16edo - Revision history

Lucius Chiaraviglio: /* Music */ ''16edo waltz'' (2025): Add the reason for keeping the short, in case anyone was thinking of eliminating it

2026-05-09T15:57:36Z

Music: ''16edo waltz'' (2025): Add the reason for keeping the short, in case anyone was thinking of eliminating it

← Older revision		Revision as of 15:57, 9 May 2026
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	* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)		* [https://www.youtube.com/shorts/H-abpioYj5k ''improv in 16edo''] (2022)
	* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)		* [https://www.youtube.com/shorts/IfVvjoRqqNk ''16edo jam''] (2025)
	* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025)		* [https://www.youtube.com/shorts/PXiWkZ9wDdU ''16edo waltz''] (2025) — includes Lumatone view
	* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) — this is the full version of the ''16edo waltz'' above		* [https://www.youtube.com/watch?v=cUgbkkIvy0g ''Waltz in 16edo''] (2025) — this is the full version of the ''16edo waltz'' above
	* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)		* [https://www.youtube.com/shorts/UA97cjUN5eE ''Doubt by Bryan Deister (microtonal 16edo snippet)''] (2025)

Lucius Chiaraviglio: /* Music */ Fix typo

2026-05-09T15:54:53Z

Music: Fix typo

← Older revision		Revision as of 15:54, 9 May 2026
Line 1,008:		Line 1,008:
	* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']		* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']

	; Stephen Weigel (on 16edo keyboard with [[Clarissa]] (vocal)		; Stephen Weigel (on 16edo keyboard) with [[Clarissa]] (vocal)
	* [https://www.youtube.com/shorts/ZUBE817kwk8 Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)		* [https://www.youtube.com/shorts/ZUBE817kwk8 Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)

Lucius Chiaraviglio: /* Music */ Add Stephen Weigel's/Clarissa's Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)

2026-05-09T15:54:09Z

Music: Add Stephen Weigel's/Clarissa's Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)

← Older revision		Revision as of 15:54, 9 May 2026
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	* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']		* [https://www.youtube.com/watch?v=0t7ZmlmrE0Q ''Shot Fades the Sum Of'']
	* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']		* [https://www.youtube.com/watch?v=2y01AlgOPvk ''When the Saints go Marching'']

			; Stephen Weigel (on 16edo keyboard with [[Clarissa]] (vocal)
			* [https://www.youtube.com/shorts/ZUBE817kwk8 Microtonal cover of ''All I Want for Christmas is You"'' by Mariah Carey] (2024)

	; [[Randy Winchester]]		; [[Randy Winchester]]

