# 277edo

 ← 276edo 277edo 278edo →
Prime factorization 277 (prime)
Step size 4.33213¢
Fifth 162\277 (701.805¢)
Semitones (A1:m2) 26:21 (112.6¢ : 90.97¢)
Consistency limit 5
Distinct consistency limit 5

277 equal divisions of the octave (abbreviated 277edo or 277ed2), also called 277-tone equal temperament (277tet) or 277 equal temperament (277et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 277 equal parts of about 4.33 ¢ each. Each step represents a frequency ratio of 21/277, or the 277th root of 2.

## Theory

277edo is a good 5-limit tuning; however, it is inconsistent in the 7-odd-limit. The equal temperament tempers out 32805/32768 (schisma) and [-11 -37 30 in the 5-limit.

The patent val 277 439 643 778] tempers out 4375/4374, 65625/65536, and 829440/823543 in the 7-limit; 540/539, 6250/6237, 15488/15435, and 35937/35840 in the 11-limit; 625/624, 729/728, 1573/1568, 2080/2079, and 2200/2197 in the 13-limit. It supports pontiac.

The 277d val 277 439 643 777] tempers out 1029/1024, 10976/10935, and 48828125/48771072 in the 7-limit; 385/384, 441/440, 19712/19683, and 234375/234256 in the 11-limit; 625/624, 847/845, 1001/1000, and 1575/1573 in the 13-limit. It supports guiron and widefourth.

### Prime harmonics

Approximation of prime harmonics in 277edo
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +0.00 -0.15 -0.75 +1.57 -1.14 -0.09 -0.98 +1.40 -0.12 +1.47 -1.35
Relative (%) +0.0 -3.5 -17.4 +36.3 -26.3 -2.2 -22.7 +32.4 -2.7 +33.9 -31.2
Steps
(reduced)
277
(0)
439
(162)
643
(89)
778
(224)
958
(127)
1025
(194)
1132
(24)
1177
(69)
1253
(145)
1346
(238)
1372
(264)

### Subsets and supersets

277edo is the 59th prime edo.

## Regular temperament properties

Subgroup Comma List Mapping Optimal
8ve Stretch (¢)
Tuning Error
Absolute (¢) Relative (%)
2.3 [-439 277 [277 439]] 0.0473 0.0473 1.09
2.3.5 32805/32768, [-11 -37 30 [277 439 643]] 0.1398 0.1364 3.15

### Rank-2 temperaments

Table of rank-2 temperaments by generator
Periods
per 8ve
Generator* Cents* Associated
ratio*
Temperaments
1 115\277 498.19 4/3 Helmholtz

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