360edo
| ← 359edo | 360edo | 361edo → |
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
Script error: No such module "primes_in_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. 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 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.
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.
Table of 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 |