70edo - Revision history

Fitzgerald Lee: /* Notation */added interval mappings of 70p and 70cd

2026-05-12T04:43:50Z

Notation: added interval mappings of 70p and 70cd

← Older revision		Revision as of 04:43, 12 May 2026
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	default [[File:70-EDO_Revo_Sagittal.svg]]		default [[File:70-EDO_Revo_Sagittal.svg]]
	</imagemap>		</imagemap>
			== Approximation to JI ==
			=== 15-odd-limit interval mappings ===
			{{Q-odd-limit intervals\|70}}
			{{Q-odd-limit intervals\|69.9\|apx=val\|header=none\|tag=none\|title=15-odd-limit intervals by 70cd val mapping}}

	== Scales ==		== Scales ==

Lériendil: Text replacement - "[[Logarithmic approximants #" to "[["

2025-10-09T14:24:56Z

Text replacement - "[[Logarithmic approximants #" to "[["

← Older revision		Revision as of 14:24, 9 October 2025
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	== Theory ==		== Theory ==
	This tuning was singled out by [[William Stoney]] in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo\|72]], [[65edo\|65]], [[58edo\|58]], [[53edo\|53]], and [[41edo\|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite its excellent perfect fifth, which is the 4th number in the convergent sequence to the [[~~Logarithmic approximants #~~Argent tuning\|silver ratio]], following [[29edo]], [[12edo]], and [[5edo]] and preceding [[169edo]]. It is the last edo to have exactly one [[5L 2s\|diatonic]] perfect fifth, and this perfect fifth, 41\70, is the true center of the diatonic tuning spectrum, as it is the [[geometric mean]] of [[5edo\|3\5edo]] and [[7edo\|4\7edo]].		This tuning was singled out by [[William Stoney]] in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo\|72]], [[65edo\|65]], [[58edo\|58]], [[53edo\|53]], and [[41edo\|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite its excellent perfect fifth, which is the 4th number in the convergent sequence to the [[Argent tuning\|silver ratio]], following [[29edo]], [[12edo]], and [[5edo]] and preceding [[169edo]]. It is the last edo to have exactly one [[5L 2s\|diatonic]] perfect fifth, and this perfect fifth, 41\70, is the true center of the diatonic tuning spectrum, as it is the [[geometric mean]] of [[5edo\|3\5edo]] and [[7edo\|4\7edo]].

	The [[patent val]] for 70edo [[tempering out\|tempers out]] [[2048/2025]], making it a [[diaschismic]] system. An alternative mapping is 70c, with a flat rather than a sharp major third, tempering out [[32805/32768]]. In the [[7-limit]], the patent val tempers out [[126/125]], [[2430/2401]] and [[5120/5103]], and provides the optimum patent val for the [[kumonga]] temperament. The 70c val tempers out [[50/49]], making it a tuning for [[doublewide]] even better than the optimal patent val. The 70cd val tempers out [[225/224]] and [[3125/3087]] instead. The alternative mapping begins to make more sense in the [[11-limit]] and higher, where the patent val tempers out [[99/98]] and [[121/120]] in the 11-limit, [[169/168]] and [[352/351]] in the [[13-limit]], and [[221/220]] in the [[17-limit]]. 70cd on the other hand, with flat 5 and 7, tempers out [[100/99]] and [[245/242]] in the 11-limit, [[105/104]] and [[196/195]] in the 13-limit, and [[154/153]] and [[170/169]] in the 17-limit. 70 also makes sense as a no-5 or -7 system, tempering out [[131769/131072]] in the 11-limit, [[352/351]] and [[2197/2187]] in the 13-limit, and [[289/288]] and [[1089/1088]] in the 17-limit.		The [[patent val]] for 70edo [[tempering out\|tempers out]] [[2048/2025]], making it a [[diaschismic]] system. An alternative mapping is 70c, with a flat rather than a sharp major third, tempering out [[32805/32768]]. In the [[7-limit]], the patent val tempers out [[126/125]], [[2430/2401]] and [[5120/5103]], and provides the optimum patent val for the [[kumonga]] temperament. The 70c val tempers out [[50/49]], making it a tuning for [[doublewide]] even better than the optimal patent val. The 70cd val tempers out [[225/224]] and [[3125/3087]] instead. The alternative mapping begins to make more sense in the [[11-limit]] and higher, where the patent val tempers out [[99/98]] and [[121/120]] in the 11-limit, [[169/168]] and [[352/351]] in the [[13-limit]], and [[221/220]] in the [[17-limit]]. 70cd on the other hand, with flat 5 and 7, tempers out [[100/99]] and [[245/242]] in the 11-limit, [[105/104]] and [[196/195]] in the 13-limit, and [[154/153]] and [[170/169]] in the 17-limit. 70 also makes sense as a no-5 or -7 system, tempering out [[131769/131072]] in the 11-limit, [[352/351]] and [[2197/2187]] in the 13-limit, and [[289/288]] and [[1089/1088]] in the 17-limit.

