954edo - Revision history

Overthink: note 29-limit

2026-01-17T00:17:10Z

note 29-limit

← Older revision		Revision as of 00:17, 17 January 2026
Line 4:		Line 4:
	954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

	Beyond the 17-limit, the 954hj [[val]] is the most accurate, with a lower [[relative error]] than any previous equal temperaments in the [[31-limit]]. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with [[wart]]s.		Beyond the 17-limit, the 954hj [[val]] is the most accurate, with a lower [[relative error]] than any previous equal temperaments in the [[29-limit\|29-]] and [[31-limit]]. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with [[wart]]s.

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

FloraC: Stop the limit creep

2025-12-26T19:31:10Z

Stop the limit creep

← Older revision		Revision as of 19:31, 26 December 2025
Line 9:		Line 9:
	{{Harmonics in equal\|954}}		{{Harmonics in equal\|954}}
	{{Harmonics in equal\|954\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}		{{Harmonics in equal\|954\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	~~{{Harmonics in equal\|954\|start=23\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}~~
	~~{{Harmonics in equal\|954\|start=34\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}~~
	~~{{Harmonics in equal\|954\|start=45\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}~~
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 954 = {{~~factorization~~\|~~954~~}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.		Since 954 factors into primes as {{nowrap\| 2 × 3<sup>2</sup> × 53 }}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
	[[Category:Hemiennealimmal]]		[[Category:Hemiennealimmal]]
	[[Category:Semihemiennealimmal]]		[[Category:Semihemiennealimmal]]

Overthink: links

2025-12-26T00:31:25Z

links

← Older revision		Revision as of 00:31, 26 December 2025
Line 4:		Line 4:
	954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

	Beyond the 17-limit, the 954hj val is the most accurate, with a lower [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with ~~warts~~.		Beyond the 17-limit, the 954hj [[val]] is the most accurate, with a lower [[relative error]] than any previous equal temperaments in the [[31-limit]]. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with [[wart]]s.

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

Overthink: grammar

2025-12-26T00:30:09Z

grammar

← Older revision		Revision as of 00:30, 26 December 2025
Line 4:		Line 4:
	954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

	Beyond the 17-limit, the 954hj val is the most accurate, with lower a [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.		Beyond the 17-limit, the 954hj val is the most accurate, with a lower [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.

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

Overthink: note 954hj, reformat tables

2025-12-26T00:29:46Z

note 954hj, reformat tables

← Older revision		Revision as of 00:29, 26 December 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	954edo is a very strong 17-limit system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

			Beyond the 17-limit, the 954hj val is the most accurate, with lower a [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|~~columns~~=13}}		{{Harmonics in equal\|954}}
	{{Harmonics in equal\|954\|start=14\|~~columns~~=17\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}		{{Harmonics in equal\|954\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	{{Harmonics in equal\|954\|start=~~31\|columns=18~~\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}		{{Harmonics in equal\|954\|start=23\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
			{{Harmonics in equal\|954\|start=34\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
			{{Harmonics in equal\|954\|start=45\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 954 = {{factorization\|954}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.		Since 954 = {{factorization\|954}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

ArrowHead294 at 16:23, 20 February 2025

2025-02-20T16:23:45Z

← Older revision		Revision as of 16:23, 20 February 2025
Line 1:		Line 1:
	{{Infobox ET}}		{{Infobox ET}}
	{{~~EDO~~ intro~~\|954~~}}		{{ED intro}}

	954edo is a very strong 17-limit system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong 17-limit system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

Lériendil at 16:28, 13 October 2024

2024-10-13T16:28:21Z

← Older revision		Revision as of 16:28, 13 October 2024
Line 6:		Line 6:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|columns=13}}		{{Harmonics in equal\|954\|columns=13}}
	{{Harmonics in equal\|954\|start=14\|columns=17\|collapsed=1}}		{{Harmonics in equal\|954\|start=14\|columns=17\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	{{Harmonics in equal\|954\|start=31\|columns=18\|collapsed=1}}		{{Harmonics in equal\|954\|start=31\|columns=18\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Lériendil: collapsed high harmonic tables

