1342edt: Difference between revisions

(2 intermediate revisions by 2 users not shown)

Line 2:

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). 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 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 in equal|1342|3|1|start = 12|collapsed = 1|intervals = odd}}

~~=== Prime harmonics ===~~

@@ Line 2: / Line 2: @@
 {{ED intro}}
-edt 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]].
+edt 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]].
-edt 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.
+edt 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.
-factors as 2 × 11 × 61, so 1342edt has subset edts {{EDTs|2, 11, 22, 61, 122, and 671}}.
+factors as 2 × 11 × 61, so 1342edt has subset [[edt]]s {{EDTs|2, 11, 22, 61, 122, and 671}}.
 === 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}}