72edo - Revision history

FloraC: /* Regular temperament properties */ + gravity as a 2.3.5.11 temp

2026-05-26T07:43:34Z

Regular temperament properties: + gravity as a 2.3.5.11 temp

← Older revision		Revision as of 07:43, 26 May 2026
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	\| 516.7		\| 516.7
	\| 27/20		\| 27/20
	\| [[~~Marvo~~]] / [[zarvo]]		\| [[Gravity]] / [[marvo]] / [[zarvo]]
	\|-		\|-
	\| 1		\| 1

FloraC: /* Regular temperament properties */ + ennealiminal

2026-05-19T10:04:56Z

Regular temperament properties: + ennealiminal

← Older revision		Revision as of 10:04, 19 May 2026
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	\| 316.7<br>(50.0)		\| 316.7<br>(50.0)
	\| 6/5<br>(36/35)		\| 6/5<br>(36/35)
	\| [[Ennealimmal]] / ennealimnic		\| [[Ennealimmal]] / ennealimnic / ennealiminal
	\|-		\|-
	\| 9		\| 9

FloraC: /* Notation */ SZG notation

2026-05-12T14:06:21Z

Notation: SZG notation

← Older revision		Revision as of 14:06, 12 May 2026
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	== Notation ==		== Notation ==
	=== ~~Ups~~ and downs notation ===		=== Stein–Zimmermann–Gould notation ===
	72edo can be notated with ups and downs, spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.		[[Stein–Zimmermann–Gould notation]] uses sharps and flats combined with quartertone accidentals and arrows:
			{{Sharpness-sharp6-szg}}

			If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:
			{{Sharpness-sharp6-qt-szg}}

			=== Kite's ups and downs notation ===
			72edo can also be notated with [[Kite's ups and downs notation\|Kite's ups and downs]], spoken as up, dup, trup, dudsharp, downsharp, sharp, upsharp etc. and down, dud, trud, dupflat etc.
	{{Ups and downs sharpness}}		{{Ups and downs sharpness}}

	Half-sharps and half-flats can be used to avoid triple arrows:		Half-sharps and half-flats can be used to avoid triple arrows:
	{{Ups and downs sharpness\|72\|true}}		{{Ups and downs sharpness\|72\|true}}

	~~[[Alternative symbols for ups and downs notation#Sharp-6\| Alternative ups and downs]] have sharps and flats with arrows borrowed from extended [[Helmholtz–Ellis notation]]:~~
	~~{{Sharpness-sharp6}}~~

	~~If double arrows are not desirable, arrows can be attached to quarter-tone accidentals:~~
	~~{{Sharpness-sharp6-qt}}~~

	=== Sagittal notation ===		=== Sagittal notation ===

Overthink: /* Music */ fix dead links

2026-05-04T01:38:02Z

Music: fix dead links

← Older revision		Revision as of 01:38, 4 May 2026
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	; [[Jake Freivald]]		; [[Jake Freivald]]
	* [http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday'']~~{{dead link}}~~ in the [[lazysunday]] scale		* [https://web.archive.org/web/20201127014336/http://micro.soonlabel.com/gene_ward_smith/Others/Freivald/Lazy%20Sunday.mp3 ''Lazy Sunday''] in the [[lazysunday]] scale

	{{Wikipedia\|In vain (Haas)}}		{{Wikipedia\|In vain (Haas)}}
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	; [[Claudi Meneghin]]		; [[Claudi Meneghin]]
	* [http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']~~{{dead link}}~~		* [https://web.archive.org/web/20201127015744/http://micro.soonlabel.com/gene_ward_smith/Others/Meneghin/Claudi-Meneghin-Twinkle-canon-72-edo.mp3 ''Twinkle canon – 72 edo'']
	* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]		* [https://www.youtube.com/watch?v=zR0NDgh4944 ''The Miracle Canon'', 3-in-1 on a Ground]
	* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']		* [https://www.youtube.com/watch?v=w6Bckog1eOM ''Sicilienne in Miracle'']
Line 2,015:		Line 2,015:

	; [[Prent Rodgers]]		; [[Prent Rodgers]]
	* [http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']~~{{dead link}}~~		* [https://web.archive.org/web/20201127012907/http://micro.soonlabel.com/gene_ward_smith/Others/Rodgers/drum12a-c-t9.mp3 ''June Gloom #9'']

	; [[Gene Ward Smith]]		; [[Gene Ward Smith]]

FloraC: Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

2026-03-13T13:38:13Z

Text replacement - "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct" to "Octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if distinct"

← Older revision		Revision as of 13:38, 13 March 2026
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	\| [[Gamelstearn]]		\| [[Gamelstearn]]
	\|}		\|}
	<nowiki/>* [[Normal ~~lists~~\|Octave-reduced form]], reduced to the first half-octave, and [[normal ~~lists~~\|minimal form]] in parentheses if distinct		<nowiki/>* [[Normal forms #Equave-reduced-generator form\|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form\|minimal form]] in parentheses if distinct

	== Octave stretch or compression ==		== Octave stretch or compression ==

Overthink: /* Proposed interval names and solfèges */ make header slightly larger

