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User:BudjarnLambeth/Substitute harmonic: Difference between revisions

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Equal Temperament Mappings


Equal Temperament Mappings
2 113 161 177 193
{| class="wikitable"
[ ⟨ 8 55 59 60 61 ]
!
⟨ 12 82 88 90 91 ] ⟩
!2
!113
!161
!177
!193
!
|-
|[ ⟨
|8
|55
|59
|60
|61
|]
|-
|⟨
|12
|82
|88
|90
| 91
|] ⟩
|}




Reduced Mapping
Reduced Mapping
{| class="wikitable"
 
!
2 113 161 177 193
!2
[ ⟨ 4 28 30 30 31 ]
!113
⟨ 0 -1 -1 0 -1 ] ⟩
!161
!177
!193
!
|-
|[ ⟨
|4
|28
|30
| 30
|31
|]
|-
|⟨
| 0
| -1
| -1
|0
| -1
|] ⟩
|}




Line 183: Line 140:
*[-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 ====
Line 194: Line 152:


Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
 
!
2 113 161 177 193
!2
[ ⟨ 22 150 161 164 167 ]
!113
⟨ 12 82 88 90 91 ] ⟩
!161
!177
!193
!
|-
|[ ⟨
|22
|150
|161
|164
|167
|]
|-
|⟨
|12
|82
|88
|90
|91
|] ⟩
|}




Reduced Mapping
Reduced Mapping
{| class="wikitable"
 
!
2 113 161 177 193
!2
[ ⟨ 2 14 15 16 15 ]
!113
⟨ 0 -2 -2 -6 1 ] ⟩
!161
!177
!193
!
|-
|[ ⟨
|2
|14
|15
|16
|15
| ]
|-
|⟨
|0
| -2
| -2
| -6
|1
|] ⟩
|}




Line 848: Line 764:


====Sahara====
====Sahara====
Melodic shape does not closely resemble any major temperament. Uses flatter substitutes for prime 3, 5, 7 and 11.
Uses flatter substitutes for prime 3, 5, 7 and 11.




Line 857: Line 773:


Equal Temperament Mappings
Equal Temperament Mappings
{| class="wikitable"
 
!
2 111 159 175 191
!2
[ ⟨ 9 61 66 67 68 ]
!111
⟨ 19 129 139 142 144 ] ⟩
!159
!175
!191
!
|-
|[ ⟨
|9
|61
|66
|67
|68
|]
|-
|⟨
|19
|129
|139
|142
|144
|] ⟩
|}




Reduced Mapping
Reduced Mapping
{| class="wikitable"
 
!
2 111 159 175 191
!2
[ ⟨ 1 7 7 8 8 ]
!111
⟨ 0 -2 3 -5 -4 ] ⟩
!159
!175
!191
!
|-
|[ ⟨
|1
|7
|7
|8
|8
|]
|-
|⟨
|0
| -2
|3
| -5
| -4
|] ⟩
|}




Line 934: Line 808:
Unison Vectors
Unison Vectors


* [-6, 2, 0, 0, -1⟩ (12321:12224)
*[-6, 2, 0, 0, -1⟩ (12321:12224)
* [8, 1, -1, -1, 0⟩ (9472:9275)
*[8, 1, -1, -1, 0⟩ (9472:9275)
* [14, -1, -1, -1, 1⟩ (3129344:3088575)
*[14, -1, -1, -1, 1⟩ (3129344:3088575)
* [-7, 1, 0, -2, 2⟩ (4049391:3920000)
*[-7, 1, 0, -2, 2⟩ (4049391:3920000)
* [2, 3, -1, -1, -1⟩ (1823508:1771525)
*[2, 3, -1, -1, -1⟩ (1823508:1771525)
* [-15, 0, 1, -1, 2⟩ (5800479:5734400)
*[-15, 0, 1, -1, 2⟩ (5800479:5734400)


'''Sahara Septatonic scale''': A nice subset of Sahara[9]. Try noodling with it in Scale Workshop:


'''Sahara Septatonic scale''': A nice subset of Sahara[9]. Try noodling with it in Scale Workshop:
*256.237
* 256.237
*384.356
* 384.356
*512.475
* 512.475
*687.525
* 687.525
*943.762
* 943.762
*1071.881
* 1071.881
*1200.
* 1200.


===...with an even mix of both===
===...with an even mix of both===
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