EDO

An equal division of the octave (EDO or edo, /ˈidoʊ/ EE-doh) is a tuning system constructed by dividing the octave into a number of equal steps.

The dominant modern tuning system may be called 12edo (12-EDO) because it divides the octave into 12 semitones that are all the same size. It may also be called 12-tone equal temperament or 12-TET, but this is discouraged because it does not specify which interval is being equally divided.

An edo with the same number of notes as a certain MOS will have crudely similar properties.

List of Edos

Very incomplete edo table. Popular edos are highlighted. Temperaments are capitalized and can be found in the List of regular temperaments.

Edo	Description	First twelve steps, from 0¢	Basic subgroup (in 2...23)	Possible erac subgroup
1	Equivalent to the 2-limit.	1200	2.17
2	Just a tritone.	600, 1200	2.11.23
3	An augmented triad.	400, 800, 1200	2.5.13
4	A diminished tetrad.	300, 600, 900, 1200	2.19.23
5	Collapsed diatonic, and the smallest edo to have strong melodic properties. Good approximation of 2.3.7 for its size.	240, 480, 720, 960, 1200	2.3.7	2.>>3.<7
6	Subset of 12edo. Good approximation of 2.9.5.7 for its size, such as in Didacus temperament.	200, 400, 600, 800, 1000, 1200	2.5.7.23	2.9.>5.>>7
7	Equalized diatonic, and the first edo to (very vaguely) support diatonic functional harmony.	171.4, 342.9, 514.3, 685.7, 857.1, 1028.6, 1200	2.3.5.13	2.<3.<<5
8	Minimal version of Ammonite temperament.	150, 300, 450, 600, 750, 900, 1050, 1200	2.19.23	2.<>3.<>5.<>7.<>11.<>13
9	The first edo to support the antidiatonic scale and temperaments like Semabila, loosely resembling the pelog scale. It contains approximations to many 7-limit intervals, but not the 7/4 itself (see erac subgroup).	133.3, 266.7, 400, 533.3, 666.7, 800, 933.3, 1066.7, 1200	2.5.11	2.<<3.>5.<<7
10	The doubling of 5edo, useful as an interval categorization archetype and as a melodic system in its own right, supporting mosh.	120, 240, 360, 480, 600, 720, 840, 960, 1080, 1200	2.3.5.7.13	2.>>3.<7.13
12	The basic tuning of diatonic, and consequently the most widespread EDO. Supports the 5-limit decently well.	100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, 1100, 1200	2.3.5.17.19	2.3.>5.>>7
13	Basic oneirotonic.	92.3, 184.6, 276.9, 369.2, 461.5, 553.8, 646.2, 738.5, 830.8, 923.1, 1015.4, 1107.7	2.5.11.13.17
14	Basic semiquartal.	85.7, 171.4, 257.1, 342.9, 428.6, 514.3, 600.0, 685.7, 771.4, 857.1, 942.9, 1028.6	2.3.13
15	The basic tuning of Zarlino's intense diatonic, a subset of Blackwood which is itself a degenerate tuning of blackdye. Supporting porcupine temperament and dubitably the 11-limit.	80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960	2.3.5.7.11.23
...	...	...		...
22	Represents the 7-limit and 11-limit decently well, serving as the primary tuning of Pajara and also a good Superpyth tuning, especially for Archy.	54.5, 109.1, 163.6, 218.2, 272.7, 327.3, 381.8, 436.4, 490.9, 545.5, 600, 654.5	2.3.5.7.11.17	2.3.5.>7.11
...	...	...		...
31	The definitive Septimal Meantone tuning.	38.7, 77.4, 116.1, 154.8, 193.5, 232.3, 271.0, 309.7, 348.4, 387.1, 425.8, 464.5	2.3.5.7.11.23	2.3.5.7