User:BudjarnLambeth/12edo as a 2.3.5.17.19 tuning: Difference between revisions
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; Sometimes composite | ; Sometimes composite | ||
* dual = [[Dual-n|Dual-n subgroup]] | * dual = [[Dual-n|Dual-n subgroup]] | ||
* | * rel = Directional subgroup | ||
** ''Example: -30rel+0 includes all primes where -30%<relative error<+0%'' | |||
** ''Example: -40rel+10 includes all primes where -40%<relative error<+10%'' | |||
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# Do whichever of the following things results in the most simple consonances being available (use your own discretion to decide): | # Do whichever of the following things results in the most simple consonances being available (use your own discretion to decide): | ||
## Add the next 4-5 prime harmonics to be approximated within 15 cents | ## Add the next 4-5 prime harmonics to be approximated within 15 cents | ||
## Add the next 4-5 prime harmonics with relative error between -a% and +b% where (a+b)<60, make a and b anything you like that fits the rule, try to make them as small as possible while still including important intervals | |||
## Add the next 4-5 prime harmonics with relative error between - | |||
## Add the 4-5 smallest odd harmonics and/or [[taxicab distance|taxicab-2]] intervals to be approximated within 15 cents | ## Add the 4-5 smallest odd harmonics and/or [[taxicab distance|taxicab-2]] intervals to be approximated within 15 cents | ||
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* [[6edo]]: 2 • 9 • 5 (''comp'') | * [[6edo]]: 2 • 9 • 5 (''comp'') | ||
; 5 basis elements | ; 5 basis elements | ||
* [[7edo]]: 2 • 3 • 5 • 11 • 29 ('' | * [[7edo]]: 2 • 3 • 5 • 11 • 29 (''-30rel+0'') | ||
* [[8edo]]: 2 • <small><sup>5</sup>/<sub>3</sub></small> • <small><sup>11</sup>/<sub>3</sub></small> • <small><sup>13</sup>/<sub>5</sub></small> • 19 (''nth-b; 15th'') | * [[8edo]]: 2 • <small><sup>5</sup>/<sub>3</sub></small> • <small><sup>11</sup>/<sub>3</sub></small> • <small><sup>13</sup>/<sub>5</sub></small> • 19 (''nth-b; 15th'') | ||
* [[9edo]]: 2 • 5 • <small><sup>7</sup>/<sub>3</sub></small> • 11 • <small><sup>13</sup>/<sub>7</sub></small> (''nth-b; 21st'') | * [[9edo]]: 2 • 5 • <small><sup>7</sup>/<sub>3</sub></small> • 11 • <small><sup>13</sup>/<sub>7</sub></small> (''nth-b; 21st'') | ||
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; 6 basis elements | ; 6 basis elements | ||
* [[13edo]]: 2 • 9 • 5 • 21 • 11 • 13 (''comp'') | * [[13edo]]: 2 • 9 • 5 • 21 • 11 • 13 (''comp'') | ||
* [[14edo]]: 2 • 3 • <5 • 7 • 11 • 17 ('' | * [[14edo]]: 2 • 3 • <5 • 7 • 11 • 17 (''-55rel+0'') | ||
* [[15edo]]: 2 • 3 • 5 • 7 • 11 • 23 (''no-n'') | * [[15edo]]: 2 • 3 • 5 • 7 • 11 • 23 (''no-n'') | ||
* [[16edo]]: 2 • 3 • 5 • 7 • 11 • 13 ('' | * [[16edo]]: 2 • 3 • 5 • 7 • 11 • 13 (''-40rel+10'') | ||
* [[17edo]]: 2 • 3 • 5> • 7 • 11 • 13 ('' | * [[17edo]]: 2 • 3 • 5> • 7 • 11 • 13 (''-0rel+55'') | ||
* [[18edo]]: 2 • 3 • 5 • 7 • 13 • 17 ('' | * [[18edo]]: 2 • 3 • 5 • 7 • 13 • 17 (''-0rel+50'') | ||
* [[19edo]]: 2 • 3 • 5 • 7 • 11 • 13 (''lim'') | * [[19edo]]: 2 • 3 • 5 • 7 • 11 • 13 (''lim'') | ||