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

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| 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| 2<sup>-8</sup> • 5<sup>1</sup> • 7<sup>2</sup>
| [[245/256]]
| [[245/256]]
|}
{| class="wikitable center-all left-2 right-3 right-5 left-6"
|+style=white-space:nowrap| Selected 7-limit commas tempered out in 12-tet
! Ratio
! Factorization
! Cents
! Limit
! - Cents
! 1 / Factorization
! 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]]
| 2<sup>-4</sup> • 3<sup>4</sup> • 5<sup>-1</sup>
| 21.506
| 5
| -21.506
| 2<sup>4</sup> • 3<sup>-4</sup> • 5<sup>1</sup>
| [[80/81]]
|-
| [[128/125]]
| 2<sup>7</sup> • 5<sup>-3</sup>
| 41.059
| 5
| -41.059
| 2<sup>-7</sup> • 5<sup>3</sup>
| [[125/128]]
|-
| [[648/625]]
| 2<sup>3</sup> • 3<sup>4</sup> • 5<sup>-4</sup>
| 62.565
| 5
| -62.565
| 2<sup>-3</sup> • 3<sup>-4</sup> • 5<sup>4</sup>
| [[625/648]]
|-
| [[2048/2025]]
| 2<sup>11</sup> • 3<sup>-4</sup> • 5<sup>-2</sup>
| 19.553
| 5
| -19.553
| 2<sup>-11</sup> • 3<sup>4</sup> • 5<sup>2</sup>
| [[2025/2048]]
|-
| [[6561/6250]]
| 2<sup>-1</sup> • 3<sup>8</sup> • 5<sup>-5</sup>
| 84.071
| 5
| -84.071
| 2<sup>1</sup> • 3<sup>-8</sup> • 5<sup>5</sup>
| [[6250/6561]]
|-
| [[6561/6400]]
| 2<sup>-8</sup> • 3<sup>8</sup> • 5<sup>-2</sup>
| 43.013
| 5
| -43.013
| 2<sup>8</sup> • 3<sup>-8</sup> • 5<sup>2</sup>
| [[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]]
|-
| [[531441/500000]]
| 2<sup>-5</sup> • 3<sup>12</sup> • 5<sup>-6</sup>
| 105.578
| 5
| -105.578
| 2<sup>5</sup> • 3<sup>-12</sup> • 5<sup>6</sup>
| [[500000/531441]]
|-
| [[531441/512000]]
| 2<sup>-12</sup> • 3<sup>12</sup> • 5<sup>-3</sup>
| 64.519
| 5
| -64.519
| 2<sup>12</sup> • 3<sup>-12</sup> • 5<sup>3</sup>
| [[512000/531441]]
|-
| [[2097152/1953125]]
| 2<sup>21</sup> • 5<sup>-9</sup>
| 123.177
| 5
| -123.177
| 2<sup>-21</sup> • 5<sup>9</sup>
| [[1953125/2097152]]
|-
| [[2125764/1953125]]
| 2<sup>2</sup> • 3<sup>12</sup> • 5<sup>-9</sup>
| 146.637
| 5
| -146.637
| 2<sup>-2</sup> • 3<sup>-12</sup> • 5<sup>9</sup>
| [[1953125/2125764]]
|-
| [[4194304/4100625]]
| 2<sup>22</sup> • 3<sup>-8</sup> • 5<sup>-4</sup>
| 39.105
| 5
| -39.105
| 2<sup>-22</sup> • 3<sup>8</sup> • 5<sup>4</sup>
| [[4100625/4194304]]
|-
| [[10616832/9765625]]
| 2<sup>17</sup> • 3<sup>4</sup> • 5<sup>-10</sup>
| 144.683
| 5
| -144.683
| 2<sup>-17</sup> • 3<sup>-4</sup> • 5<sup>10</sup>
| [[9765625/10616832]]
|-
| [[33554432/31640625]]
| 2<sup>25</sup> • 3<sup>-4</sup> • 5<sup>-8</sup>
| 101.670
| 5
| -101.670
| 2<sup>-25</sup> • 3<sup>4</sup> • 5<sup>8</sup>
| [[31640625/33554432]]
|-
| [[43046721/39062500]]
| 2<sup>-2</sup> • 3<sup>16</sup> • 5<sup>-10</sup>
| 168.143
| 5
| -168.143
| 2<sup>2</sup> • 3<sup>-16</sup> • 5<sup>10</sup>
| [[39062500/43046721]]
|-
| [[43046721/40000000]]
| 2<sup>-9</sup> • 3<sup>16</sup> • 5<sup>-7</sup>
| 127.084
| 5
| -127.084
| 2<sup>9</sup> • 3<sup>-16</sup> • 5<sup>7</sup>
| [[40000000/43046721]]
|-
| [[43046721/40960000]]
| 2<sup>-16</sup> • 3<sup>16</sup> • 5<sup>-4</sup>
| 86.025
| 5
| -86.025
| 2<sup>16</sup> • 3<sup>-16</sup> • 5<sup>4</sup>
| [[40960000/43046721]]
|-
| [[43046721/41943040]]
| 2<sup>-23</sup> • 3<sup>16</sup> • 5<sup>-1</sup>
| 44.966
| 5
| -44.966
| 2<sup>23</sup> • 3<sup>-16</sup> • 5<sup>1</sup>
| [[41943040/43046721]]
|-
| [[53747712/48828125]]
| 2<sup>13</sup> • 3<sup>8</sup> • 5<sup>-11</sup>
| 166.189
| 5
| -166.189
| 2<sup>-13</sup> • 3<sup>-8</sup> • 5<sup>11</sup>
| [[48828125/53747712]]
|-
| [[67108864/66430125]]
| 2<sup>26</sup> • 3<sup>-12</sup> • 5<sup>-3</sup>
| 17.599
| 5
| -17.599
| 2<sup>-26</sup> • 3<sup>12</sup> • 5<sup>3</sup>
| [[66430125/67108864]]
|}
|}

