1342edt - Revision history

Lériendil: izar

2024-12-29T22:29:41Z

izar

← Older revision		Revision as of 22:29, 29 December 2024
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	{{ED intro}}		{{ED intro}}

	1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 1342edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].		1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Even with this level of accuracy, it still supports the (relatively) simple temperament [[Izar]], equating six intervals of [[49/45]] to [[5/3]]. Despite the very good tuning of prime harmonics 3, 5 and 7, 1342edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].

	1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is [[consistent]] in the (no-twos) [[27-odd-limit]] (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the (no-twos) no-29s [[39-odd-limit]] (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.		1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is [[consistent]] in the (no-twos) [[27-odd-limit]] (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the (no-twos) no-29s [[39-odd-limit]] (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.
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	=== Harmonics ===		=== Harmonics ===
	{{Harmonics in equal\|1342\|3\|1}}		{{Harmonics in equal\|1342\|3\|1\|intervals = prime\|columns = 9}}
			{{Harmonics in equal\|1342\|3\|1\|start = 12\|collapsed = 1\|intervals = odd}}
	~~=== Prime harmonics ===~~
	{{Harmonics in equal\|1342\|3\|1\|intervals=~~prime~~}}

Lériendil at 10:42, 26 August 2024

2024-08-26T10:42:15Z

← Older revision		Revision as of 10:42, 26 August 2024
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	{{ED intro}}		{{ED intro}}

	1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, ~~27208edt~~ misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].		1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 1342edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].

	1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is [[consistent]] in the (no-twos) [[27-odd-limit]] (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the (no-twos) no-29s [[39-odd-limit]] (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.		1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is [[consistent]] in the (no-twos) [[27-odd-limit]] (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the (no-twos) no-29s [[39-odd-limit]] (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.

Akselai at 14:32, 29 April 2024

2024-04-29T14:32:54Z

← Older revision		Revision as of 14:32, 29 April 2024
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	1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].		1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments\|no-twos]] [[7-limit]], with the [[5/1\|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1\|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].

	1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is consistent in the 27-odd-limit (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the no-29s 39-odd-limit (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.		1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is [[consistent]] in the (no-twos) [[27-odd-limit]] (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the (no-twos) no-29s [[39-odd-limit]] (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.

	1342 factors as 2 × 11 × 61, so 1342edt has subset ~~edts~~ {{EDTs\|2, 11, 22, 61, 122, and 671}}.		1342 factors as 2 × 11 × 61, so 1342edt has subset [[edt]]s {{EDTs\|2, 11, 22, 61, 122, and 671}}.

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

Akselai: Created page with "{{Infobox ET}} {{ED intro}} 1342edt provides a ''very good approximation'' to the no-twos 7-limit, with the 5th harmonic tuned 0..."

2024-04-29T11:56:19Z

Created page with "{{Infobox ET}} {{ED intro}} 1342edt provides a ''very good approximation'' to the no-twos 7-limit, with the 5th harmonic tuned 0..."

New page

{{Infobox ET}}
{{ED intro}}

1342edt provides a ''very good approximation'' to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the [[5/1|5th harmonic]] tuned 0.55% sharp (approximately 1/181 of a step), and the [[7/1|7th harmonic]] tuned 1.29% flat (approximately 1/110 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by 29% (larger than 1/4 of a step), making it incomparable with its related [[edo]]s, [[847edo]] and [[848edo]].

1342edt is a no-twos [[zeta]] peak and integer peak edt, and can represent prime harmonics from 3 up to 41 with less than 30% of error. It is consistent in the 27-odd-limit (with [[29/19]] being the first interval 1342edt fails to represent consistently) and in the no-29s 39-odd-limit (failing at 41/19). 1342edt can thus be seen as the edt counterpart to [[1578edo]], a zeta edo with similar size, approximation to primes, and consistency limit.

1342 factors as 2 × 11 × 61, so 1342edt has subset edts {{EDTs|2, 11, 22, 61, 122, and 671}}.

=== Harmonics ===
{{Harmonics in equal|1342|3|1}}

=== Prime harmonics ===
{{Harmonics in equal|1342|3|1|intervals=prime}}