Overthink: /* Intervals */ rearrange intervals in table

2026-03-18T22:08:55Z

Intervals: rearrange intervals in table

← Older revision		Revision as of 22:08, 18 March 2026
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	! colspan="3" \| Approximate ratios		! colspan="3" \| Approximate ratios
	\|-		\|-
	! ~~[[2.3.5.11 subgroup]]~~		! 7-limit
	! ~~Additional ratios<br>of 7 and~~ 13		! 13-limit
	! No-3 approach*		! No-3 approach*
	\|-		\|-
Line 58:		Line 58:
	\| 1		\| 1
	\| 75		\| 75
	~~\| [[25/24]]~~		\| ''[[15/14]]'', [[21/20]], [[25/24]]
	\| ''[[15/14]]'', [[21/20]], [[22/21]], [[26/25]]		\| [[22/21]], [[26/25]]
	\| [[28/27]], [[27/26]]		\| [[28/27]], [[27/26]]
	\|-		\|-
	\| 2		\| 2
	\| 150		\| 150
	\| ''[[9/8]]'', [[11/10]], [[12/11]], ~~''[[16/15]]''~~		\| ''[[9/8]]'', ''[[16/15]]''
	\| [[13/12]], [[14/13]]		\| [[11/10]], [[12/11]], [[13/12]], [[14/13]]
	\| 12/11, [[35/32]]		\| 12/11, [[35/32]]
	\|-		\|-
	\| 3		\| 3
	\| 225		\| 225
	\| ''[[10/9]]'', [[25~~/22~~]]		\| [[8/7]], ''[[10/9]]'', [[28/25]]
	\| ~~[[8/7]],~~ [[15/13]], [[28/25]]		\| [[15/13]], [[25/22]]
	\| 8/7		\| 8/7
	\|-		\|-
	\| 4		\| 4
	\| 300		\| 300
	\| [[6/5]]		\| [[6/5]], [[7/6]], [[25/21]]
	\| [[7/6]], [[13/11]], [[25/21]]		\| [[13/11]]
	\| [[19/16]], [[32/27]]		\| [[19/16]], [[32/27]]
	\|-		\|-
	\| 5		\| 5
	\| 375		\| 375
	\| [[5/4]], [[11/9]]		\| [[5/4]], ''[[9/7]]''
	\| ''[[9/7]]'', [[16/13]], [[26/21]]		\| [[11/9]], [[16/13]], [[26/21]]
	\| 5/4, 16/13, 26/21		\| 5/4, 16/13, 26/21
	\|-		\|-
	\| 6		\| 6
	\| 450		\| 450
	\| [[32/25]]		\| [[21/16]], [[32/25]]
	\| [[14/11]], [[13/10~~]], [[21/16~~]]		\| [[14/11]], [[13/10]]
	\| 13/10, [[35/27]]		\| 13/10, [[35/27]]
	\|-		\|-
	\| 7		\| 7
	\| 525		\| 525
	\| [[4/3]], [[11/8]], [[15/11]]		\| [[4/3]]
	\| ''[[18/13]]''		\| [[11/8]], ''[[18/13]]'', [[15/11]]
	\| [[19/14]], [[27/20]], [[35/26]]		\| [[19/14]], [[27/20]], [[35/26]]
	\|-		\|-
	\| 8		\| 8
	\| 600		\| 600
	\| [[25/18]], [[36/25]]		\| [[7/5]], [[10/7]], [[25/18]], [[36/25]]
	\| [[7/5]], [[10/7]]		\|
	\| 7/5, 10/7		\| 7/5, 10/7
	\|-		\|-
	\| 9		\| 9
	\| 675		\| 675
	\| [[3/2]], [[16/11]], [[22/15]]		\| [[3/2]]
	\| ''[[13/9]]''		\| [[16/11]], ''[[13/9]]'', [[22/15]]
	\| [[28/19]], [[40/27]], [[52/35]]		\| [[28/19]], [[40/27]], [[52/35]]
	\|-		\|-
	\| 10		\| 10
	\| 750		\| 750
	\| [[25/16]]		\| [[25/16]], [[32/21]]
	\| [[11/7]], [[20/13~~]], [[32/21~~]]		\| [[11/7]], [[20/13]]
	\| 20/13, [[54/35]]		\| 20/13, [[54/35]]
	\|-		\|-
	\| 11		\| 11
	\| 825		\| 825
	\| [[8/5]], [[18/11]]		\| [[8/5]], ''[[14/9]]''
	\| ''[[14/9]]'', [[13/8]], [[21/13]]		\| [[18/11]], [[13/8]], [[21/13]]
	\| 8/5, 13/8, 21/13		\| 8/5, 13/8, 21/13
	\|-		\|-
	\| 12		\| 12
	\| 900		\| 900
	\| [[5/3]]		\| [[5/3]], [[12/7]], [[42/25]]
	\| [[12/7]], [[22/13]], [[42/25]]		\| [[22/13]]
	\| [[27/16]], [[32/19]]		\| [[27/16]], [[32/19]]
	\|-		\|-
	\| 13		\| 13
	\| 975		\| 975
	\| ''[[9/5]]'', [[44/25]]		\| [[7/4]], ''[[9/5]]'', [[25/14]]
	\| ~~[[7/4]],~~ [[26/15]], [[25~~/14~~]]		\| [[26/15]], [[44/25]]
	\| 7/4		\| 7/4
	\|-		\|-
	\| 14		\| 14
	\| 1050		\| 1050
	\| ''[[16/9]]'', [[20/11]], [[11/6]], ~~''[[15/8]]''~~		\| ''[[16/9]]'', ''[[15/8]]''
	\| [[24/13]], [[13/7]]		\| [[20/11]], [[11/6]], [[24/13]], [[13/7]]
	\| [[11/6]], 64/35		\| [[11/6]], 64/35
	\|-		\|-
	\| 15		\| 15
	\| 1125		\| 1125
	~~\| [[48/25]]~~		\| ''[[28/15]]'', [[40/21]], [[48/25]]
	\| ''[[28/15]]'', [[40/21]], [[21/11]], [[25/13]]		\| [[21/11]], [[25/13]]
	\| [[27/14]], [[52/27]]		\| [[27/14]], [[52/27]]
	\|-		\|-
Line 149:		Line 149:
	\| 1200		\| 1200
	\| [[2/1]]		\| [[2/1]]
	\| [[2/1]]		\| 2/1
	\| [[2/1]]		\| 2/1
	\|}		\|}

FloraC: /* Intervals */ table title rows & formatting

2026-02-25T05:16:16Z

Intervals: table title rows & formatting

← Older revision		Revision as of 05:16, 25 February 2026
Line 40:		Line 40:
	Inconsistent intervals are in ''italics''.		Inconsistent intervals are in ''italics''.

