2964edo: Difference between revisions

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{{Infobox ET}}
{{Infobox ET}}
The '''2964 equal divisions of the octave''' ('''2964edo'''), or the '''2964(-tone) equal temperament''' ('''2964tet''', '''2964et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 2964 [[equal]] parts of about 0.4048583 [[cent]]s each.
{{EDO intro|2964}}


== Theory ==
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 than [[494edo]] excepting for the 7th harmonic, which is corrected in an extremely precise way (absolute error 0.00000446 cents, relative error 0.0011%).


=== Prime harmonics ===
=== Prime harmonics ===
{{Harmonics in equal|2964|columns=11|prec=3}}
{{Harmonics in equal|2964|columns=11|prec=3}}


=== Miscellaneous properties ===
=== Subsets and supersets ===
Since 2964 = 6 × 494, 2964edo contains [[494edo]] as a subset.
Since 2964 = 6 × 494, 2964edo contains [[494edo]] as a subset.
[[Category:Equal divisions of the octave|####]] <!-- four-digit number -->

Revision as of 11:36, 15 October 2023

← 2963edo 2964edo 2965edo →
Prime factorization 22 × 3 × 13 × 19
Step size 0.404858 ¢ 
Fifth 1734\2964 (702.024 ¢) (→ 289\494)
Semitones (A1:m2) 282:222 (114.2 ¢ : 89.88 ¢)
Consistency limit 7
Distinct consistency limit 7

Template:EDO intro

In the 13-limit, 2964edo shares the same patent val with 494edo except for the 7th harmonic, which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%).

Prime harmonics

Approximation of prime harmonics in 2964edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.069 -0.079 +0.000 +0.099 -0.042 -0.097 +0.058 +0.066 -0.023 -0.096
Relative (%) +0.0 +17.1 -19.5 +0.0 +24.5 -10.3 -24.0 +14.3 +16.2 -5.6 -23.8
Steps
(reduced)
2964
(0)
4698
(1734)
6882
(954)
8321
(2393)
10254
(1362)
10968
(2076)
12115
(259)
12591
(735)
13408
(1552)
14399
(2543)
14684
(2828)

Subsets and supersets

Since 2964 = 6 × 494, 2964edo contains 494edo as a subset.