42edo: Difference between revisions
m →Octave stretch: Split into two tables |
|||
| Line 16: | Line 16: | ||
42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[octave stretching]] or [[octave shrinking]]. Both approaches work about equally well but in opposite directions, giving two quite different flavors of tuning to play with. | 42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[octave stretching]] or [[octave shrinking]]. Both approaches work about equally well but in opposite directions, giving two quite different flavors of tuning to play with. | ||
The following table compares three stretched | The following table compares three stretched tunings of 42edo: | ||
{| class="wikitable" | {| class="wikitable" | ||
| Line 24: | Line 24: | ||
! [[1ed28.7c|APS720jot]] | ! [[1ed28.7c|APS720jot]] | ||
! [[zpi|189zpi]] | ! [[zpi|189zpi]] | ||
! [[42edo]] | |||
|- | |||
! Steps / octave | |||
| ~41.77 | |||
| ~41.81 | |||
| ~41.83 | |||
| 42.00 | |||
|- | |||
! Approximation <br>of harmonics | |||
| great: 5 <br>good: 2, 3, 7 <br>okay: <br>bad: 11, 13 | |||
| great: 5 <br>good: 2, 3 <br>okay: 7, 11, 13 <br>bad: | |||
| great: 5 <br>good: 2, 13 <br>okay: 3, 11 <br>bad: 7 | |||
| great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13 | |||
|- | |||
| colspan="5" | <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small> | |||
|} | |||
The following table compares three compressed tunings of 42edo: | |||
{| class="wikitable" | |||
|+ | |||
!Tuning | |||
! [[42edo]] | ! [[42edo]] | ||
! [[1ed28.5c|APS715jot]] | ! [[1ed28.5c|APS715jot]] | ||
| Line 30: | Line 52: | ||
|- | |- | ||
! Steps / octave | ! Steps / octave | ||
| 42.00 | | 42.00 | ||
| ~42.10 | | ~42.10 | ||
| Line 39: | Line 58: | ||
|- | |- | ||
! Approximation <br>of harmonics | ! Approximation <br>of harmonics | ||
| great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13 | | great: 2, 7 <br>good: <br>okay: 11 <br>bad: 3, 5, 13 | ||
| great: 2 <br>good: 3, 5, 7, 13 <br>okay: 11 <br>bad: | | great: 2 <br>good: 3, 5, 7, 13 <br>okay: 11 <br>bad: | ||
| Line 47: | Line 63: | ||
| great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7 | | great: 3, 5, 11 <br>good: 2 <br>okay: 13 <br>bad: 7 | ||
|- | |- | ||
| colspan=" | | colspan="5" | <small><div style="text-align: center;">''“great” = 0-12.5% relative error • “good” = 12.5-27.5% • “okay” = 27.5-40% • “bad” = 40-50%''</div></small> | ||
|} | |} | ||