Lériendil: Text replacement - "rgent temperament" to "rgent tuning"

2025-10-09T14:10:43Z

Text replacement - "rgent temperament" to "rgent tuning"

← Older revision		Revision as of 14:10, 9 October 2025
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	== Theory ==		== Theory ==
	This tuning was singled out by [[William Stoney]] in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo\|72]], [[65edo\|65]], [[58edo\|58]], [[53edo\|53]], and [[41edo\|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite its excellent perfect fifth, which is the 4th number in the convergent sequence to the [[Logarithmic approximants #Argent ~~temperament~~\|silver ratio]], following [[29edo]], [[12edo]], and [[5edo]] and preceding [[169edo]]. It is the last edo to have exactly one [[5L 2s\|diatonic]] perfect fifth, and this perfect fifth, 41\70, is the true center of the diatonic tuning spectrum, as it is the [[geometric mean]] of [[5edo\|3\5edo]] and [[7edo\|4\7edo]].		This tuning was singled out by [[William Stoney]] in his article "Theoretical Possibilities for Equally Tempered Systems" (in the book [https://monoskop.org/images/c/c3/Lincoln_Harry_B_ed_The_Computer_and_Music_1970.pdf The Computer and Music]) as one of the six best systems of size 72 or smaller, along with [[72edo\|72]], [[65edo\|65]], [[58edo\|58]], [[53edo\|53]], and [[41edo\|41]]. These other systems have had notice paid to them, but the same does not seem to be true of 70, which seems to have been ignored ever since, despite its excellent perfect fifth, which is the 4th number in the convergent sequence to the [[Logarithmic approximants #Argent tuning\|silver ratio]], following [[29edo]], [[12edo]], and [[5edo]] and preceding [[169edo]]. It is the last edo to have exactly one [[5L 2s\|diatonic]] perfect fifth, and this perfect fifth, 41\70, is the true center of the diatonic tuning spectrum, as it is the [[geometric mean]] of [[5edo\|3\5edo]] and [[7edo\|4\7edo]].

	The [[patent val]] for 70edo [[tempering out\|tempers out]] [[2048/2025]], making it a [[diaschismic]] system. An alternative mapping is 70c, with a flat rather than a sharp major third, tempering out [[32805/32768]]. In the [[7-limit]], the patent val tempers out [[126/125]], [[2430/2401]] and [[5120/5103]], and provides the optimum patent val for the [[kumonga]] temperament. The 70c val tempers out [[50/49]], making it a tuning for [[doublewide]] even better than the optimal patent val. The 70cd val tempers out [[225/224]] and [[3125/3087]] instead. The alternative mapping begins to make more sense in the [[11-limit]] and higher, where the patent val tempers out [[99/98]] and [[121/120]] in the 11-limit, [[169/168]] and [[352/351]] in the [[13-limit]], and [[221/220]] in the [[17-limit]]. 70cd on the other hand, with flat 5 and 7, tempers out [[100/99]] and [[245/242]] in the 11-limit, [[105/104]] and [[196/195]] in the 13-limit, and [[154/153]] and [[170/169]] in the 17-limit. 70 also makes sense as a no-5 or -7 system, tempering out [[131769/131072]] in the 11-limit, [[352/351]] and [[2197/2187]] in the 13-limit, and [[289/288]] and [[1089/1088]] in the 17-limit.		The [[patent val]] for 70edo [[tempering out\|tempers out]] [[2048/2025]], making it a [[diaschismic]] system. An alternative mapping is 70c, with a flat rather than a sharp major third, tempering out [[32805/32768]]. In the [[7-limit]], the patent val tempers out [[126/125]], [[2430/2401]] and [[5120/5103]], and provides the optimum patent val for the [[kumonga]] temperament. The 70c val tempers out [[50/49]], making it a tuning for [[doublewide]] even better than the optimal patent val. The 70cd val tempers out [[225/224]] and [[3125/3087]] instead. The alternative mapping begins to make more sense in the [[11-limit]] and higher, where the patent val tempers out [[99/98]] and [[121/120]] in the 11-limit, [[169/168]] and [[352/351]] in the [[13-limit]], and [[221/220]] in the [[17-limit]]. 70cd on the other hand, with flat 5 and 7, tempers out [[100/99]] and [[245/242]] in the 11-limit, [[105/104]] and [[196/195]] in the 13-limit, and [[154/153]] and [[170/169]] in the 17-limit. 70 also makes sense as a no-5 or -7 system, tempering out [[131769/131072]] in the 11-limit, [[352/351]] and [[2197/2187]] in the 13-limit, and [[289/288]] and [[1089/1088]] in the 17-limit.

