40ed10 - Revision history

ArrowHead294: /* See also */

2025-06-10T13:27:39Z

ArrowHead294 at 13:20, 10 June 2025

2025-06-10T13:20:32Z

← Older revision		Revision as of 13:20, 10 June 2025
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	* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]		* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]

			[[Category:12edo]]
	[[Category:Sonifications]]		[[Category:Sonifications]]

ArrowHead294 at 13:20, 10 June 2025

2025-06-10T13:20:18Z

← Older revision		Revision as of 13:20, 10 June 2025
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	== Theory ==		== Theory ==
	40ed10 is related to [[12edo]], but with 10/1 instead of 2/1 being just. The octave~~, which comes from [[10ed10]],~~ is compressed from pure by ~~about~~ 4.~~1 cents~~.		40ed10 is related to [[12edo]], but with 10/1 instead of 2/1 being just. The octave is compressed from pure by 4.106{{c}}, a small but significant deviation.

	=== Harmonics ===		=== Harmonics ===
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	<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;		<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;

	which lies in the ~~basis~~ of using a "decimal" prefix to an otherwise binary unit of information.		which lies in the obsolete practice of using a decimal prefix to an otherwise binary unit of information.

	== Intervals ==		== Intervals ==

FloraC: /* See also */ +++

2025-01-15T15:09:26Z

FloraC: +subsets and supersets

2025-01-15T14:42:43Z

+subsets and supersets

@@ Line 8: / Line 8: @@
 {{Harmonics in equal|40|10|1|intervals=integer}}
 {{Harmonics in equal|40|10|1intervals=integer|start=12|columns=12|collapsed=1|title=Approximation of harmonics in 40ed10 (continued)}}
 == Intervals ==
@@ Line 180: / Line 190: @@
 | [[10/1]]
 |}
 == Regular temperaments ==

FloraC: /* Intervals */ rework (I'm only putting the simplest interpretations)

2025-01-15T14:39:50Z

Intervals: rework (I'm only putting the simplest interpretations)

Show changes

FloraC: Cleanup; -duplicate data

2025-01-15T13:59:53Z

Cleanup; -duplicate data

Show changes

FloraC: Recategorize

2023-08-08T07:32:51Z

Recategorize

← Older revision		Revision as of 07:32, 8 August 2023
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	* [[18/17s equal temperament\|AS18/17]] - relative [[AS\|ambitonal sequence]]		* [[18/17s equal temperament\|AS18/17]] - relative [[AS\|ambitonal sequence]]

	[[Category:~~Equal-step tuning]]~~		[[Category:Sonifications]]
	~~[[Category:Ed10]]~~
	~~[[Category:Real-life sonifications~~]]

Eliora: decibel tuning is 10ed10

2023-07-23T18:34:58Z

decibel tuning is 10ed10

← Older revision		Revision as of 18:34, 23 July 2023
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	The '''division of the 10th harmonic into 40 equal parts''' (40ED10) is related to [[12edo\|12EDO]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] is very close to 1\12 (one step of 12 EDO).		The '''division of the 10th harmonic into 40 equal parts''' (40ED10) is related to [[12edo\|12EDO]], but with 10/1 instead of 2/1 being just. The step size (99.657843 [[cent]]s) of this [[equal-step tuning]] is very close to 1\12 (one step of 12 EDO).

	~~It is possible to call this division a form of '''decibel tuning''' or '''kilobyte tuning''', as~~		The octave, which is 12\40 = 3\10, is compressed by about 4.1 cents.

	~~<math>10^{\frac{1}{10}} \approx 2^{\frac{1}{3}} = 1.2589254 \approx 1.2599210</math>;~~

	~~which lies in the basis of the definition of decibel. In addition, as a consequence of the previous formula,~~

	~~<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;~~

	~~which lies in the basis of using a "decimal" prefix to an otherwise binary unit of information.~~ The octave, which is 12\40 = 3\10, is compressed by about 4.1 cents.

	== Theory ==		== Theory ==
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	\| \|		\| \|
	\|}		\|}

			=== Miscellany ===
			It is possible to call this division a form of '''kilobyte tuning''', as

			<math>2^{10} \approx 10^{3} = 1024 \approx 1000</math>;

			which lies in the basis of using a "decimal" prefix to an otherwise binary unit of information.

	== Regular temperaments ==		== Regular temperaments ==

Cmloegcmluin: "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

2023-05-07T18:49:21Z

"optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence

Show changes

← Older revision		Revision as of 13:27, 10 June 2025
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	* [[34ed7]] – relative ed7		* [[34ed7]] – relative ed7
	* [[42ed11]] – relative ed11		* [[42ed11]] – relative ed11
			* [[76ed80]] – close to the zeta-optimized tuning for 12edo
	* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]		* [[1ed18/17\|AS18/17]] – relative [[AS\|ambitonal sequence]]

	[[Category:12edo]]		[[Category:12edo]]
	[[Category:Sonifications]]		[[Category:Sonifications]]

← Older revision		Revision as of 15:09, 15 January 2025
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	== See also ==		== See also ==
			* [[7edf]] – relative edf
	* [[12edo]] – relative edo		* [[12edo]] – relative edo
	* [[~~19ed3~~]] – relative ~~ed3~~		* [[19edt]] – relative edt
	* [[28ed5]] – relative ed5		* [[28ed5]] – relative ed5
	* [[31ed6]] – relative ed6		* [[31ed6]] – relative ed6