2026-01-15T05:10:41Z

Proposed interval names and solfèges: make header slightly larger

← Older revision		Revision as of 05:10, 15 January 2026
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	=== Proposed interval names and solfèges ===		=== Proposed interval names and solfèges ===
	{\| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"		{\| class="wikitable center-all right-2 left-4 left-7 mw-collapsible mw-collapsed"
	\|+ style="white-space: nowrap;" \| Table of proposed interval names and solfèges		\|+ style="font-size: 105%; white-space: nowrap;" \| Table of proposed interval names and solfèges
	\|-		\|-
	! #		! #

Overthink: /* Intervals */ mark inconsistencies

2026-01-14T21:26:07Z

Intervals: mark inconsistencies

← Older revision		Revision as of 21:26, 14 January 2026
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	\| 20		\| 20
	\| 333.3		\| 333.3
	\| [[17/14]], [[39/32]], [[40/33]]		\| [[17/14]], ''[[39/32]]'', [[40/33]]
	\| {{UDnote\|step=20}}		\| {{UDnote\|step=20}}
	\|-		\|-
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	\| 52		\| 52
	\| 866.7		\| 866.7
	\| [[28/17]], [[33/20]], [[64/39]]		\| [[28/17]], [[33/20]], ''[[64/39]]''
	\| {{UDnote\|step=52}}		\| {{UDnote\|step=52}}
	\|-		\|-

Overthink: /* Intervals */ + 21/19 and 38/21

2026-01-14T21:22:03Z

Intervals: + 21/19 and 38/21

← Older revision		Revision as of 21:22, 14 January 2026
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	\| 10		\| 10
	\| 166.7		\| 166.7
	\| [[11/10]]		\| [[11/10]], [[21/19]]
	\| {{UDnote\|step=10}}		\| {{UDnote\|step=10}}
	\|-		\|-
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	\| 62		\| 62
	\| 1033.3		\| 1033.3
	\| [[20/11]]		\| [[20/11]], [[38/21]]
	\| {{UDnote\|step=62}}		\| {{UDnote\|step=62}}
	\|-		\|-

FloraC: /* Theory */ rework and expand on its 19-limit capability

2026-01-14T18:35:46Z

Theory: rework and expand on its 19-limit capability

← Older revision		Revision as of 18:35, 14 January 2026
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	== Theory ==		== Theory ==
	72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is [[consistent]] in the [[17-odd-limit]] and ~~is the ninth [[zeta integral edo]]. It is~~ the second edo (after ~~[[58edo\|~~58]]) to be [[consistency\|distinctly consistent]] in the [[11-odd-limit]], ~~and~~ the first edo to be [[consistency\|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% relative error (about 4 cents).		72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is the second edo (after [[58edo\|58]]) to be [[consistent]] in the [[17-odd-limit]], and the second edo (also after 58) to be [[consistency\|distinctly consistent]] in the [[11-odd-limit]], but it is the first edo to be [[consistency\|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% [[relative interval error\|relative error]] (about 4 cents). It also has pretty good accuracy for the [[19-limit]], being almost consistent to the entire [[21-odd-limit]] with the only inconsistency occurring at [[19/13]] and its [[octave complement]]. It is the ninth [[zeta integral edo]].

	The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.		The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.

	The 13th harmonic (~~octave reduced~~) is ~~so closely mapped on~~ [[acoustic phi]] ~~that 72edo could be treated as a 2.3.5.7.11.ϕ.~~17 ~~temperament~~.		The [[octave reduction\|octave reduced]] [[13/1\|13th harmonic]] is mapped on 50\72, an interval inherited from [[36edo]] (25\36) that is a very close approximation to [[acoustic phi]], and the [[17/1\|17th]] and [[19/1\|19th harmonics]] come from 12edo.

	72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].		72edo is the smallest multiple of 12edo that (just barely) has another diatonic fifth, 43\72, an extremely hard diatonic fifth suitable for a 5edo [[circulating temperament]].

FloraC: /* Theory */ notability

2026-01-14T09:55:10Z

Theory: notability

← Older revision		Revision as of 09:55, 14 January 2026
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	== Theory ==		== Theory ==
	72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is [[consistent]] in the [[17-odd-limit]] and is the ninth [[zeta integral edo]]. It is the second edo (after [[58edo\|58]]) to be [[consistency\|distinctly consistent]] in the [[11-odd-limit]], the first edo to be [[consistency\|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% relative error (about 4 cents)~~, and the first edo to be consistent in the 12- and 13-[[odd prime sum limit\|odd-prime-sum-limit]]~~.		72edo approximates [[11-limit]] [[just intonation]] exceptionally well. It is [[consistent]] in the [[17-odd-limit]] and is the ninth [[zeta integral edo]]. It is the second edo (after [[58edo\|58]]) to be [[consistency\|distinctly consistent]] in the [[11-odd-limit]], and the first edo to be [[consistency\|consistent to distance 2]] in the 11-odd-limit, meaning every interval in the 11-odd-limit is approximated with less than 25% relative error (about 4 cents).

	The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.		The octave, fifth and fourth are the same size as they would be in 12edo, 72, 42 and 30 steps respectively, but the classic major third ([[5/4]]) measures 23 steps, not 24, and other [[5-limit]] major intervals are one step flat of 12edo while minor ones are one step sharp. The septimal minor seventh ([[7/4]]) is 58 steps, while the undecimal semiaugmented fourth ([[11/8]]) is 33.