	{\| class="wikitable center-~~all~~ right-2"		{\| class="wikitable center-1 right-2"
	\|-		\|-
	! rowspan="2" \| ~~Degree~~		! rowspan="2" \| #
	! rowspan="2" \| [[Cent]]s		! rowspan="2" \| [[Cent]]s
	! colspan="3" \| Approximate ratios		! colspan="3" \| Approximate ratios
	\|-		\|-
	! [[2.3.5.11 subgroup~~\|2.3.5.11~~]] ~~mavila~~		! [[2.3.5.11 subgroup]]
	! 13~~-limit armodue~~		! Additional ratios<br>of 7 and 13
	! ~~JI approximation~~*		! No-3 approach*
	\|-		\|-
	\| 0		\| 0

Overthink: /* Intervals */ add simpler ratios

2026-02-25T00:55:36Z

Intervals: add simpler ratios

← Older revision		Revision as of 00:55, 25 February 2026
Line 38:		Line 38:

	== Intervals ==		== Intervals ==
			Inconsistent intervals are in ''italics''.

	{\| class="wikitable center-all"		{\| class="wikitable center-all right-2"
	~~\|+ style="font~~-~~size: 105%~~" ~~\| Intervals of 16edo~~
	\|-		\|-
	! Degree		! rowspan="2" \| Degree
	! [[Cent]]s		! rowspan="2" \| [[Cent]]s
	! Approximate ratios*		! colspan="3" \| Approximate ratios
			\|-
			! [[2.3.5.11 subgroup\|2.3.5.11]] mavila
			! 13-limit armodue
			! JI approximation*
	\|-		\|-
	\| 0		\| 0
	\| 0		\| 0
			\| [[1/1]]
			\| 1/1
	\| 1/1		\| 1/1
	\|-		\|-
	\| 1		\| 1
	\| 75		\| 75
	\| 28/27, 27/26		\| [[25/24]]
			\| ''[[15/14]]'', [[21/20]], [[22/21]], [[26/25]]
			\| [[28/27]], [[27/26]]
	\|-		\|-
	\| 2		\| 2
	\| 150		\| 150
	\| 12/11, 35/32		\| ''[[9/8]]'', [[11/10]], [[12/11]], ''[[16/15]]''
			\| [[13/12]], [[14/13]]
			\| 12/11, [[35/32]]
	\|-		\|-
	\| 3		\| 3
	\| 225		\| 225
			\| ''[[10/9]]'', [[25/22]]
			\| [[8/7]], [[15/13]], [[28/25]]
	\| 8/7		\| 8/7
	\|-		\|-
	\| 4		\| 4
	\| 300		\| 300
	\| 19/16, 32/27		\| [[6/5]]
			\| [[7/6]], [[13/11]], [[25/21]]
			\| [[19/16]], [[32/27]]
	\|-		\|-
	\| 5		\| 5
	\| 375		\| 375
			\| [[5/4]], [[11/9]]
			\| ''[[9/7]]'', [[16/13]], [[26/21]]
	\| 5/4, 16/13, 26/21		\| 5/4, 16/13, 26/21
	\|-		\|-
	\| 6		\| 6
	\| 450		\| 450
	\| 13/10, 35/27		\| [[32/25]]
			\| [[14/11]], [[13/10]], [[21/16]]
			\| 13/10, [[35/27]]
	\|-		\|-
	\| 7		\| 7
	\| 525		\| 525
	\| 19/14, 27/20, 35/26		\| [[4/3]], [[11/8]], [[15/11]]
			\| ''[[18/13]]''
			\| [[19/14]], [[27/20]], [[35/26]]
	\|-		\|-
	\| 8		\| 8
	\| 600		\| 600
			\| [[25/18]], [[36/25]]
			\| [[7/5]], [[10/7]]
	\| 7/5, 10/7		\| 7/5, 10/7
	\|-		\|-
	\| 9		\| 9
	\| 675		\| 675
	\| 28/19, 40/27, 52/35		\| [[3/2]], [[16/11]], [[22/15]]
			\| ''[[13/9]]''
			\| [[28/19]], [[40/27]], [[52/35]]
	\|-		\|-
	\| 10		\| 10
	\| 750		\| 750
	\| 20/13, 54/35		\| [[25/16]]
			\| [[11/7]], [[20/13]], [[32/21]]
			\| 20/13, [[54/35]]
	\|-		\|-
	\| 11		\| 11
	\| 825		\| 825
			\| [[8/5]], [[18/11]]
			\| ''[[14/9]]'', [[13/8]], [[21/13]]
	\| 8/5, 13/8, 21/13		\| 8/5, 13/8, 21/13
	\|-		\|-
	\| 12		\| 12
	\| 900		\| 900
	\| 27/16, 32/19		\| [[5/3]]
			\| [[12/7]], [[22/13]], [[42/25]]
			\| [[27/16]], [[32/19]]
	\|-		\|-
	\| 13		\| 13
	\| 975		\| 975
			\| ''[[9/5]]'', [[44/25]]
			\| [[7/4]], [[26/15]], [[25/14]]
	\| 7/4		\| 7/4
	\|-		\|-
	\| 14		\| 14
	\| 1050		\| 1050
	\| 11/6, 64/35		\| ''[[16/9]]'', [[20/11]], [[11/6]], ''[[15/8]]''
			\| [[24/13]], [[13/7]]
			\| [[11/6]], 64/35
	\|-		\|-
	\| 15		\| 15
	\| 1125		\| 1125
	\| 27/14, 52/27		\| [[48/25]]
			\| ''[[28/15]]'', [[40/21]], [[21/11]], [[25/13]]
			\| [[27/14]], [[52/27]]
	\|-		\|-
	\| 16		\| 16
	\| 1200		\| 1200
	\| 2/1		\| [[2/1]]
			\| [[2/1]]
			\| [[2/1]]
	\|}		\|}