Revision as of 14:20, 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

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
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
Selected 7-limit commas tempered out in 12-tet
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
6561/6400 2-8 • 38 • 5-2 43.013 5 -43.013 28 • 3-8 • 52 6400/6561
16384/15625 214 • 5-6 82.118 5 -82.118 2-14 • 56 15625/16384
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
419904/390625 26 • 38 • 5-8 125.130 5 -125.130 2-6 • 3-8 • 58 390625/419904
531441/500000 2-5 • 312 • 5-6 105.578 5 -105.578 25 • 3-12 • 56 500000/531441
531441/512000 2-12 • 312 • 5-3 64.519 5 -64.519 212 • 3-12 • 53 512000/531441
2097152/1953125 221 • 5-9 123.177 5 -123.177 2-21 • 59 1953125/2097152
2125764/1953125 22 • 312 • 5-9 146.637 5 -146.637 2-2 • 3-12 • 59 1953125/2125764
4194304/4100625 222 • 3-8 • 5-4 39.105 5 -39.105 2-22 • 38 • 54 4100625/4194304
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
43046721/39062500 2-2 • 316 • 5-10 168.143 5 -168.143 22 • 3-16 • 510 39062500/43046721
43046721/40000000 2-9 • 316 • 5-7 127.084 5 -127.084 29 • 3-16 • 57 40000000/43046721
43046721/40960000 2-16 • 316 • 5-4 86.025 5 -86.025 216 • 3-16 • 54 40960000/43046721
43046721/41943040 2-23 • 316 • 5-1 44.966 5 -44.966 223 • 3-16 • 51 41943040/43046721
53747712/48828125 213 • 38 • 5-11 166.189 5 -166.189 2-13 • 3-8 • 511 48828125/53747712
67108864/66430125 226 • 3-12 • 5-3 17.599 5 -17.599 2-26 • 312 • 53 66430125/67108864
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