60edf - Revision history

Lucius Chiaraviglio: Add Category:Nonoctave

2025-11-05T04:57:14Z

← Older revision		Revision as of 04:57, 5 November 2025
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	* [[205ed4]] – relative ed4		* [[205ed4]] – relative ed4
	* [[265ed6]] - relative ed6		* [[265ed6]] - relative ed6

			[[Category:Nonoctave]]

Lucius Chiaraviglio: /* Intervals */ Insert Instruments section after this with link to Lumatone mapping for 60edf

2025-10-20T01:59:31Z

Intervals: Insert Instruments section after this with link to Lumatone mapping for 60edf

← Older revision		Revision as of 01:59, 20 October 2025
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	== Intervals ==		== Intervals ==
	{{Interval table}}		{{Interval table}}

			== Instruments ==

			A [[Lumatone mapping for 60edf]] is now available.

	== Music ==		== Music ==

BudjarnLambeth: /* Theory */

2025-10-17T23:28:34Z

Theory

← Older revision		Revision as of 23:28, 17 October 2025
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	So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n\|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.		So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n\|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.
	{{Harmonics in equal\|60\|3\|2\|intervals=prime\|columns=13\|title=Approximation of primes in 60edf ~~(continued)~~}}		{{Harmonics in equal\|60\|3\|2\|intervals=prime\|columns=13\|title=Approximation of primes in 60edf}}
	{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of integers in 60edf ~~(continued)~~}}		{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of integers in 60edf }}
	{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of integers in 60edf (continued)}}		{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of integers in 60edf (continued)}}

BudjarnLambeth: /* Subsets and supersets */

2025-10-17T23:26:23Z

Subsets and supersets

← Older revision		Revision as of 23:26, 17 October 2025
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	This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos/ed4s) simultaneously.		This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos/ed4s) simultaneously.

	The relative edos of its subsets are: [[7ed4]], [[5edo]], [[9edo]]/[[17ed4]], [[21ed4]], [[31ed4]], [[17edo]], [[21edo]]/[[41ed4]], [[26edo]], [[34edo]] and [[51edo]]/[[103ed4]].		The relative edos/ed4s of its subsets are: [[7ed4]], [[5edo]], [[9edo]]/[[17ed4]], [[21ed4]], [[31ed4]], [[17edo]], [[21edo]]/[[41ed4]], [[26edo]], [[34edo]] and [[51edo]]/[[103ed4]].

	The simplest supersets of 60edf are [[120edf]] and [[180edf]].		The simplest supersets of 60edf are [[120edf]] and [[180edf]].

BudjarnLambeth: /* Subsets and supersets */

2025-10-17T23:25:34Z

Subsets and supersets

← Older revision		Revision as of 23:25, 17 October 2025
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	As a highly composite edf, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].		As a highly composite edf, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].

	This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos) simultaneously.		This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos/ed4s) simultaneously.

			The relative edos of its subsets are: [[7ed4]], [[5edo]], [[9edo]]/[[17ed4]], [[21ed4]], [[31ed4]], [[17edo]], [[21edo]]/[[41ed4]], [[26edo]], [[34edo]] and [[51edo]]/[[103ed4]].

	The simplest supersets of 60edf are [[120edf]] and [[180edf]].		The simplest supersets of 60edf are [[120edf]] and [[180edf]].

BudjarnLambeth: /* Subsets and supersets */

2025-10-17T23:16:44Z

Subsets and supersets

← Older revision		Revision as of 23:16, 17 October 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	As a highly composite ~~EDF~~, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].		As a highly composite edf, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].

	This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos) simultaneously.		This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos) simultaneously.

BudjarnLambeth at 23:15, 17 October 2025

2025-10-17T23:15:36Z

← Older revision		Revision as of 23:15, 17 October 2025
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	The simplest supersets of 60edf are [[120edf]] and [[180edf]].		The simplest supersets of 60edf are [[120edf]] and [[180edf]].

			== Intervals ==
			{{Interval table}}

	== Music ==		== Music ==

BudjarnLambeth at 23:15, 17 October 2025

2025-10-17T23:15:10Z

← Older revision		Revision as of 23:15, 17 October 2025
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	* [[205ed4]] – relative ed4		* [[205ed4]] – relative ed4
	* [[265ed6]] - relative ed6		* [[265ed6]] - relative ed6

	~~{{Stub}}~~

BudjarnLambeth: /* Subsets and supersets */

2025-10-17T23:14:56Z

Subsets and supersets

← Older revision		Revision as of 23:14, 17 October 2025
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	~~{{todo\|complete section\|inline=1}}~~		As a highly composite EDF, 60edf includes as subsets: [[2edf]], [[3edf]], [[5edf]], [[6edf]], [[9edf]], [[10edf]], [[12edf]], [[15edf]], [[20edf]] and [[30edf]].

			This makes it potentially a good [[polymicrotonal]] system for using multiple edfs (or their stretched/compressed relative edos) simultaneously.

			The simplest supersets of 60edf are [[120edf]] and [[180edf]].

	== Music ==		== Music ==

BudjarnLambeth: /* Theory */

2025-10-17T23:11:52Z

Theory

← Older revision		Revision as of 23:11, 17 October 2025
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	== Theory ==		== Theory ==
	60edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], ~~and as such~~ it inherits ~~some of the~~ properties of both those ~~systems~~. ~~It's~~ very similar to [[205ed4]].		60edf can be thought of as a very [[octave stretch]]ed version of [[103edo]], or a very compressed version of [[102edo]], but it actually inherits few properties from either.
	~~{{todo\|complete section\|inline=1}}~~
			It makes available [[dual-n\|dual]] versions of [[prime]]s 2 and 3 from both systems. Yet its mappings of primes 5, 7, 11, 13 and up are actually all different from either of those edos. For example mapping prime 5 to the 238th step (not 237 as in 102edo, nor 239 as in 103edo).

			60edf is very similar to [[205ed4]].

	=== Harmonics ===		=== Harmonics ===

← Older revision		Revision as of 23:28, 17 October 2025
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	So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n\|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.		So perhaps a reasonable - if clunky - way to interpret 60edf, is as a [[dual-n\|dual]]-2, dual-3, dual-13 [[31-limit]] tuning. Extending it to the [[37-limit]] could also be an option.
	{{Harmonics in equal\|60\|3\|2\|intervals=prime\|columns=13\|title=Approximation of primes in 60edf ~~(continued)~~}}		{{Harmonics in equal\|60\|3\|2\|intervals=prime\|columns=13\|title=Approximation of primes in 60edf}}
	{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of integers in 60edf ~~(continued)~~}}		{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=11\|collapsed=true\|title=Approximation of integers in 60edf }}
	{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of integers in 60edf (continued)}}		{{Harmonics in equal\|60\|3\|2\|intervals=integer\|columns=12\|start=12\|collapsed=true\|title=Approximation of integers in 60edf (continued)}}