User:BudjarnLambeth/Substitute harmonic: Difference between revisions
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== Temperaments using substitute harmonics == | == Temperaments using substitute harmonics == | ||
== See also == | ===Daggerminished=== | ||
* [[Dual-fifth temperaments]] | Vaguely similar melodic shape to [[Diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | ||
* [[List of octave-reduced harmonics]] | |||
* [[Naughty and nice harmonics]] | |||
Subgroup | |||
2.113.161.177.193 | |||
Equal Temperament Mappings | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!113 | |||
!161 | |||
!177 | |||
!193 | |||
! | |||
|- | |||
|[ ⟨ | |||
|8 | |||
|55 | |||
|59 | |||
|60 | |||
|61 | |||
|] | |||
|- | |||
|⟨ | |||
|12 | |||
|82 | |||
|88 | |||
|90 | |||
|91 | |||
|] ⟩ | |||
|} | |||
Reduced Mapping | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!113 | |||
!161 | |||
!177 | |||
!193 | |||
! | |||
|- | |||
|[ ⟨ | |||
|4 | |||
|28 | |||
|30 | |||
|30 | |||
|31 | |||
|] | |||
|- | |||
|⟨ | |||
|0 | |||
| -1 | |||
| -1 | |||
|0 | |||
| -1 | |||
|] ⟩ | |||
|} | |||
POTE Generator Tunings (cents) | |||
⟨300.0000, 185.4640] | |||
POTE Step Tunings (cents) | |||
⟨43.60795, 70.92803] | |||
POTE Tuning Map (cents) | |||
⟨1200.000, 8214.536, 8814.536, 9000.000, 9114.536] | |||
POTE Mistunings (cents) | |||
⟨0.000, 30.321, 17.436, 38.873, 3.588] | |||
Unison Vectors | |||
* [7, -1, 1, -1, 0⟩ (20608:20001) | |||
* [-1, -2, 2, 0, 0⟩ (25921:25538) | |||
* [8, 1, -1, -1, 0⟩ (28928:28497) | |||
* [15, 0, 0, -2, 0⟩ (32768:31329) | |||
* [-1, -1, -1, 0, 2⟩ (37249:36386) | |||
* [6, -2, 0, -1, 2⟩ (2383936:2260113) | |||
===Pajaraxe=== | |||
Identical melodic shape to [[Pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | |||
Subgroup | |||
2.113.161.177.193 | |||
Equal Temperament Mappings | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!113 | |||
!161 | |||
!177 | |||
!193 | |||
! | |||
|- | |||
|[ ⟨ | |||
|22 | |||
|150 | |||
|161 | |||
|164 | |||
|167 | |||
|] | |||
|- | |||
|⟨ | |||
|12 | |||
|82 | |||
|88 | |||
|90 | |||
|91 | |||
|] ⟩ | |||
|} | |||
Reduced Mapping | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!113 | |||
!161 | |||
!177 | |||
!193 | |||
! | |||
|- | |||
|[ ⟨ | |||
|2 | |||
|14 | |||
|15 | |||
|16 | |||
|15 | |||
|] | |||
|- | |||
|⟨ | |||
|0 | |||
| -2 | |||
| -2 | |||
| -6 | |||
|1 | |||
|] ⟩ | |||
|} | |||
POTE Generator Tunings (cents) | |||
⟨600.0000, 106.8797] | |||
POTE Step Tunings (cents) | |||
⟨41.27832, 24.32309] | |||
POTE Tuning Map (cents) | |||
⟨1200.000, 8186.241, 8786.241, 8958.722, 9106.880] | |||
POTE Mistunings (cents) | |||
⟨0.000, 2.026, -10.860, -2.405, -4.069] | |||
Unison Vectors | |||
* [-1, -2, 2, 0, 0⟩ (25921:25538) | |||
* [13, -3, 0, 1, 0⟩ (1449984:1442897) | |||
* [-14, 1, 2, -1, 0⟩ (2929073:2899968) | |||
* [-22, 1, 0, 0, 2⟩ (4209137:4194304) | |||
* [-9, -2, 0, 1, 2⟩ (6593073:6537728) | |||
* [8, 0, 2, -1, -2⟩ (6635776:6593073) | |||
==See also== | |||
*[[Dual-fifth temperaments]] | |||
*[[List of octave-reduced harmonics]] | |||
*[[Naughty and nice harmonics]] | |||
[[Category:Harmonic series]] | [[Category:Harmonic series]] | ||