1641edo

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← 1640edo1641edo1642edo →
Prime factorization 3 × 547
Step size 0.731261¢
Fifth 960\1641 (702.011¢) (→320\547)
Semitones (A1:m2) 156:123 (114.1¢ : 89.95¢)
Consistency limit 11
Distinct consistency limit 11

1641 equal divisions of the octave (abbreviated 1641edo), or 1641-tone equal temperament (1641tet), 1641 equal temperament (1641et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1641 equal parts of about 0.731 ¢ each. Each step of 1641edo represents a frequency ratio of 21/1641, or the 1641st root of 2.

Theory

This EDO corrects the mappings of 547edo for the 7-prime and the 11-prime, but is only consistent up to the 11-limit.

Prime harmonics

Approximation of prime harmonics in 1641edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error absolute (¢) +0.000 +0.056 -0.208 +0.095 +0.053 -0.308 +0.346 +0.110 -0.121 +0.039 +0.120
relative (%) +0 +8 -28 +13 +7 -42 +47 +15 -17 +5 +16
Steps
(reduced)
1641
(0)
2601
(960)
3810
(528)
4607
(1325)
5677
(754)
6072
(1149)
6708
(144)
6971
(407)
7423
(859)
7972
(1408)
8130
(1566)