360edo

← 359edo

360edo

361edo →

Prime factorization	22 × 32 × 5
Step size	3.33333 ¢
Fifth	211\360 (703.333 ¢)
Semitones (A1:m2)	37:25 (123.3 ¢ : 83.33 ¢)
Dual sharp fifth	211\360 (703.333 ¢)
Dual flat fifth	210\360 (700 ¢) (→ 7\12)
Dual major 2nd	61\360 (203.333 ¢)
Consistency limit	7
Distinct consistency limit	7

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 about 3.33 ¢ each, a step size known as the Dröbisch angle.

360edo is used in the 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

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.

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.

Its 5-limit patent val supports 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 linus comma, meaning 15/14 corresponds to 1/10th of the octave, 36 steps.

Much better is 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

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 [0, -19, -10, 19⟩.

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

Periods per octave	Generator (reduced)	Cents (reduced)	Associated ratio	Temperaments
1	119\360	396.67	44/35	Squarschmidt
2	53\360	176.67		Quatracot
3	211\360 (91\360)	703.33 (303.33)	3/2	Misty
4	23\360	76.67		Reenactment
9	211\360 (11\360)	703.33 (36.67)	3/2	Trimisty
20	211\360 (13\360)	703.33 (43.33)	3/2 (45/44)	Degrees

Table of intervals

Table of selected intervals

Step	Name	Calendar notation (if unison is Jan 1)	Ratio
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	Dodecaphonic perfect fifth	August 1	442/295
211	Just perfect fifth	August 2	3/2
240		September 1
270		October 1
291	Harmonic seventh	October 21
300		November 1
330		December 1
360	Octave	January 1

Music

• Idyllic Tribe by Eliora