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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|1080}}
{{ED intro}}


== Theory ==
== Theory ==
1080 is a largely composite EDO, meaning it's notable for its divisors. 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's abundancy index is 2.33..., or exactly 7/3.
1080edo is [[enfactoring|enfactored]] in the 13-limit, with the same tuning as [[270edo]]. Aside from the patent val, there are a number of mappings to be cosidered. The 1080e val, {{mapping|1080​ 1712​ 2508​ 3032 ​'''3737'''}}, [[Tempering out|tempers out]] 114345/114244, and the 1080ef val, {{mapping|1080​ 1712​ 2508 ​3032 '''​3737​ 3997'''}} it tempers out [[2080/2079]].  


Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.
=== Odd harmonics ===
{{Harmonics in equal|1080}}


=== Regular temperament theory ===
=== Subsets and supersets ===
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]].  
1080 is a largely composite edo, meaning it is notable for its divisors. Its 32 [[number of the divisors|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, and 1080. 1080's abundancy index is 2.33…, or exactly 7/3.


=== Harmonics ===
Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to the [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak edos, zeta integral edos and zeta gap edos]]. However, the [[patent val]] of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite edo.
{{Harmonics in equal|1080}}
 
As every 4th step of [[4320edo]], it is a good tuning for the 2.5/3.7 subgroup, and has strong representation for [[19/12]], [[19/10]], [[17/13]], [[23/13]], and [[23/17]].


== Table of intervals ==
== Selected intervals ==
{| class="wikitable"
{| class="wikitable mw-collapsible mw-collapsed"
|+
!Step
!Name
!Associated ratio
!Comments
|-
|-
|0
! Step
|Prime
! Eliora's Naming System
|
! Approximate Ratio
|
! Comments
|-
|-
|3
| 0
|Degree
| Prime
|
|  
|Derives from 360edo.
|  
|-
|-
|4
| 3
|Ducentiseptuagesima
| Degree
|
|  
|Derives from 270edo
| Derives from 360edo.
|-
|-
|7
| 4
|Septimal kelisma
| Ducentiseptuagesima
|
|  
|
| Derives from 270edo
|-
|-
|15
| 7
|Moria
| Septimal kelisma
|
|  
|Derives form 72edo.
|  
|-
|-
|90
| 15
|Dodecaphonic semitone
| Moria
|
|  
|
| Derives form 72edo.
|-
|-
|94
| 90
|Septendecimal semitone
| Dodecaphonic semitone
|17/16
|  
|
|  
|-
|-
|240
| 94
|Septimal submajor second
| Septendecimal semitone
|7/6
| 17/16
|Derives form 9edo.
|  
|-
|-
|360
| 240
|Landscape major third
| Septimal submajor second
|63/50
| 7/6
|
| Derives form 9edo.
|-
|-
|495
| 360
|24-phonic superfourth
| Landscape major third
|
| 63/50
|Derives from 24edo.
|  
|-
|-
|496
| 495
|Undecimal superfourth
| 24-phonic superfourth
|11/8
|  
|
| Derives from 24edo.
|-
|-
|630
| 496
|Dodecaphonic fifth
| Undecimal superfourth
|
| 11/8
|
|  
|-
|-
|632
| 630
|135-phonic Fifth
| Dodecaphonic fifth
|3/2
|  
|
|  
|-
|-
|756
| 632
|Tridecimal neutral sixth, 13th harmonic
| 135-phonic Fifth
|13/8
| 3/2
|Derives from 10edo.
|  
|-
|-
|1080
| 756
|Octave
| Tridecimal neutral sixth, 13th harmonic
|
| 13/8
|
| Derives from 10edo.
|-
| 1080
| Octave
|  
|  
|}
|}
== Music ==
; [[No Clue Music]]
* [https://www.youtube.com/watch?v=hQOvnQhAcKU ''Not Torture Music''] (2024)


[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
Retrieved from "https://en.xen.wiki/w/1080edo"