2964edo - Revision history

FloraC: - spam

2025-11-09T08:36:58Z

- spam

2025-11-08T23:43:53Z

Commas of the 2.3.5.7.11.13 subgroup tempered out in 2964edo patent val

2025-11-08T21:54:03Z

← Older revision		Revision as of 21:54, 8 November 2025
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	In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap\|26 × 57 × 2}}.		In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap\|26 × 57 × 2}}.

			A basis for the 13-limit commas consists of [[4225/4224]], [[6656/6655]], and [[43940/43923]].

	=== Prime harmonics ===		=== Prime harmonics ===

2025-11-08T21:41:15Z

Commas of the 2.3.5.7.11.13 subgroup tempered out in 2964edo patent val

← Older revision		Revision as of 21:41, 8 November 2025
Line 15:		Line 15:
	Commas with numerator <= 2^32:		Commas with numerator <= 2^32:

	{\| class="wikitable mw-collapsible mw-collapsed"		{\| class="wikitable mw-collapsible mw-collapsed sortable"
	! [[Ratio]]		! [[Ratio]]
	! [[Monzo]]		! [[Monzo]]

2025-11-08T21:38:56Z

2025-03-03T16:04:20Z

← Older revision		Revision as of 16:04, 3 March 2025
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	{{ED intro}}		{{ED intro}}

	In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{cc}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as 26 × 57 × 2.		In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap\|26 × 57 × 2}}.

	=== Prime harmonics ===		=== Prime harmonics ===

2025-02-20T23:12:30Z

← Older revision		Revision as of 23:12, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|2964~~}}		{{ED intro}}

	In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{cc}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as 26 × 57 × 2.		In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{cc}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as 26 × 57 × 2.

2025-01-28T16:32:12Z

← Older revision		Revision as of 16:32, 28 January 2025
Line 2:		Line 2:
	{{EDO intro\|2964}}		{{EDO intro\|2964}}

	In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is a denominator to [[convergent]] to log<sub>2</sub>7.		In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{cc}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as 26 × 57 × 2.

	=== Prime harmonics ===		=== Prime harmonics ===

2023-12-21T22:03:26Z

← Older revision		Revision as of 22:03, 21 December 2023
Line 2:		Line 2:
	{{EDO intro\|2964}}		{{EDO intro\|2964}}

	In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%).		In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1\|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is a denominator to [[convergent]] to log<sub>2</sub>7.

	=== Prime harmonics ===		=== Prime harmonics ===

2023-10-30T10:02:11Z

Adopt template: Factorization

← Older revision		Revision as of 10:02, 30 October 2023
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	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 2964 = 6 × 494, ~~2964edo contains [[494edo]] as a subset~~.		Since 2964 factors into {{factorization\|2964}}, 2964edo has subset edos {{EDOs\| 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482 }}.