EDO: Difference between revisions
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| 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 | ||
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| 7 || The basic [[equiheptatonic]], and the first edo to (very vaguely) support diatonic functional harmony. || 171.4, 342.9, 514.3, 685.7, 857.1, 1028.6, 1200 | |style="background-color:#cb9" | 7 || The basic [[equiheptatonic]], and the first edo to (very vaguely) support diatonic functional harmony. || 171.4, 342.9, 514.3, 685.7, 857.1, 1028.6, 1200 | ||
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| 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. || 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. || 133.3, 266.7, 400, 533.3, 666.7, 800, 933.3, 1066.7, 1200 | ||
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| 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 | ||
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| 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 | |style="background-color:#cb9" | 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 | ||
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| 15 || The basic tuning of Zarlino's [[Diatonic|intense diatonic]], supporting porcupine temperament and dubitably the 11-limit. || 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960 | |style="background-color:#cb9" | 15 || The basic tuning of Zarlino's [[Diatonic|intense diatonic]], supporting porcupine temperament and dubitably the 11-limit. || 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960 | ||
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| 22 || Represents the 7-limit and 11-limit decently well, serving as the primary tuning of [[diaschismic|pajara]] and also a decent [[archy]] tuning. || 54.5, 109.1, 163.6, 218.2, 272.7, 327.3, 381.8, 436.4, 490.9, 545.5, 600, 654.5 | |style="background-color:#cb9" | 22 || Represents the 7-limit and 11-limit decently well, serving as the primary tuning of [[diaschismic|pajara]] and also a decent [[archy]] tuning. || 54.5, 109.1, 163.6, 218.2, 272.7, 327.3, 381.8, 436.4, 490.9, 545.5, 600, 654.5 | ||
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Revision as of 00:52, 11 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.
List of Edos
| Edo | Description | First twelve steps, from 0¢ | Possible erac subgroup |
|---|---|---|---|
| 5 | The basic equipentatonic, and the smallest edo to have strong melodic properties. Good approximation of 2.3.7 for its size. | 240, 480, 720, 960, 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 | |
| 7 | The basic equiheptatonic, and the first edo to (very vaguely) support diatonic functional harmony. | 171.4, 342.9, 514.3, 685.7, 857.1, 1028.6, 1200 | |
| 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. | 133.3, 266.7, 400, 533.3, 666.7, 800, 933.3, 1066.7, 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 | |
| 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 | |
| ... | ... | ... | ... |
| 15 | The basic tuning of Zarlino's intense diatonic, supporting porcupine temperament and dubitably the 11-limit. | 80, 160, 240, 320, 400, 480, 560, 640, 720, 800, 880, 960 | |
| ... | ... | ... | ... |
| 22 | Represents the 7-limit and 11-limit decently well, serving as the primary tuning of pajara and also a decent archy tuning. | 54.5, 109.1, 163.6, 218.2, 272.7, 327.3, 381.8, 436.4, 490.9, 545.5, 600, 654.5 | |
| ... | ... | ... | ... |
| 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 |