2024-10-13T16:27:37Z

collapsed high harmonic tables

← Older revision		Revision as of 16:27, 13 October 2024
Line 6:		Line 6:
	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|columns=13}}		{{Harmonics in equal\|954\|columns=13}}
	{{Harmonics in equal\|954\|start=14\|columns=17}}		{{Harmonics in equal\|954\|start=14\|columns=17\|collapsed=1}}
	{{Harmonics in equal\|954\|start=31\|columns=18}}		{{Harmonics in equal\|954\|start=31\|columns=18\|collapsed=1}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

Godtone: this is a strict zeta EDO (minus integer peak) so does well in very high limits

2024-10-13T15:40:25Z

this is a strict zeta EDO (minus integer peak) so does well in very high limits

← Older revision		Revision as of 15:40, 13 October 2024
Line 5:		Line 5:

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|columns=11}}		{{Harmonics in equal\|954\|columns=13}}
			{{Harmonics in equal\|954\|start=14\|columns=17}}
			{{Harmonics in equal\|954\|start=31\|columns=18}}

	=== Subsets and supersets ===		=== Subsets and supersets ===

FloraC: Adopt template: Factorization; misc. cleanup

2023-11-02T11:22:27Z

Adopt template: Factorization; misc. cleanup

← Older revision		Revision as of 11:22, 2 November 2023
Line 2:		Line 2:
	{{EDO intro\|954}}		{{EDO intro\|954}}

	954edo is a very strong 17-limit system, ~~uniquely~~ [[consistent]] in the 17-limit, and is a [[~~The Riemann~~ zeta ~~function and tuning #Zeta EDO lists~~\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and it tempers out the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong 17-limit system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|columns=11}}		{{Harmonics in equal\|954\|columns=11}}

	=== ~~Divisors~~ ===		=== Subsets and supersets ===
	Since 954 = ~~2 × 3<sup>2</sup> × 53~~, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.		Since 954 = {{factorization\|954}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.

	~~[[Category:Equal divisions of the octave\|###]] <!-- 3-digit number -->~~
	[[Category:Ennealimmal]]		[[Category:Ennealimmal]]
	[[Category:Hemiennealimmal]]		[[Category:Hemiennealimmal]]
	[[Category:Semihemiennealimmal]]		[[Category:Semihemiennealimmal]]

← Older revision		Revision as of 00:29, 26 December 2025
Line 2:		Line 2:
	{{ED intro}}		{{ED intro}}

	954edo is a very strong 17-limit system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.		954edo is a very strong [[17-limit]] system, [[consistency\|distinctly consistent]] in the 17-limit, and is a [[zeta edo\|zeta peak, integral and gap edo]]. The tuning of the primes to 17 are all flat, and the equal temperament [[tempering out\|tempers out]] the [[ennealimma]], {{monzo\| 1 -27 18 }}, in the 5-limit and [[2401/2400]] and [[4375/4374]] in the 7-limit, so that it [[support]]s the [[ennealimmal]] temperament. In the 11-limit it tempers out [[3025/3024]], [[9801/9800]], 43923/43904, and 151263/151250 so that it supports hemiennealimmal. In the 13-limit it tempers out [[4225/4224]] and [[10648/10647]] and in the 17-limit 2431/2430 and [[2601/2600]]. It supports and gives the [[optimal patent val]] for the [[semihemiennealimmal]] temperament.

			Beyond the 17-limit, the 954hj val is the most accurate, with lower a [[relative error]] than any previous equal temperaments in the 31-limit. In the 954hj val, [[19/16]], [[29/16]], and their [[octave complement]]s are the only inconsistent intervals in the [[35-odd-limit]], which are in fact the very primes with warts.

	=== Prime harmonics ===		=== Prime harmonics ===
	{{Harmonics in equal\|954\|~~columns~~=13}}		{{Harmonics in equal\|954}}
	{{Harmonics in equal\|954\|start=14\|~~columns~~=17\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}		{{Harmonics in equal\|954\|start=12\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	{{Harmonics in equal\|954\|start=~~31\|columns=18~~\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}		{{Harmonics in equal\|954\|start=23\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
			{{Harmonics in equal\|954\|start=34\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
			{{Harmonics in equal\|954\|start=45\|collapsed=1\|title=Approximation of prime harmonics in 954edo (continued)}}
	=== Subsets and supersets ===		=== Subsets and supersets ===
	Since 954 = {{factorization\|954}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.		Since 954 = {{factorization\|954}}, 954edo has subset edos {{EDOs\| 2, 3, 6, 9, 18, 53, 106, 159, 318, 477 }}.