# 81/80 equal-step tuning

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Prime factorization
n/a
Step size
21.5063¢
Octave
56\1ed81/80 (1204.35¢)

(convergent)
Fifth
33\1ed81/80 (709.708¢)

(convergent)
Semitones (A1:m2)
0:8 (0¢ : 172.1¢)
Dual sharp fifth
33\1ed81/80 (709.708¢)

(convergent)
Dual flat fifth
32\1ed81/80 (688.201¢)

(convergent)
Dual major 2nd
9\1ed81/80 (193.557¢)

(convergent)
Consistency limit
2
Distinct consistency limit
1
Special properties

← 0ed81/80 | 1ed81/80 | 2ed81/80 → |

(convergent)

(convergent)

(convergent)

(convergent)

(convergent)

**81/80 equal-step tuning** (AS81/80, ambitonal sequence 81/80) is an equal multiplication of the syntonic comma. It corresponds to 55.79763 edo.

## Theory

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 | -44 | +40 | +44 | -23 | +36 | -39 | +13 | -36 | -3 | -3 | |

Step | 56 | 88 | 112 | 130 | 144 | 157 | 167 | 177 | 185 | 193 | 200 |

81/80 equal-step tuning 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.