EDO: Difference between revisions

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!Description
!Description
!First twelve steps, from 0¢  
!First twelve steps, from 0¢  
!Fifth
!Example basic (in 2...23) and [[erac]] subgroups
!Example basic (in 2...23) and [[erac]] subgroups
|
|-
|-
|rowspan=2 | 1
|rowspan=2 | 1
|rowspan=2 | Equivalent to the 2-limit.
|rowspan=2 | Equivalent to the 2-limit.
|rowspan=2 | 1200
|rowspan=2 | 1200
| rowspan="2" |1200
|2
|2
|
|-
|-
|2
|2
|
|-
|-
|rowspan=2 | 2
|rowspan=2 | 2
|rowspan=2 | Just a 12edo tritone.
|rowspan=2 | Just a 12edo tritone.
|rowspan=2 | 600, 1200
|rowspan=2 | 600, 1200
| rowspan="2" |600
|2.11.23
|2.11.23
|-
|-
|2.<3.>>5.>>7
|2.<3.>>5.>>7
|
|-
|-
|3
|3
|A 12edo augmented triad.
|A 12edo augmented triad.
|400, 800, 1200
|400, 800, 1200
|800
|2.5.13
|2.5.13
|
|
Line 38: Line 46:
|A diminished tetrad.
|A diminished tetrad.
|300, 600, 900, 1200
|300, 600, 900, 1200
|600
|2.19.23
|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
| 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
|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
| 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
|2.5.7.23
|2.9.>5.>>7
|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
| 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
|2.3.5.13
|2.<3.<<5
|2.<3.<<5
Line 56: Line 68:
|Minimal version of Ammonite temperament.
|Minimal version of Ammonite temperament.
|150, 300, 450, 600, 750, 900, 1050, 1200
|150, 300, 450, 600, 750, 900, 1050, 1200
|750
|2.19.23
|2.19.23
|2.<>3.<>5.<>7.<>11.<>13
|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
| 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
|2.5.11
|2.<<3.>5.<<7
|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
| 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
|2.3.5.7.13
|2.>>3.<7.13
|2.>>3.<7.13
|-
|-
| 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
| 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
|2.3.5.17.19
|2.3.>5.>>7
|2.3.>5.>>7
Line 74: Line 90:
|Basic [[oneirotonic]].
|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
|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
|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  
| 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||
|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
| 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
|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
|
|-
|17
|Weird sharp neogothic edo. Lacks 5-limit or 7-limit intervals, but functions as a melodically-oriented tuning of diatonic.
|{{First 12 edo intervals|edo=17}}
|705.9
|2.3.13.19.23
|
|-
|...
|...
|
|
|
|
|-
|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
| 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
|2.3.5.7.11.17
|2.3.5.>7.11
|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  
| 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
|2.3.5.7.11.23|| 2.3.5.7
|}
|}

Revision as of 23:31, 12 December 2025

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¢ 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
3 A 12edo augmented triad. 400, 800, 1200 800 2.5.13
4 A diminished tetrad. 300, 600, 900, 1200 600 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 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
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 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
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
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 2.5.7.13.19
17 Weird sharp neogothic edo. Lacks 5-limit or 7-limit intervals, but functions as a melodically-oriented tuning of diatonic. 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
... ...
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
... ...
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
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