User:Contribution/Exploring Selected Modes in 12-EDO: Difference between revisions
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12edo remains consistent within the 9-odd-limit. Therefore, it's worthwhile to explore ratios tempered out in the 7-limit, particularly those with simple factorizations that facilitate quick harmonic operations. | 12edo remains consistent within the 9-odd-limit. Therefore, it's worthwhile to explore ratios tempered out in the 7-limit, particularly those with simple factorizations that facilitate quick harmonic operations. | ||
{| class="wikitable center-all left-2 right-3 right-5 left-6" | {| class="wikitable center-all left-2 right-3 right-5 left-6" | ||
|+style=white-space:nowrap| 7-limit commas tempered out in 12-tet with Benedetti height < | |+style=white-space:nowrap| 7-limit commas tempered out in 12-tet with Benedetti height < 10<sup>6</sup> | ||
! Ratio | ! Ratio | ||
! Factorization | ! Factorization | ||
| Line 187: | Line 187: | ||
| 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup> | | 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup> | ||
| [[245/256]] | | [[245/256]] | ||
|- | |||
| [[360/343]] | |||
| 2<sup>3</sup> • 3<sup>2</sup> • 5<sup>1</sup> • 7<sup>-3</sup> | |||
| 83.746 | |||
| 7 | |||
| -83.746 | |||
| 2<sup>-3</sup> • 3<sup>-2</sup> • 5<sup>-1</sup> • 7<sup>3</sup> | |||
| [[343/360]] | |||
|- | |||
| [[405/392]] | |||
| 2<sup>-3</sup> • 3<sup>4</sup> • 5<sup>1</sup> • 7<sup>-2</sup> | |||
| 56.482 | |||
| 7 | |||
| -56.482 | |||
| 2<sup>3</sup> • 3<sup>-4</sup> • 5<sup>-1</sup> • 7<sup>2</sup> | |||
| [[392/405]] | |||
|- | |||
| [[729/686]] | |||
| 2<sup>-1</sup> • 3<sup>6</sup> • 7<sup>-3</sup> | |||
| 105.252 | |||
| 7 | |||
| -105.252 | |||
| 2<sup>1</sup> • 3<sup>-6</sup> • 7<sup>3</sup> | |||
| [[686/729]] | |||
|- | |||
| [[729/700]] | |||
| 2<sup>-2</sup> • 3<sup>6</sup> • 5<sup>-2</sup> • 7<sup>-1</sup> | |||
| 70.277 | |||
| 7 | |||
| -70.277 | |||
| 2<sup>2</sup> • 3<sup>-6</sup> • 5<sup>2</sup> • 7<sup>1</sup> | |||
| [[700/729]] | |||
|} | |} | ||