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{{Infobox ET}}
{{Infobox ET}}
'''360 equal divisions of the octave''' ('''360edo'''), or '''360-tone equal temperament''' ('''360tet'''), '''360 equal temperament''' ('''360et''') when viewed from a [[regular temperament]] perspective, is the tuning system that divides the [[octave]] into 360 [[equal]] parts of {{ExactlyOrAbout| {{#expr: 1200/360 round 16}} }}{{cent}} each, a step size known as '''the Dröbisch angle'''.
'''360 equal divisions of the octave''' ('''360edo'''), or '''360-tone equal temperament''' ('''360tet'''), '''360 equal temperament''' ('''360et''') when viewed from a [[regular temperament]] perspective, is the tuning system that divides the [[octave]] into 360 [[equal]] parts of {{ExactlyOrAbout| {{#expr: 1200/360 round 16}} }}{{cent}} each, a step size known as '''the Dröbisch angle'''.
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.


== Theory ==
== Theory ==
{{Primes in edo|360|columns=10}}
{{Primes in edo|360|columns=10}}
360 has 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. 360 is the 13th [[superabundant EDO]].
360 has 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.


Its 23-limit patent val is <360 571 836 1011 1245 1332 1471 1529 1628|. This val tempers out the kalisma, the triaphonisma, the septendecimal bridge comma, the misty comma, hemimage, dimicomp, 2*(14/15)^10, 289/288, 352/351, 589824/588245 and 2560000000/2542277421.  
360 is the 13th [[highly composite EDO]].  


Its 5-limit patent val [[support]]s [[misty]] temperament.  
Its 5-limit patent val [[support]]s [[misty]] temperament.  


In the 7-limit, 360edo supports the [[trimisty]] (name proposed by Eliora) 63&99 temperament with wedgie <<9 -36 9 -78 -11 122|| which tempers out misty but has a period of 1/9 rather than 1/3 octave,. Two other seven limit temperaments it supports and also provides the optimal patent val for are 41&360 = <<11 76 51 95 50 -95|| and 12&360 = <<12 -48 -108 -104 -205 -116||; neither is very good though 41&360 has a TE badness lower than any alternative 7-limit temperament for which 360 gives the optimal patent val. In the 7-limit, 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 in the 7-limit. In it, it 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 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. 
 
Eliora proposes a 7-limit reenactment temperament for 360edo, defined as 188 & 360 and named after the YouTubers cs188 and radicalfaith360. It has a comma basis 2097152/2083725 and {{Monzo|0, -19, -10, 19}}. 


Much better is [[Hemimage_temperaments#Degrees|degrees temperament]], the 80&140 temperament with period 20, for which 360 supplies the optimal patent val in the 11-limit and which it supports and provides an excellent tuning for in the 13-limit. In the 
=== Proposed notation ===
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]].


=== Miscellaneous properties ===
In the 360b val, 360edo's fifth is the same as 12edo. Coincidentally, the difference between a just fifth and a 12edo one is known as the grad, being a variant of translation of "degree", and 1/360th of a circle is a degree.
In the 360b val, 360edo's fifth is the same as 12edo. Coincidentally, the difference between a just fifth and a 12edo one is known as the grad, being a variant of translation of "degree", and 1/360th of a circle is a degree.


Eliora proposes a 7-limit reenactment temperament for 360edo, defined as 188 & 360 and named after the YouTubers cs188 and radicalfaith360. It tempers out 2097152/2083725 and {{Monzo|0, -19, -10, 19}}.
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.
 
==== Proposed notation ====
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]].


== Rank two temperaments by generator ==
== Rank two temperaments by generator ==
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