# 1955edo

← 1954edo | 1955edo | 1956edo → |

**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 2^{1/1955}, 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

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.