1080edo: Difference between revisions
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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]]. | 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 == | === Divisors === | ||
The prime factorization of 1080 is | The prime factorization of 1080 is | ||
<math>1080 = 2^{3} \cdot 3^{3} \cdot 5</math> | <math>1080 = 2^{3} \cdot 3^{3} \cdot 5</math> | ||
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Its [[number of the divisors|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. | Its [[number of the divisors|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 == | |||
{| class="wikitable" | |||
|+ | |||
!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 | |||
| | |||
| | |||
|} | |||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||