User:Contribution/Exploring Selected Modes in 12-EDO: Difference between revisions
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| 2<sup>1</sup> • 3<sup>-8</sup> • 5<sup>5</sup> | | 2<sup>1</sup> • 3<sup>-8</sup> • 5<sup>5</sup> | ||
| [[6250/6561]] | | [[6250/6561]] | ||
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| [[32805/32768]] | | [[32805/32768]] | ||
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| 2<sup>-18</sup> • 3<sup>4</sup> • 5<sup>5</sup> | | 2<sup>-18</sup> • 3<sup>4</sup> • 5<sup>5</sup> | ||
| [[253125/262144]] | | [[253125/262144]] | ||
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| [[531441/500000]] | | [[531441/500000]] | ||
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| 2<sup>5</sup> • 3<sup>-12</sup> • 5<sup>6</sup> | | 2<sup>5</sup> • 3<sup>-12</sup> • 5<sup>6</sup> | ||
| [[500000/531441]] | | [[500000/531441]] | ||
|- | |- | ||
| [[2125764/1953125]] | | [[2125764/1953125]] | ||
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| 2<sup>-2</sup> • 3<sup>-12</sup> • 5<sup>9</sup> | | 2<sup>-2</sup> • 3<sup>-12</sup> • 5<sup>9</sup> | ||
| [[1953125/2125764]] | | [[1953125/2125764]] | ||
|- | |- | ||
| [[10616832/9765625]] | | [[10616832/9765625]] | ||
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| 2<sup>-25</sup> • 3<sup>4</sup> • 5<sup>8</sup> | | 2<sup>-25</sup> • 3<sup>4</sup> • 5<sup>8</sup> | ||
| [[31640625/33554432]] | | [[31640625/33554432]] | ||
|- | |- | ||
| [[53747712/48828125]] | | [[53747712/48828125]] | ||
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| 2<sup>-13</sup> • 3<sup>-8</sup> • 5<sup>11</sup> | | 2<sup>-13</sup> • 3<sup>-8</sup> • 5<sup>11</sup> | ||
| [[48828125/53747712]] | | [[48828125/53747712]] | ||
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Revision as of 14:24, 2 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 |
Nonatonic modes (tempering out 32805/32768)
| Alteration | Modes |
|---|---|
| Schisma | 2 2 1 1 1 2 1 1 1 |
Heptatonic modes (tempering out 5120/5103)
| 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 |
Pentatonic modes (tempering out 81/80)
| Alteration | Modes |
|---|---|
| Tetra | 2 5 2 3 |
| Penta MOS | 2 2 3 2 3 |
| Penta b7 9 | 3 3 2 2 2 |
| Penta #5 9 #11 | 2 2 4 2 2 |
Blues scales (tempering out 2048/2025)
| Added notes | Modes |
|---|---|
| #1 b3 #5/b6 | 1 1 1 1 3 1 1 3 |
| #1 b3 | 1 1 1 1 3 2 3 |
| #1 | 1 1 2 3 2 3 |
| b3 | 2 1 1 3 2 3 |
| None | 2 2 3 2 3 |
Tempered commas
| 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 |
| 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 |
| Ratio | Factorization | Cents | Limit | - Cents | 1 / Factorization | 1 / Ratio |
|---|---|---|---|---|---|---|
| 531441/524288 | 2-19 • 312 | 23.460 | 3 | -23.460 | 219 • 3-12 | 524288/531441 |
| 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 |
| 32805/32768 | 2-15 • 38 • 51 | 1.954 | 5 | -1.954 | 215 • 3-8 • 5-1 | 32768/32805 |
| 82944/78125 | 210 • 34 • 5-7 | 103.624 | 5 | -103.624 | 2-10 • 3-4 • 57 | 78125/82944 |
| 262144/253125 | 218 • 3-4 • 5-5 | 60.611 | 5 | -60.611 | 2-18 • 34 • 55 | 253125/262144 |
| 531441/500000 | 2-5 • 312 • 5-6 | 105.578 | 5 | -105.578 | 25 • 3-12 • 56 | 500000/531441 |
| 2125764/1953125 | 22 • 312 • 5-9 | 146.637 | 5 | -146.637 | 2-2 • 3-12 • 59 | 1953125/2125764 |
| 10616832/9765625 | 217 • 34 • 5-10 | 144.683 | 5 | -144.683 | 2-17 • 3-4 • 510 | 9765625/10616832 |
| 33554432/31640625 | 225 • 3-4 • 5-8 | 101.670 | 5 | -101.670 | 2-25 • 34 • 58 | 31640625/33554432 |
| 53747712/48828125 | 213 • 38 • 5-11 | 166.189 | 5 | -166.189 | 2-13 • 3-8 • 511 | 48828125/53747712 |