720edo: Difference between revisions
Rework on theory; clarify the title row of the rank-2 temp table |
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== Theory == | == Theory == | ||
720edo is only [[consistent]] to the [[5-odd-limit]], but it has a reasonable approximation of the full 17-limit using the [[patent val]]. It tempers out the [[schisma]] in the 5-limit. In the 11-limit, it is a tuning for the [[Schismatic family #Octant|octant]] temperament. | 720edo is only [[consistent]] to the [[5-odd-limit]], but it has a reasonable approximation of the full 17-limit using the [[patent val]]. It [[tempering out|tempers out]] the [[schisma]] in the 5-limit. In the 11-limit, it is a tuning for the [[Schismatic family #Octant|octant]] temperament. | ||
The patent val can also be thought of as a 2.3.17.23.31.43 subgroup-suited val, because these harmonics have error of less than 1 standard deviaiton away from step. In it, it supports the 195 & 720 temperament, period 15 with comma basis 1377/1376, 19683/19652, 67797/67712, 177147/176824. | The patent val can also be thought of as a 2.3.17.23.31.43 [[subgroup]]-suited val, because these harmonics have error of less than 1 standard deviaiton away from step. In it, it supports the 195 & 720 temperament, period 15 with comma basis 1377/1376, 19683/19652, 67797/67712, 177147/176824. | ||
=== Prime harmonics === | === Prime harmonics === | ||
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! Generator* | ! Generator* | ||
! Cents* | ! Cents* | ||
! Associated<br>Ratio | ! Associated<br>Ratio* | ||
! Temperaments | ! Temperaments | ||
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