# 1ed81/80

 ← 0ed81/80 1ed81/80 2ed81/80 →
Prime factorization n/a
Step size 21.5063¢
Octave 56\1ed81/80 (1204.35¢)
(convergent)
Twelfth 88\1ed81/80 (1892.55¢)
(convergent)
Consistency limit 2
Distinct consistency limit 1
Special properties

1 equal division of 81/80 (1ed81/80), also known as ambitonal sequence of 81/80 (AS81/80) or 81/80 equal-step tuning, is an equal multiplication of the syntonic comma. It corresponds to 55.79763 edo.

## Theory

Approximation of harmonics in 1ed81/80
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +4.35 -9.40 +8.70 +9.50 -5.05 +7.66 -8.45 +2.70 -7.65 -0.60 -0.70
Relative (%) +20.2 -43.7 +40.5 +44.2 -23.5 +35.6 -39.3 +12.6 -35.6 -2.8 -3.2
Step 56 88 112 130 144 157 167 177 185 193 200

1ed81/80 can be regarded as a subset of 5-limit just intonation. Some intervals it approximates well are 5/4, 7/4, 12/11, 14/13, and 15/11. In addition, it represents well certain compound intervals such as 8/3, 11/1, 12/1 while omitting their octave reductions. With a stretch, 53edo can be regarded as its edo equivalent. However, the closest direct approximation is 56edo.

AS81/80 has a good representation of the 11.17.19 prime number subgroup. This time, the octave equivalence is not applied.