43edo: Difference between revisions
Contribution (talk | contribs) No edit summary |
ArrowHead294 (talk | contribs) m Formatting + notes |
||
| Line 463: | Line 463: | ||
|- | |- | ||
! [[Harmonic limit|Prime<br>limit]] | ! [[Harmonic limit|Prime<br>limit]] | ||
! [[Ratio]]<ref group="note"> | ! [[Ratio]]<ref group="note">{{rd}}</ref> | ||
! [[Monzo]] | ! [[Monzo]] | ||
! [[Cent]]s | ! [[Cent]]s | ||
| Line 866: | Line 866: | ||
== Zeta properties == | == Zeta properties == | ||
===Zeta peak index=== | === Zeta peak index === | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
!ZPI | ! colspan="3" | Tuning | ||
!Steps per octave | ! colspan="3" | Strength | ||
!Step size (cents) | ! colspan="2" | Closest EDO | ||
!Height | ! colspan="2" | Integer limit | ||
!Integral | |- | ||
! ZPI | |||
! Steps per octave | |||
! Step size (cents) | |||
! Height | |||
! Integral | |||
! Gap | ! Gap | ||
!EDO | ! EDO | ||
!Octave (cents) | ! Octave (cents) | ||
!Consistent | ! Consistent | ||
!Distinct | ! Distinct | ||
|- | |- | ||
|[[196zpi]] | | [[196zpi]] | ||
|43.0264994477693 | | 43.0264994477693 | ||
|27.8897892090130 | | 27.8897892090130 | ||
|6.166118 | | 6.166118 | ||
|1.035628 | | 1.035628 | ||
|15.545919 | | 15.545919 | ||
|43edo | | 43edo | ||
| 1199.26093598756 | | 1199.26093598756 | ||
| 8 | | 8 | ||
| 8 | | 8 | ||
|} | |} | ||
== Detemperaments == | == Detemperaments == | ||
=== Ringer 43 === | === Ringer 43 === | ||
| Line 906: | Line 908: | ||
== Scales == | == Scales == | ||
=== Harmonic scales === | === Harmonic scales === | ||
43edo represents the first 16 overtones of the [[harmonic series]] well (written as a ratio of 8:9:10:11:12:13:14:15:16 in [[just intonation]]) with degrees 0, 7, 14, 20, 25, 30, 35, 39, and 43, and scale steps of 7, 7, 6, 5, 5, 5, 4, and 4. | 43edo represents the first 16 overtones of the [[harmonic series]] well (written as a ratio of 8:9:10:11:12:13:14:15:16 in [[just intonation]]) with degrees 0, 7, 14, 20, 25, 30, 35, 39, and 43, and scale steps of 7, 7, 6, 5, 5, 5, 4, and 4. | ||
| Line 1,048: | Line 1,049: | ||
A possible isomorphic keyboard layout for 43edo: | A possible isomorphic keyboard layout for 43edo: | ||
[[File:Fifth Comma Meantone Keyboard Layout.svg|800px|none|thumb]] | [[File:Fifth Comma Meantone Keyboard Layout.svg|800px|none|thumb]] | ||
== Notes == | |||
<references group="note" /> | |||
== References == | == References == | ||