# 1ed81/80

(Redirected from 81/80 equal-step tuning)

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(convergent)

(convergent)

**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

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.