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''70edo prelude'' (2025)

2025-09-27T20:40:23Z

Music: Add Bryan Deister's ''70edo prelude'' (2025)

← Older revision		Revision as of 20:40, 27 September 2025
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	* [https://www.youtube.com/watch?v=Uc0c-AYq-zM ''Waltz in 70edo''] (2025)		* [https://www.youtube.com/watch?v=Uc0c-AYq-zM ''Waltz in 70edo''] (2025)
	* [https://www.youtube.com/watch?v=-NEq3jKHjzs ''Improv in 70edo''] (2025)		* [https://www.youtube.com/watch?v=-NEq3jKHjzs ''Improv in 70edo''] (2025)
			* [https://www.youtube.com/shorts/ZDU75YabROE ''70edo prelude''] (2025)

	; [[James Kukula]]		; [[James Kukula]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Improv in 70edo'' (2025)

2025-09-16T22:15:18Z

Music: Add Bryan Deister's ''Improv in 70edo'' (2025)

← Older revision		Revision as of 22:15, 16 September 2025
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	* [https://www.youtube.com/shorts/gp42aya9TL0 ''Drift Away - Steven Universe (microtonal cover in 70edo)''] (2025)		* [https://www.youtube.com/shorts/gp42aya9TL0 ''Drift Away - Steven Universe (microtonal cover in 70edo)''] (2025)
	* [https://www.youtube.com/watch?v=Uc0c-AYq-zM ''Waltz in 70edo''] (2025)		* [https://www.youtube.com/watch?v=Uc0c-AYq-zM ''Waltz in 70edo''] (2025)
			* [https://www.youtube.com/watch?v=-NEq3jKHjzs ''Improv in 70edo''] (2025)

	; [[James Kukula]]		; [[James Kukula]]

Lucius Chiaraviglio: /* Music */ Add Bryan Deister's ''Waltz in 70edo'' (2025)

2025-08-07T06:41:09Z

Music: Add Bryan Deister's ''Waltz in 70edo'' (2025)

← Older revision		Revision as of 06:41, 7 August 2025
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	* [https://www.youtube.com/shorts/I42JQ98WPZI ''microtonal improvisation in 70edo''] (2025)		* [https://www.youtube.com/shorts/I42JQ98WPZI ''microtonal improvisation in 70edo''] (2025)
	* [https://www.youtube.com/shorts/gp42aya9TL0 ''Drift Away - Steven Universe (microtonal cover in 70edo)''] (2025)		* [https://www.youtube.com/shorts/gp42aya9TL0 ''Drift Away - Steven Universe (microtonal cover in 70edo)''] (2025)
			* [https://www.youtube.com/watch?v=Uc0c-AYq-zM ''Waltz in 70edo''] (2025)

	; [[James Kukula]]		; [[James Kukula]]

