EDO

2025-12-13T20:09:04Z

CellularAutomaton: improved the description of 17edo

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==

{| class="wikitable"
|+ 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¢
!Fifth
!Example basic (in 2...23) and [[erac]] subgroups
|
|-
|rowspan=2 | 1
|rowspan=2 | Equivalent to the 2-limit.
|rowspan=2 | 1200
| rowspan="2" |1200
|2
|
|-
|2
|
|-
|rowspan=2 | 2
|rowspan=2 | Just a 12edo tritone.
|rowspan=2 | 600, 1200
| rowspan="2" |600
|2.11.23
|-
|2.<3.>>5.>>7
|
|-
|3
|A 12edo augmented triad.
|400, 800, 1200
|800
|2.5.13
|
|-
|4
|A diminished tetrad.
|300, 600, 900, 1200
|600
|2.19.23
|
|-
| class="thl" | 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
|800
|2.5.7.23
|2.9.>5.>>7
|-
| class="thl" | 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.<>3.<>5.<>7.<>11.<>13
|-
| 9 || The first edo to support the [[antidiatonic]] scale and temperaments like [[Mabilic|Semabila]], loosely resembling the pelog scale. It contains approximations to many [[Prime limit|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
|2.9.7.11.15
|
|-
| class="thl" | 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
|-
|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
|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
|2.3.13||
|-
| class="thl" | 15 || The basic tuning of Zarlino's [[Diatonic|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
|2.5.7.13.19
|
|-
| class="thl" |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 diatonic scale. Noted for its melodically tense third-tone, subminor chords, and approximation to the 13th harmonic.
|{{First 12 edo intervals|edo=17}}
|705.9
|2.3.13.19.23
|
|-
|...
|...
|
|
|
|
|-
| class="thl" |19
|A simple tuning of meantone, with a very accurate 6/5 and a reasonably good 5/4 and 9/7. Supports semaphore temperament.
|{{First 12 edo intervals|edo=19}}
|694.7
|2.3.5.23
|
|-
| ... || ... || ...
|
| || ...
|-
| class="thl" | 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
|-
|...
|...
|
|
|
|
|-
|24
|Regular old quarter-tones. Good at representing neutral intervals like 11/9, and tempers artoneutral and tendoneutral thirds to the same interval.
|{{First 12 edo intervals|edo=24}}
|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.
|{{First 12 edo intervals|edo=25}}
|720
|2.5.7.19
|
|-
|26
|A simple tuning of Flattone. Has an absurdly accurate 7/4.
|{{First 12 edo intervals|edo=26}}
|692.7
|2.3.7.11.13
|
|-
|27
|A good tuning for [[Archy]] and [[Sensi]]. It has 3/2 at 16 steps.
|{{First 12 edo intervals|edo=27}}
|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.
|{{First 12 edo intervals|edo=29}}
|703.4
|2.3.19.23
|
|-
| ... || ... || ...
|
| || ...
|-
| class="thl" | 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
|}

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EDO