1080edo
| ← 1079edo | 1080edo | 1081edo → |
1080 tone equal temperament, also called 1080-EDO divides the octave in 1080 equal steps of approximately 1.11 cents.
Theory
Script error: No such module "primes_in_edo". Since 1080 = 4 * 270 and 1080 = 15 * 72, it contains 270edo and 72edo as subsets, both belonging to the zeta peak edos, zeta integral edos and zeta gap edos sequences.
In the 13-limit, 1080edo is contorted order-4, with the same tuning as 270edo. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out 2080/2079.
Divisors
The prime factorization of 1080 is [math]\displaystyle{ 1080 = 2^{3} \cdot 3^{3} \cdot 5 }[/math]
Its 32 divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540, 1080.
1080's abundancy index is 2.33333... = exactly 7/3.
Table of intervals
| Step | Name | Associated ratio | Comments |
|---|---|---|---|
| 0 | Prime | ||
| 3 | Degree | Derives from 360edo. | |
| 4 | Ducentiseptuagesima | Derives from 270edo | |
| 7 | Septimal kelisma | ||
| 15 | Moria | Derives form 72edo. | |
| 21 | Pythagorean comma | ||
| 90 | Dodecaphonic semitone | ||
| 94 | Septendecimal semitone | 17/16 | |
| 240 | Septimal submajor second | 7/6 | Derives form 9edo. |
| 360 | Landscape major third | 63/50 | |
| 495 | 24-phonic superfourth | Derives from 24edo. | |
| 496 | Undecimal superfourth | 11/8 | |
| 630 | Dodecaphonic fifth | ||
| 632 | 270-phonic Fifth | 3/2 | |
| 756 | Tridecimal neutral sixth, 13th harmonic | 13/8 | Derives from 10edo. |
| 1080 | Octave |