User:Contribution/Exploring Selected Modes in 12-EDO: Difference between revisions

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Line 81: Line 81:
! 1 / Factorization
! 1 / Factorization
! 1 / Ratio
! 1 / Ratio
|-
| [[531441/524288]]
| 2<sup>-19</sup> • 3<sup>12</sup>
| 23.460
| 3
| -23.460
| 2<sup>19</sup> • 3<sup>-12</sup>
| [[524288/531441]]
|-
|-
| [[81/80]]
| [[81/80]]
Line 137: Line 129:
| 2<sup>8</sup> • 3<sup>-8</sup> • 5<sup>2</sup>
| 2<sup>8</sup> • 3<sup>-8</sup> • 5<sup>2</sup>
| [[6400/6561]]
| [[6400/6561]]
|-
| [[16384/15625]]
| 2<sup>14</sup> • 5<sup>-6</sup>
| 82.118
| 5
| -82.118
| 2<sup>-14</sup> • 5<sup>6</sup>
| [[15625/16384]]
|-
| [[32805/32768]]
| 2<sup>-15</sup> • 3<sup>8</sup> • 5<sup>1</sup>
| 1.954
| 5
| -1.954
| 2<sup>15</sup> • 3<sup>-8</sup> • 5<sup>-1</sup>
| [[32768/32805]]
|-
| [[82944/78125]]
| 2<sup>10</sup> • 3<sup>4</sup> • 5<sup>-7</sup>
| 103.624
| 5
| -103.624
| 2<sup>-10</sup> • 3<sup>-4</sup> • 5<sup>7</sup>
| [[78125/82944]]
|-
| [[262144/253125]]
| 2<sup>18</sup> • 3<sup>-4</sup> • 5<sup>-5</sup>
| 60.611
| 5
| -60.611
| 2<sup>-18</sup> • 3<sup>4</sup> • 5<sup>5</sup>
| [[253125/262144]]
|-
| [[419904/390625]]
| 2<sup>6</sup> • 3<sup>8</sup> • 5<sup>-8</sup>
| 125.130
| 5
| -125.130
| 2<sup>-6</sup> • 3<sup>-8</sup> • 5<sup>8</sup>
| [[390625/419904]]
|-
|-
| [[36/35]]
| [[36/35]]

Revision as of 00:18, 1 September 2023

Modes

Modes of limited transposition

Period Modes
1\12 1
2\12 2
3\12 3 ; 1 2
4\12 4 ; 1 3 ; 1 1 2
6\12 6 ; 1 5 ; 2 4 ; 1 1 4 ; 1 2 3 ; 1 3 2 ; 1 1 1 3 ; 1 1 2 2 ; 1 1 1 1 2
12\12 12

Pentatonic modes

MOS Modes
2L 3s 2 2 3 2 3 (2 1 1 3 2 3) ; 2 2 2 3 3
1L 4s 2 2 2 2 4

Heptatonic modes

Alteration Modes
Ion 2 2 1 2 2 2 1
Ion b3 2 1 2 2 2 2 1
Ion b6 2 2 1 2 1 3 1
Ion b3 b6 2 1 2 2 1 3 1
Ion b2 1 3 1 2 2 2 1
Ion b2 b3 1 2 2 2 2 2 1
Ion b2 b6 1 3 1 2 1 3 1
Ion b2 b3 b6 1 2 2 2 1 3 1

Tempered commas

Selected 7-limit commas tempered out in 12-tet
Ratio Factorization Cents Limit - Cents 1 / Factorization 1 / Ratio
81/80 2-4 • 34 • 5-1 21.506 5 -21.506 24 • 3-4 • 51 80/81
128/125 27 • 5-3 41.059 5 -41.059 2-7 • 53 125/128
648/625 23 • 34 • 5-4 62.565 5 -62.565 2-3 • 3-4 • 54 625/648
2048/2025 211 • 3-4 • 5-2 19.553 5 -19.553 2-11 • 34 • 52 2025/2048
6561/6250 2-1 • 38 • 5-5 84.071 5 -84.071 21 • 3-8 • 55 6250/6561
6561/6400 2-8 • 38 • 5-2 43.013 5 -43.013 28 • 3-8 • 52 6400/6561
36/35 22 • 32 • 5-1 • 7-1 48.770 7 -48.770 2-2 • 3-2 • 51 • 71 35/36
50/49 21 • 52 • 7-2 34.976 7 -34.976 2-1 • 5-2 • 72 49/50
64/63 26 • 3-2 • 7-1 27.264 7 -27.264 2-6 • 32 • 71 63/64
126/125 21 • 32 • 5-3 • 71 13.795 7 -13.795 2-1 • 3-2 • 53 • 7-1 125/126
225/224 2-5 • 32 • 52 • 7-1 7.712 7 -7.712 25 • 3-2 • 5-2 • 71 224/225
256/245 28 • 5-1 • 7-2 76.034 7 -76.034 2-8 • 51 • 72 245/256
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