	<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible.		<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible. Odd 27 is approximated via [[direct approximation]].

	== Notation ==		== Notation ==

Lucius Chiaraviglio: /* Intervals */ Reorder subgroup to conform to most other pages

2026-02-25T00:37:58Z

Intervals: Reorder subgroup to conform to most other pages

← Older revision		Revision as of 00:37, 25 February 2026
Line 115:		Line 115:
	\|}		\|}

	<nowiki />* Based on treating 16edo as a 2.5.7.13.19~~.27~~ subgroup temperament; other approaches are possible.		<nowiki />* Based on treating 16edo as a 2.27.5.7.13.19 subgroup temperament; other approaches are possible.

	== Notation ==		== Notation ==

Overthink: /* Intervals */ remove 256/189 and 189/128 as they make the table wide (and are more complex than the rest)

2026-02-25T00:22:28Z

Intervals: remove 256/189 and 189/128 as they make the table wide (and are more complex than the rest)

← Older revision		Revision as of 00:22, 25 February 2026
Line 76:		Line 76:
	\| 7		\| 7
	\| 525		\| 525
	\| 19/14, 27/20, 35/26~~, 256/189~~		\| 19/14, 27/20, 35/26
	\|-		\|-
	\| 8		\| 8
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	\| 9		\| 9
	\| 675		\| 675
	\| 28/19, 40/27, 52/35~~, 189/128~~		\| 28/19, 40/27, 52/35
	\|-		\|-
	\| 10		\| 10

Overthink: section properly

2026-02-25T00:16:08Z

section properly

← Older revision		Revision as of 00:16, 25 February 2026
Line 38:		Line 38:

	== Intervals ==		== Intervals ==
	~~{{Mavila}}~~

	~~Alternatively, one can use Armodue nine-nominal notation.~~

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
Line 119:		Line 116:

	<nowiki />* Based on treating 16edo as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.		<nowiki />* Based on treating 16edo as a 2.5.7.13.19.27 subgroup temperament; other approaches are possible.

			== Notation ==
			{{Mavila}}

			Alternatively, one can use Armodue nine-nominal notation.

	{\| class="wikitable center-all"		{\| class="wikitable center-all"
Line 286:		Line 288:
	\|}		\|}


	~~== Notation ==~~
	16edo notation can be easy utilizing [[Goldsmith's Circle]] of keys, nominals, and respective notation{{clarify}}. The nominals for a 6 line staff can be switched for [[Erv Wilson]]'s Beta and Epsilon additions to A–G. The Armodue model uses a 4-line staff for 16edo.		16edo notation can be easy utilizing [[Goldsmith's Circle]] of keys, nominals, and respective notation{{clarify}}. The nominals for a 6 line staff can be switched for [[Erv Wilson]]'s Beta and Epsilon additions to A–G. The Armodue model uses a 4-line staff for 16edo.

Overthink: /* Intervals */ split table

2026-02-25T00:14:19Z

Intervals: split table

Show changes