User:BudjarnLambeth/Substitute harmonic: Difference between revisions
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== Temperaments using substitute harmonics == | == Temperaments using substitute harmonics == | ||
===Daggerminished=== | ===...with mostly sharp substitutes=== | ||
Name these after sharp weapons. If they closely resemble another temperament, reference that temperament in the name. | |||
====Daggerminished==== | |||
Same melodic shape as [[diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | Same melodic shape as [[diminished]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | ||
| Line 119: | Line 122: | ||
|88 | |88 | ||
|90 | |90 | ||
|91 | | 91 | ||
|] ⟩ | |] ⟩ | ||
|} | |} | ||
| Line 138: | Line 141: | ||
|28 | |28 | ||
|30 | |30 | ||
|30 | | 30 | ||
|31 | |31 | ||
|] | |] | ||
|- | |- | ||
|⟨ | |⟨ | ||
|0 | | 0 | ||
| -1 | | -1 | ||
| -1 | | -1 | ||
| Line 174: | Line 177: | ||
Unison Vectors | Unison Vectors | ||
* [7, -1, 1, -1, 0⟩ (20608:20001) | *[7, -1, 1, -1, 0⟩ (20608:20001) | ||
* [-1, -2, 2, 0, 0⟩ (25921:25538) | *[-1, -2, 2, 0, 0⟩ (25921:25538) | ||
* [8, 1, -1, -1, 0⟩ (28928:28497) | *[8, 1, -1, -1, 0⟩ (28928:28497) | ||
* [15, 0, 0, -2, 0⟩ (32768:31329) | *[15, 0, 0, -2, 0⟩ (32768:31329) | ||
* [-1, -1, -1, 0, 2⟩ (37249:36386) | *[-1, -1, -1, 0, 2⟩ (37249:36386) | ||
* [6, -2, 0, -1, 2⟩ (2383936:2260113) | *[6, -2, 0, -1, 2⟩ (2383936:2260113) | ||
===Pajaraxe=== | ====Pajaraxe ==== | ||
Same melodic shape as [[pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | Same melodic shape as [[pajara]]. Uses sharper substitutes for prime 3, 5, 7 and 11. | ||
| Line 234: | Line 237: | ||
|16 | |16 | ||
|15 | |15 | ||
|] | | ] | ||
|- | |- | ||
|⟨ | |⟨ | ||
| Line 268: | Line 271: | ||
Unison Vectors | Unison Vectors | ||
* [-1, -2, 2, 0, 0⟩ (25921:25538) | *[-1, -2, 2, 0, 0⟩ (25921:25538) | ||
* [13, -3, 0, 1, 0⟩ (1449984:1442897) | *[13, -3, 0, 1, 0⟩ (1449984:1442897) | ||
* [-14, 1, 2, -1, 0⟩ (2929073:2899968) | *[-14, 1, 2, -1, 0⟩ (2929073:2899968) | ||
* [-22, 1, 0, 0, 2⟩ (4209137:4194304) | *[-22, 1, 0, 0, 2⟩ (4209137:4194304) | ||
* [-9, -2, 0, 1, 2⟩ (6593073:6537728) | *[-9, -2, 0, 1, 2⟩ (6593073:6537728) | ||
* [8, 0, 2, -1, -2⟩ (6635776:6593073) | *[8, 0, 2, -1, -2⟩ (6635776:6593073) | ||
===...with mostly flat substitutes=== | |||
Name these after flat regions like deserts. If they closely resemble another temperament, reference that temperament in the name. | |||
====Sahara==== | |||
Melodic shape does not resemble any major temperament. Uses flatter substitutes for prime 3, 5, 7 and 11. | |||
Subgroup | |||
2.111.159.175.191 | |||
Equal Temperament Mappings | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!111 | |||
!159 | |||
!175 | |||
!191 | |||
! | |||
|- | |||
|[ ⟨ | |||
|9 | |||
|61 | |||
|66 | |||
|67 | |||
|68 | |||
|] | |||
|- | |||
|⟨ | |||
|19 | |||
|129 | |||
|139 | |||
|142 | |||
|144 | |||
|] ⟩ | |||
|} | |||
Reduced Mapping | |||
{| class="wikitable" | |||
! | |||
!2 | |||
!111 | |||
!159 | |||
!175 | |||
!191 | |||
! | |||
|- | |||
|[ ⟨ | |||
|1 | |||
|7 | |||
|7 | |||
|8 | |||
|8 | |||
|] | |||
|- | |||
|⟨ | |||
|0 | |||
| -2 | |||
|3 | |||
| -5 | |||
| -4 | |||
|] ⟩ | |||
|} | |||
POTE Generator Tunings (cents) | |||
⟨1200.0000, 128.1188] | |||
POTE Step Tunings (cents) | |||
⟨34.25808, 46.93038] | |||
POTE Tuning Map (cents) | |||
⟨1200.000, 8143.762, 8784.357, 8959.406, 9087.525] | |||
POTE Mistunings (cents) | |||
⟨0.000, -9.537, 8.897, 17.952, -5.390] | |||
Unison Vectors | |||
* [-6, 2, 0, 0, -1⟩ (12321:12224) | |||
* [8, 1, -1, -1, 0⟩ (9472:9275) | |||
* [14, -1, -1, -1, 1⟩ (3129344:3088575) | |||
* [-7, 1, 0, -2, 2⟩ (4049391:3920000) | |||
* [2, 3, -1, -1, -1⟩ (1823508:1771525) | |||
* [-15, 0, 1, -1, 2⟩ (5800479:5734400) | |||
===...with an even mix of both=== | |||
Name these after dishes which involve mixing things (e.g. stirfry, salad). If they closely resemble another temperament, reference that temperament in the name. | |||
==See also== | ==See also== | ||