# 1277edo

 ← 1276edo 1277edo 1278edo →
Prime factorization 1277 (prime)
Step size 0.939702¢
Fifth 747\1277 (701.958¢)
Semitones (A1:m2) 121:96 (113.7¢ : 90.21¢)
Consistency limit 11
Distinct consistency limit 11

1277 equal divisions of the octave (abbreviated 1277edo or 1277ed2), also called 1277-tone equal temperament (1277tet) or 1277 equal temperament (1277et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 1277 equal parts of about 0.94 ¢ each. Each step represents a frequency ratio of 21/1277, or the 1277th root of 2.

## Theory

1277edo is consistent to the 11-odd-limit. The equal temperament tempers out 4375/4374, 52734375/52706752, 645700815/645657712 (starscape comma) and [51 -13 -1 -10 (technologisma) in the 7-limit; 151263/151250, 759375/758912, and 2097152/2096325 in the 11-limit. It supports monzismic, supermajor, revopent, as well as the rank-3 temperament bragi.

### Prime harmonics

Approximation of prime harmonics in 1277edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.000 +0.003 -0.096 +0.007 +0.287 -0.434 +0.291 +0.373 +0.387 +0.337 +0.462
Relative (%) +0.0 +0.3 -10.2 +0.8 +30.6 -46.2 +31.0 +39.7 +41.1 +35.8 +49.1
Steps
(reduced)
1277
(0)
2024
(747)
2965
(411)
3585
(1031)
4418
(587)
4725
(894)
5220
(112)
5425
(317)
5777
(669)
6204
(1096)
6327
(1219)

### Subsets and supersets

1277edo is the 206th prime edo. 2554edo, which divides the edostep in two, is the smallest edo distinctly consistent through the 41-odd-limit, and provides correction for harmonics 11 through 41.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [2024 -1277 [1277 2024]] -0.0009 0.0009 0.10
2.3.5 [54 -37 2, [-67 -9 35 [1277 2024 2965]] +0.0132 0.0199 2.12
2.3.5.7 4375/4374, 52734375/52706752, [51 -13 -1 -10 [1277 2024 2965 3585]] +0.0093 0.0186 1.98
2.3.5.7.11 4375/4374, 151263/151250, 759375/758912, 2097152/2096325 [1277 2024 2965 3585 4418]] -0.0092 0.0405 4.31

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
Ratio*
Temperaments
1 265\1277 249.021 [-27 11 3 1 Monzismic
1 380\1277 357.087 768/625 Dodifo
1 463\1277 435.082 9/7 Supermajor

* octave-reduced form, reduced to the first half-octave, and minimal form in parentheses if it is distinct

## Music

Francium
• "mututhery" from albumwithoutspaces (2024) – Spotify | Bandcamp | YouTube – monzismic[19] in 1277edo tuning