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{{Infobox ET}}
{{Infobox ET}}
{{EDO intro|360}}
{{ED intro}}


== Theory ==
== Theory ==
360edo is consistent in the 7-limit. Its 5-limit patent val [[support]]s [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis 10976/10935, 2097152/2083725, which is similar to the misty temperament but has a period of 1/9 rather than 1/3 octave. In addition, 360edo provides the optimal patent val for the 41 & 360 temperament with comma basis 10976/10935, 16384000000/16209796869, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports 12 & 360 with the comma basis 390625/388962, 67108864/66430125. 360edo tempers out the [[15/14 equal-step tuning|linus comma]], meaning 15/14 corresponds to 1/10th of the octave, 36 steps.  
360edo is [[consistent]] to the [[7-odd-limit]], but [[harmonic]] [[3/1|3]] is about halfway between its steps. It can also be used with 2.5.9.13 subgroup.
 
In the 5-limit, the [[patent val]] [[support]]s the [[misty]] temperament, and in the 7-limit 360edo supports the [[trimisty]] (name proposed by Eliora) 63 & 99 temperament with the comma basis {[[10976/10935]], 2097152/2083725}, which is similar to the misty temperament but has a period of 1/9- rather than 1/3-octave.
 
360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for [[degrees]], the {{nowrap|140 & 220}} temperament with period 1\20. Aside from that, it provides the optimal patent val for the {{nowrap|41 & 360}} temperament with comma basis {10976/10935, 16384000000/16209796869}, on which it has lower badness than any other 7-limit temperament for which 360edo gives the optimal patent val. It also supports {{nowrap|12 & 360}} with the comma basis {[[390625/388962]], 67108864/66430125}. 
 
Aside from the patent val, there is a number of mappings to be considered. The 360d val, {{val|360 571 836 '''1010'''}}, tempers out 3136/3125, 5120/5103, and extends the misty temperament in to the 7-limit. It is also a tuning for the 12th-octave [[magnesium]] temperament.  


360edo provides the optimal patent val in the 11-limit, and otherwise a good tuning in the 13-limit for the [[Hemimage_temperaments#Degrees|degrees temperament]], the 80&140 temperament with period 20.
=== As an interval size measure ===
360 is the 13th [[highly composite EDO]], with many proper divisors: 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180.
One step of 360edo is known as '''the Dröbisch angle''', being first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".
=== Odd harmonics ===
=== Odd harmonics ===
{{harmonics in equal|360}}
{{Harmonics in equal|360}}
 
=== Subsets and supersets ===
360 is the 13th [[highly composite edo]], with many proper divisors: {{EDOs| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, 180 }}. One step of 360edo is known as '''the Dröbisch angle''', an [[interval size measure]] first proposed by Moritz Dröbisch in the 19th century at first merely by the name "angle".


== Table of intervals ==
== Table of intervals ==
Eliora proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].
[[Eliora]] proposes notating 360edo with calendar dates, Jan 1 being the tonic, Jan 2 being the next step, etc, and each month having even 30 days. The notation is convenient because 1 month in this scenario is equal to 1 semitone, and corresponds to [[12edo]].


Any other notation system involving the number 360 can also be used.
Any other notation system involving the number 360 can also be used.


{| class="wikitable mw-collapsible mw-collapsed"
See: [[Table of 360edo intervals]]
|+Table of selected intervals
 
