42edo: Difference between revisions
ArrowHead294 (talk | contribs) mNo edit summary |
ArrowHead294 (talk | contribs) mNo edit summary |
||
| Line 15: | Line 15: | ||
== JI approximation == | == JI approximation == | ||
{{Q-odd-limit intervals}} | {{Q-odd-limit intervals}} | ||
== Regular temperament properties == | |||
{| class="wikitable center-4 center-5 center-6" | |||
|- | |||
! rowspan="2" | [[Subgroup]] | |||
! rowspan="2" | [[Comma list]] | |||
! rowspan="2" | [[Mapping]] | |||
! rowspan="2" | Optimal<br>8ve stretch (¢) | |||
! colspan="2" | Tuning error | |||
|- | |||
! [[TE error|Absolute]] (¢) | |||
! [[TE simple badness|Relative]] (%) | |||
|- | |||
| 2.3 | |||
| {{monzo| 67 -42 }} | |||
| {{mapping| 42 67 }} | |||
| −3.89 | |||
| 3.88 | |||
| 13.57 | |||
|- | |||
| 2.3.5 | |||
| 128/125, 5000000/4782969 | |||
| {{mapping| 42 67 98 }} | |||
| −4.55 | |||
| 3.30 | |||
| 11.55 | |||
|- | |||
| 2.3.5.7 | |||
| 64/63, 126/125, 6860/6561 | |||
| {{mapping| 22 35 51 62 }} | |||
| −3.65 | |||
| 3.26 | |||
| 11.42 | |||
|} | |||
=== Octave stretch === | === Octave stretch === | ||
42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[ | 42edo’s inaccurate 3rd and 5th harmonics can be greatly improved through [[stretched and compressed tuning|stretching or compressing]] octaves. 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 tunings of 42edo: | The following table compares three stretched tunings of 42edo: | ||
| Line 341: | Line 375: | ||
Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chords and Chord Progressions]]. | Chords can be named using ups and downs as C upminor, D downmajor seven, etc. See [[Ups and Downs Notation #Chords and Chord Progressions]]. | ||
== Notation == | == Notation == | ||