# 20160edo

← 20159edo | 20160edo | 20161edo → |

^{6}× 3^{2}× 5 × 7**20160 equal divisions of the octave** (abbreviated **20160edo**), or **20160-tone equal temperament** (**20160tet**), **20160 equal temperament** (**20160et**) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 20160 equal parts of about 0.0595 ¢ each. Each step of 20160edo represents a frequency ratio of 2^{1/20160}, or the 20160th root of 2.

20160edo is the 23rd highly composite edo, although it is not a member of the superabundant edos. It is also a highly factorable number edo, carrying the trait of being broken down into subsets into more ways than any number before it.

Aside from divisors, it is an excellent no-7s 29-limit system, having errors of 25% or less, and with the 28% error on the 7th harmonic it is overall a satisfactory 29-limit tuning, making it a candidate for an interval size measure.

Eliora proposes that one step of 20160edo be called *pian*, since piano manufacturers have a tendency to avoid the prominence of 7th harmonic in their sound. A semitone is therefore 1680 pians, a step of 224edo is 90 pians, and the Dröbisch angle, one step of 360edo, is 56 pians.

### Prime harmonics

Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Error | absolute (¢) | +0.0000 | +0.0093 | -0.0042 | -0.0164 | -0.0084 | +0.0081 | -0.0149 | -0.0130 | -0.0005 | +0.0061 | +0.0240 |

relative (%) | +0 | +16 | -7 | -28 | -14 | +14 | -25 | -22 | -1 | +10 | +40 | |

Steps (reduced) |
20160 (0) |
31953 (11793) |
46810 (6490) |
56596 (16276) |
69742 (9262) |
74601 (14121) |
82403 (1763) |
85638 (4998) |
91195 (10555) |
97937 (17297) |
99877 (19237) |