# 1955edo

 ← 1954edo 1955edo 1956edo →
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 (abbreviated 1955edo or 1955ed2), also called 1955-tone equal temperament (1955tet) or 1955 equal temperament (1955et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1955 equal parts of about 0.614 ¢ each. Each step represents a frequency ratio of 21/1955, or the 1955th root of 2.

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 (%) +39.8 -36.9 -37.9 -20.3 -18.9 -36.0 +2.9 +1.0 +30.2 +1.9 +43.6
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.