User:Moremajorthanmajor/15edX
15edX is the scale which occurs as the dominant minor edX (equal division of a tenth interval). It also gives the period of the 15th-decade Alfincavallo branch of the Carrera temperament family.
Intervals
| Decade | Period | Notes |
|---|---|---|
| 6\5 | 96.000 | Intense Aeolian-Subpental Dorian mode begins |
| 17\14 | 97.143 | |
| 11\9 | 97.778 | Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins |
| 16\13 | 98.462 | |
| 21\17 | 98.824 | |
| 26\21 | 99.048 | |
| 5\4 | 100.000 | Subpental Dorian mode ends, Pental Dorian mode begins |
| 19\15 | 101.333 | |
| 14\11 | 101.818 | Pental Dorian mode ends, Superpental Dorian mode begins |
| 23\18 | 102.222 | |
| 9\7 | 102.857 | Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins |
| 31\24 | 103.333 | |
| 22\17 | 103.529 | Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins |
| 35\27 | 103.704 | |
| 13\10 | 104.000 | Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins |
| 17\13 | 104.615 | |
| 21\16 | 105.000 | Subpental Mixolydian mode ends, Pental Mixolydian mode begins |
| 25\19 | 105.263 | |
| 4\3 | 106.667 | Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins |
| 31\23 | 107.826 | |
| 27\20 | 108.000 | |
| 23\17 | 108.235 | |
| 19\14 | 108.571 | |
| 15\11 | 109.091 | Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins |
| 26\19 | 109.474 | |
| 11\8 | 110.000 | Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins |
| 18\13 | 110.769 | |
| 25\18 | 111.111 | |
| 7\5 | 112.500 | Mixolydian-Ionian mode ends |
Relative cents
| Degrees | Enneatonic | Intense Aeolian-Subpental Dorian | Dorian | Dorian-Mixolydian | Subpental-Soft Superpental Mixolydian | Intense Superpental Mixolydian ~ Mixolydian-Ionian | |
|---|---|---|---|---|---|---|---|
| 1 | G#/Jb | G#/Ab | 96.6 | 100 | 103.3 | 106.6 | 110 |
| 2 | J | A | 193.3 | 200 | 206.6 | 213.3 | 220 |
| 3 | J#/Ab | A#/Bb | 290 | 300 | 310 | 320 | 330 |
| 4 | A | B | 386.6 | 400 | 413.3 | 426.6 | 440 |
| 5 | B | C | 483.3 | 500 | 516.6 | 533.3 | 550 |
| 6 | B#/Cb | C#/Qb | 580 | 600 | 620 | 640 | 660 |
| 7 | C | Q | 676.6 | 700 | 723.3 | 746.6 | 770 |
| 8 | C#/Qb | Q#/Db | 773.3 | 800 | 826.6 | 853.3 | 880 |
| 9 | Q | D | 870 | 900 | 930 | 960 | 990 |
| 10 | D | S | 966.6 | 1000 | 1033.3 | 1066.6 | 1100 |
| 11 | D#/Eb | S#/Eb | 1063.3 | 1100 | 1136.6 | 1173.3 | 1210 |
| 12 | E | 1160 | 1200 | 1240 | 1280 | 1320 | |
| 13 | E#/Fb | 1256.6 | 1300 | 1343.3 | 1386.6 | 1430 | |
| 14 | F | 1353.3 | 1400 | 1446.6 | 1493.3 | 1540 | |
| 15 | G | 1450 | 1500 | 1550 | 1600 | 1650 | |
By a surprising coincidence, the 15ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden and Pyrite tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Intense Aeolian-Subpental Dorian), 9ed(5/3)/equal multiples of 18/17 (Subpental Dorian), 13ed(15/7) (Pental Dorian), 2ed(9/8) (Superpental Dorian), -1/12-syntonic comma 3ed(6/5) (Dorian-Mixolydian), 14ed(7/3)/equal multiples of 17/16/100π\3 cents (Subpental Mixolydian), 3ed(6/5) (Pental Mixolydian), 4ed(9/7)/+1/36-syntonic comma 14ed(12/5) (Soft Superpental Mixolydian), 12ed(32/15) (Intense Superpental Mixolydian) and 8ed(5/3)/-1/9 schismic 9ed(16/9)/14ed(22/9) (Mixolydian-Ionian) respectively.