User:Contribution/Exploring Selected Modes in 19-EDO
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Mapping
sharpness = 1
L = 3 ; s = 2
| Degree | Notation | Approximate Ratios | Approximate Ratios | Notation | Degree |
|---|---|---|---|---|---|
| 0 | P1 | 1/1 | 2/1 | P8 | 19 |
| 1 | A1, d2 | A7, d8 | 18 | ||
| 2 | m2 | 16/15, 15/14, 14/13, 13/12 | 24/13, 13/7, 28/15, 15/8 | M7 | 17 |
| 3 | M2 | 10/9, 9/8 | 16/9, 9/5 | m7 | 16 |
| 4 | A2, d3 | 8/7, 15/13, 7/6 | 12/7, 26/15, 7/4 | A6, d7 | 15 |
| 5 | m3 | 6/5 | 5/3 | M6 | 14 |
| 6 | M3 | 16/13, 5/4 | 8/5, 13/8 | m6 | 13 |
| 7 | A3, d4 | 9/7, 13/10 | 20/13, 14/9 | A5, d6 | 12 |
| 8 | P4 | 4/3 | 3/2 | P5 | 11 |
| 9 | A4 | 18/13, 7/5 | 10/7, 13/9 | d5 | 10 |
Rank-2 5-limit temperaments
| Period | Generator | Temperaments | 5-limit commas |
|---|---|---|---|
| 19\19 | 1\19 | Unicorn | 1594323/1562500 |
| 19\19 | 2\19 | Negri | 16875/16384 |
| 19\19 | 3\19 | Unsmate | 17578125/16777216 |
| 19\19 | 4\19 | Hogzilla | 4428675/4194304 |
| 19\19 | 5\19 | Kleismic | 15625/15552 |
| 19\19 | 6\19 | Magic | 3125/3072 |
| 19\19 | 7\19 | Sensi | 78732/78125 |
| 19\19 | 8\19 | Meantone | 81/80 |
| 19\19 | 9\19 | Stump | 273375/262144 |
MOS Modes
| Period | Generator | Modes | Names |
|---|---|---|---|
| 19\19 | 2\19 | 2 2 2 2 2 1 2 2 2 2 | Negri[10] |
| 19\19 | 3\19 | 1 2 1 2 1 2 1 2 1 2 1 2 1 | Unsmate[13] |
| 19\19 | 4\19 | 3 1 3 1 3 1 3 1 3 | Hogzilla[9] |
| 1 2 1 1 2 1 2 1 1 2 1 1 2 1 | Hogzilla[14] | ||
| 19\19 | 5\19 | 1 3 1 1 3 1 3 1 1 3 1 | Kleismic[11] |
| 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 | Kleismic[15] | ||
| 19\19 | 6\19 | 1 4 1 1 4 1 1 1 4 1 | Magic[10] |
| 1 1 3 1 1 1 3 1 1 1 3 1 1 | Magic[13] | ||
| 1 1 2 1 1 1 1 2 1 1 1 1 1 2 1 1 | Magic[16] | ||
| 19\19 | 7\19 | 2 1 2 2 2 1 2 2 2 1 2 | Sensi[11] |
| 19\19 | 8\19 | 2 1 2 1 2 2 1 2 1 2 1 2 | Meantone[12] |
| 1\19 | 1\19 | 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 | 19edo |