BudjarnLambeth: /* Music */ add 1

2025-07-10T02:15:29Z

Music: add 1

← Older revision		Revision as of 02:15, 10 July 2025
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	; [[James Kukula]]		; [[James Kukula]]
	* [https://app.box.com/s/i9vvgcplpmksrm8rubz2h3asee2cnr26 ''piece from Stepping Outside''] (2025)		* [https://app.box.com/s/i9vvgcplpmksrm8rubz2h3asee2cnr26 ''piece from Stepping Outside''] (2025)

			; [[Budjarn Lambeth]]
			* [https://www.youtube.com/watch?v=dyEH-pP2dJU ''Improv in 70edo (Polymicrotonal 10edo+14edo Scale)''] (2025)

	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: /* Kukula's 2.3.13 70edo MOS */ add subsets

2025-07-10T00:53:43Z

Kukula's 2.3.13 70edo MOS: add subsets

← Older revision		Revision as of 00:53, 10 July 2025
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	=== Kukula's 2.3.13 70edo MOS ===		=== Kukula's 2.3.13 70edo MOS ===
	In July 2025, composer and theorist [[James Kukula]] created a 17-tone [[MOS scale]] for his piece in the [[Monthly Tunings]] project. The scale is generated by stacking the interval 33\70, 17 times, then [[octave reduction\|octave reducing]] the result. It is designed to approximate the 2.3.13 [[subgroup]] very accurately. He discusses it in his blog post titled ''[https://interdependentscience.blogspot.com/2025/07/stepping-outside.html Stepping Outside]''.		In July 2025, composer and theorist [[James Kukula]] created a 17-tone [[MOS scale]] for his piece in the [[Monthly Tunings]] project. The scale is generated by stacking the interval 33\70, 17 times, then [[octave reduction\|octave reducing]] the result. It is designed to approximate the 2.3.13 [[subgroup]] very accurately. He discusses it in his blog post titled ''[https://interdependentscience.blogspot.com/2025/07/stepping-outside.html Stepping Outside]''.

			; Subsets
			* Kukula-Lambeth tridecimal neutral octatonic{{idiosyncratic}}: 8 13 8 12 8 9 8 4
			* Kukula-Lambeth tridecimal neutral heptatonic{{idiosyncratic}}: 8 13 8 12 8 9 12

	== Instruments ==		== Instruments ==

BudjarnLambeth: /* Music */

2025-07-09T05:08:29Z

Music

← Older revision		Revision as of 05:08, 9 July 2025
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	; [[James Kukula]]		; [[James Kukula]]
	* [https://app.box.com/s/i9vvgcplpmksrm8rubz2h3asee2cnr26 ''Stepping Outside''] (2025)		* [https://app.box.com/s/i9vvgcplpmksrm8rubz2h3asee2cnr26 ''piece from Stepping Outside''] (2025)

	[[Category:Listen]]		[[Category:Listen]]

BudjarnLambeth: /* Kukula's 2.3.13 70edo MOS */

2025-07-09T05:08:00Z

Kukula's 2.3.13 70edo MOS

← Older revision		Revision as of 05:08, 9 July 2025
Line 55:		Line 55:
	== Scales ==		== Scales ==
	=== Kukula's 2.3.13 70edo MOS ===		=== Kukula's 2.3.13 70edo MOS ===
	In July 2025, composer and theorist [[James Kukula]] created a 17-tone MOS scale for his piece in the [[Monthly Tunings]] project. The scale is generated by stacking the interval 33\70, 17 times, then [[octave reduction\|octave reducing]] the result. It is designed to approximate the 2.3.13 [[subgroup]] very accurately. He discusses it in his blog post titled ''[https://interdependentscience.blogspot.com/2025/07/stepping-outside.html Stepping Outside]''.		In July 2025, composer and theorist [[James Kukula]] created a 17-tone [[MOS scale]] for his piece in the [[Monthly Tunings]] project. The scale is generated by stacking the interval 33\70, 17 times, then [[octave reduction\|octave reducing]] the result. It is designed to approximate the 2.3.13 [[subgroup]] very accurately. He discusses it in his blog post titled ''[https://interdependentscience.blogspot.com/2025/07/stepping-outside.html Stepping Outside]''.

	== Instruments ==		== Instruments ==