervals: center-align first column; shorter header

← Older revision		Revision as of 03:33, 25 May 2026
Line 25:		Line 25:
	== Intervals ==		== Intervals ==
	Inconsistent intervals are in ''italics''.		Inconsistent intervals are in ''italics''.
	{\| class="wikitable ~~right~~-1 right-2"		{\| class="wikitable center-1 right-2"
	\|-		\|-
	! ~~Steps~~		! #
	! Cents		! Cents
	! Approximate Ratios*		! Approximate Ratios*

Lucius Chiaraviglio: /* Music */ ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)'': dead link

2026-05-19T17:44:29Z

Music: ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)'': dead link

← Older revision		Revision as of 17:44, 19 May 2026
Line 887:		Line 887:
	; [[Stephen Weigel]]		; [[Stephen Weigel]]
	* [https://soundcloud.com/overtoneshock/little-fugue-21-edo?in=overtoneshock/sets/xenharmonic-microtonal ''Iridescent Wenge Fugue''] (accepted to [https://www.seamusonline.org/ SEAMUS 2018] and [http://eabarndance.com/ Electroacoustic Barn Dance 2018])		* [https://soundcloud.com/overtoneshock/little-fugue-21-edo?in=overtoneshock/sets/xenharmonic-microtonal ''Iridescent Wenge Fugue''] (accepted to [https://www.seamusonline.org/ SEAMUS 2018] and [http://eabarndance.com/ Electroacoustic Barn Dance 2018])
	* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)''], an album of xenharmonic Christmas covers, many are in 21 EDO		* [https://xenharmonicgod.bandcamp.com/album/weigel-family-christmas-xenharmonic-chocolate ''WEIGEL FAMILY CHRISTMAS (xenharmonic chocolate)'']{{dead link}}, an album of xenharmonic Christmas covers, many are in 21 EDO

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

Lucius Chiaraviglio: /* Music */ Add Claudi Meneghin's ''Trio Sonata for Baroque Trio in 21 EDO'' (2026); add some dates

2026-05-18T12:24:38Z

Music: Add Claudi Meneghin's ''Trio Sonata for Baroque Trio in 21 EDO'' (2026); add some dates

← Older revision		Revision as of 12:24, 18 May 2026
Line 862:		Line 862:
	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]
	* [http://soonlabel.com/xenharmonic/archives/2336 ''21-penny jingle''] {{dead link}}		* [http://soonlabel.com/xenharmonic/archives/2336 ''21-penny jingle''] {{dead link}}
	* [https://www.youtube.com/watch?v=lpcqXD8tpXc ''Trio Sonata in 21edo for Organ (The Sewing Machine)'']		* [https://www.youtube.com/watch?v=lpcqXD8tpXc ''Trio Sonata in 21edo for Organ (The Sewing Machine)''] (2018)
	* [https://www.youtube.com/watch?v=n0QA0ZQHPvk ''21edo Chacony, for two Harpsichords'']		* [https://www.youtube.com/watch?v=n0QA0ZQHPvk ''21edo Chacony, for two Harpsichords''] (2019)
	* [https://www.youtube.com/watch?v=r0aKutu0gVg ''Twinkle Twinkle Little Star, with Shepard Effect''] (2023)		* [https://www.youtube.com/watch?v=r0aKutu0gVg ''Twinkle Twinkle Little Star, with Shepard Effect''] (2023)
			* [https://www.youtube.com/watch?v=XlpAbSdy_sg ''Trio Sonata for Baroque Trio in 21 EDO''] (2026)

	; [[Nick, The NRG]]		; [[Nick, The NRG]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''21edo groove'' (2026)

2026-05-08T04:05:05Z

Music: Add Bryan Deister's ''21edo groove'' (2026)

← Older revision		Revision as of 04:05, 8 May 2026
Line 836:		Line 836:
	* [https://www.youtube.com/shorts/yLSIZxJnMh8 ''21edo waltz''] (2025)		* [https://www.youtube.com/shorts/yLSIZxJnMh8 ''21edo waltz''] (2025)
	* [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026)		* [https://www.youtube.com/watch?v=1S4C-m_Dcno ''21edo improv''] (2026)
			* [https://www.youtube.com/shorts/9a-nJ_Ml9z8 ''21edo groove''] (2026)

	; [[Fabrizio Fiale]]		; [[Fabrizio Fiale]]

Lucius Chiaraviglio: /* Intervals */ Had duplicate of 128/105 where 105/64 should be

2026-05-08T04:01:55Z

Intervals: Had duplicate of 128/105 where 105/64 should be

← Older revision		Revision as of 04:01, 8 May 2026
Line 93:		Line 93:
	\| 15		\| 15
	\| 857.14		\| 857.14
	\| [[64/39]], [[~~128~~/~~105~~]], [[13/8]]		\| [[64/39]], [[105/64]], [[13/8]]
	\|-		\|-
	\| 16		\| 16

Overthink: /* Approximation to JI */ add 15-odd-limit intervals

2026-05-07T23:35:03Z

Approximation to JI: add 15-odd-limit intervals

← Older revision		Revision as of 23:35, 7 May 2026
Line 510:		Line 510:

	Note: In the second column, the ratios 9/5, 11/9, 13/9, and their octave complements are all included here, being expressable as 27/15, 33/27, and 39/27 respectively. These ratios are mapped inconsistently to their second-best approximations in the patent val.		Note: In the second column, the ratios 9/5, 11/9, 13/9, and their octave complements are all included here, being expressable as 27/15, 33/27, and 39/27 respectively. These ratios are mapped inconsistently to their second-best approximations in the patent val.

			=== 15-odd-limit interval mappings ===
			{{Q-odd-limit intervals}}

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

Overthink: /* Intervals */ link

2026-05-01T00:24:12Z

Intervals: link

← Older revision		Revision as of 00:24, 1 May 2026
Line 119:		Line 119:
	\| [[2/1]]		\| [[2/1]]
	\|}		\|}
	<nowiki/>*As a 2.3.5.7.13-subgroup temperament		<nowiki/>*As a [[2.3.5.7.13 subgroup\|2.3.5.7.13-subgroup]] temperament

	== Notation ==		== Notation ==

Overthink: move higher limits to dedicated section

2026-04-30T21:58:20Z

move higher limits to dedicated section

Show changes