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 (¢)	Fifth (¢)	Example basic (in 2...23) and erac subgroups
1	Equivalent to the 2-limit.	1200	1200	2
				2
2	Just a 12edo tritone.	600, 1200	600	2.11.23
				2.<3.>>5.>>7 (100)
3	A 12edo augmented triad.	400, 800, 1200	800	2.5.13
				2.>3.5
4	A diminished tetrad.	300, 600, 900, 1200	600	2.19.23
				2.<3.<5.<7
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	720	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	600, 800	2.9.5.7.23	2.x3.5.7
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	685.7	2.3.5.13	2.<3.<<5
8	Minimal version of Ammonite temperament.	150, 300, 450, 600, 750, 900, 1050, 1200	750	2.19.23	2.x3.x5.x7.x11.x13
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	666.7	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	720	2.3.5.7.13	2.>>3.<7.13
11	Basic smitonic and checkertonic.	109.1, 218.2, 327.3, 436.4, 545.5, 654.5, 763.6, 872.7, 981.8, 1090.9	654.5, 763.6	2.9.7.11.15
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	700	2.3.5.17.19	2.3.>5.>>7.17.19
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	646.2, 738.5	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	685.7	2.3.7.13
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	720	2.3.5.7.11.23
16	The most popular antidiatonic edo, which supports Trismegistus and Mavila.	75, 150, 225, 300, 375, 450, 525, 600, 675, 750, 825, 900	675, 750	2.5.7.13.19
17	Smallest non-12 edo whose fifth is of comparable quality to 12edo's; thus, unless you're satisfied with 7edo, the first xen edo that also allows use of the MOS diatonic scale. Noted for its melodically tense third-tone, neogothic minor chords, and approximation to the 13th harmonic.	70.6, 141.2, 211.8, 282.4, 352.9, 423.5, 494.1, 564.7, 635.3, 705.9, 776.5, 847.1	705.9	2.3.13.19.23
18	Straddle-3 version of 12edo	66.6, 133.3, 200, 266.6, 333.3, 400, 466.6, 533.3, 600, 666.6, 733.3, 800	666.6, 733.3	2.5.7.13	2.xx3.>5.>>7
19	A simple tuning of Meantone, with a very accurate 6/5 and a reasonably good 5/4 and 9/7. Supports Semaphore temperament.	63.2, 126.3, 189.5, 252.6, 315.8, 378.9, 442.1, 505.3, 568.4, 631.6, 694.7, 757.9	694.7	2.3.5.23
...	...	...			...
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	709.1	2.3.5.7.11.17	2.3.5.>7.11
23	The largest edo without a diatonic, 5edo, or 7edo fifth.	52.2, 104.3, 156.5, 208.7, 260.9, 313, 365.2, 417.4, 469.6, 521.7, 573.9, 626.1	678.3	2.<>3.<>5.<>7.<>11.13
24	Regular old quarter-tones. Good at representing neutral intervals like 11/9, and tempers artoneutral and tendoneutral thirds to the same interval.	50, 100, 150, 200, 250, 300, 350, 400, 450, 500, 550, 600	700	2.3.11.13.17.19
25	A straddle-fifth tuning with a 672c fifth that supports Mavila, or that can be used as the generator for Trismegistus with the more accurate 720c fifth. Also supports Blackwood and Didacus.	48, 96, 144, 192, 240, 288, 336, 384, 432, 480, 528, 576	720	2.5.7.19
26	A simple tuning of Flattone. Has an absurdly accurate 7/4.	46.2, 92.3, 138.5, 184.6, 230.8, 276.9, 323.1, 369.2, 415.4, 461.5, 507.7, 553.8	692.7	2.3.7.11.13
27	A good tuning for Archy and Sensi. It has 3/2 at 16 steps.	44.4, 88.9, 133.3, 177.8, 222.2, 266.7, 311.1, 355.6, 400, 444.4, 488.9, 533.3	711.1	2.3.7.13.23
...	...
29	Another neogothic tuning, and the first edo to have a more accurate perfect fifth than 12edo, so it also functions as an approximation of Pythagorean tuning, and as is typical with small Pythagorean edos, Garibaldi. It has 4/3 at 12 steps.	41.4, 82.8, 124.1, 165.5, 206.9, 248.3, 289.7, 331, 372.4, 413.8, 455.2, 496.6	703.4	2.3.19.23
...	...	...			...
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	696.8	2.3.5.7.11.23	2.3.5.7
...	...	...			...
34	The definitive non-Meantone medium-sized 5-limit edo.	35.3, 70.6, 105.9, 141.2, 176.5, 211.8, 247.1, 282.4, 317.6, 352.9, 388.2, 423.5	705.9	2.3.5.13.23	2.3.5.x7.13.x19.23