!Degree
== Regular temperament properties ==
!Name
=== Rank-2 temperaments ===
!Calendar notation (if unison is Jan 1)
{| class="wikitable center-all left-5"
!Ratio
|+ style="font-size: 105%;" | Table of rank-2 temperaments by generator
|-
|0
|Prime, unison
|January 1
|1/1
|-
|1
|Degree, grad, schisma
|January 2
|32805/32768
|-
|30
|Dodecaphonic semitone
|February 1
|89/84
|-
|36
|Septimal diatonic semitone, decioctave
|February 6
|[[15/14]]
|-
|60
|Dodecaphonic major second
|March 1
|
|-
|90
|Dodecaphonic minor third
|April 1
|
|-
|116
|Classical major third
|April 26
|
|-
|120
|
|May 1
|
|-
|150
|
|June 1
|
|-
|180
|Symmetric tritone
|July 1
|
|-
|-
|210
! Periods<br />per 8ve
|Dodecaphonic perfect fifth
! Generator*
|August 1
! Cents*
|442/295
! Associated<br />ratio*
! Temperaments
|-
|-
|211
| 1
|Just perfect fifth
| 119\360
|August 2
| 396.67
|3/2
| 44/35
| [[Squarschmidt]]
|-
|-
|240
| 2
|
| 53\360
|September 1
| 176.67
|
| 448/405
| Quatracot
|-
|-
|270
| 3
|
| 149\360<br />(29\360)
|October 1
| 703.33<br />(303.33)
|
| 4/3<br />(135/128)
| [[Misty]]
|-
|-
|291
| 4
|Harmonic seventh
| 23\360
|October 21
| 76.67
|
| 4302592/4100625
| [[Reenactment]]
|-
|-
|300
| 9
|
| 149\360<br />(29\360)
|November 1
| 703.33<br />(36.67)
|
| 4/3<br />(135/128)
| [[Trimisty]]
|-
|-
|330
| 12
|
| 73\360<br />(13\360)
|December 1
| 243.333<br />(43.333)
|
| 3145728/2734375<br />(?)
| [[Magnesium]] (360d)
|-
|-
|360
| 20
|Octave
| 149\360<br />(5\360)
|January 1
| 703.33<br />(43.33)
|
| 4/3<br />(126/125)
| [[Degrees]]
|}
|}
<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct


==Regular temperament properties==
== Music ==
===Rank-2 temperaments ===
; [[User:Eliora|Eliora]]
{| class="wikitable center-all left-5"
* [https://www.youtube.com/watch?v=VSKqwJkWu_U ''Idyllic Tribe''] (2022)
!Periods<br>per 8ve
!Generator<br>(reduced)
!Cents<br>(reduced)
!Associated<br>ratio
!Temperaments
|-
|1
|119\360
|396.67
|44/35
|[[Squarschmidt]]
|-
|2
|53\360
|176.67
|448/405
|[[Ragismic microtemperaments#Quatracot|Quatracot]]
|-
|3
|211\360<br>(91\360)
|703.33<br>(303.33)
|3/2
|[[Misty]]
|-
|4
|23\360
|76.67
|4302592/4100625
|[[Reenactment]]
|-
|9
|211\360<br>(11\360)
|703.33<br>(36.67)
|3/2
|[[Trimisty]]
|-
|20
|211\360<br>(13\360)
|703.33<br>(43.33)
|3/2<br>(45/44)
|[[Degrees]]
|}


==Music==
== Application as a logarithmic scale outside of music ==
* [https://www.youtube.com/watch?v=VSKqwJkWu_U Idyllic Tribe] by [[User:Eliora|Eliora]]
360edo is used in the {{w|eyeborg}}, which maps its scale degrees onto color hues, thus converting color into sound waves. The device was originally intended to help colorblind individuals.
==References==
* [https://www.huygens-fokker.org/docs/measures.html Logarithmic size measures]
==Application as a logarithmic scale outside of music==
360edo is used in the [[wikipedia:Eyeborg|eyeborg]], which maps its scale degrees onto color hues, thus converting color into sound waves. The device was originally intended to help colorblind individuals.


[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
[[Category:Sonifications]]
[[Category:Highly composite]]
[[Category:Real-life sonifications]]
[[Category:Listen]]
[[Category:Listen]]
{{Todo| cleanup |comment=move trimisty away}}
Retrieved from "https://en.xen.wiki/w/360edo"