1955edo

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← 1954edo1955edo1956edo →
Prime factorization 5 × 17 × 23
Step size 0.613811¢
Fifth 1144\1955 (702.199¢)
Semitones (A1:m2) 188:145 (115.4¢ : 89¢)
Dual sharp fifth 1144\1955 (702.199¢)
Dual flat fifth 1143\1955 (701.586¢)
Dual major 2nd 332\1955 (203.785¢)
Consistency limit 3
Distinct consistency limit 3

1955 equal divisions of the octave (1955edo), or 1955-tone equal temperament (1955tet), 1955 equal temperament (1955et) when viewed from a regular temperament perspective, is the tuning system that divides the octave into 1955 equal parts of about 0.614 ¢ each.

1955edo is inconsistent to the 5-odd-limit and harmonics 3, 5, and 7 are all about halfway between its steps. As such, it commends itself to a 2.9.15.21.11.17 subgroup interpretation, with a comma basis {43923/43904, 163863/163840, 334125/334084, 1285956/1285625, 1434818/1434375}.

In particular, 1955edo is an excellent 2.15.17.21 subgroup tuning with harmonics are represented to within 3% error, with the comma basis {2000033/2000000, 2.15.17.21 [80 -8 -13 1, and 2.15.17.21 [73 -15 4 -7}. The 1955 & 6003 temperament in the 2.15.17.21 subgroup has only 0.000396 cents per octave of TE error. It is period-23 and has a comma basis {2000033/2000000, 2.5.17.21 [-101 -12 48 -11}.

Odd harmonics

Approximation of odd harmonics in 1955edo
Harmonic 3 5 7 9 11 13 15 17 19 21 23
Error absolute (¢) +0.244 -0.227 -0.233 -0.125 -0.116 -0.221 +0.018 +0.006 +0.185 +0.012 +0.268
relative (%) +40 -37 -38 -20 -19 -36 +3 +1 +30 +2 +44
Steps
(reduced)
3099
(1144)
4539
(629)
5488
(1578)
6197
(332)
6763
(898)
7234
(1369)
7638
(1773)
7991
(171)
8305
(485)
8587
(767)
8844
(1024)

Subsets and supersets

Since 1955 factors into 5 × 17 × 23, 1955edo has subset edos 5, 17, 23, 85, 115, 391.