User:Moremajorthanmajor/15edX
15edX is the scale which occurs as the dominant minor edX.
This is the neutral scale of the Middletown temperament family.
Intervals
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | ||||||||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | ||||||||||||||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | |||||||||||||||||
| Soft | Intense | |||||||||||||||||||||
| Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | Minimum | Maximum | |||
| 1 | F#/Gb | 96 | 97.778 | 100 | 101.818 | 102.857 | 104 | 105 | 106.667 | 107.586 | 110.345 | 112 | ||||||||||
| 2 | G | 192 | 195.556 | 200 | 203.636 | 205.714 | 208 | 210 | 213.333 | 215.172 | 220.69 | 224 | ||||||||||
| 3 | G#/Jb | G#/Ab | 288 | 293.333 | 300 | 305.4545 | 308.571 | 312 | 315 | 320 | 322.759 | 331.034 | 336 | |||||||||
| 4 | J | A | 384 | 391.111 | 400 | 407.273 | 411.429 | 416 | 420 | 426.667 | 430.345 | 441.379 | 448 | |||||||||
| 5 | A | B | 480 | 488.889 | 500 | 509.091 | 514.286 | 520 | 525 | 533.333 | 537.931 | 551.724 | 560 | |||||||||
| 6 | A#/Bb | B#/Hb | 576 | 586.667 | 600 | 610.909 | 617.143 | 624 | 630 | 640 | 645.517 | 662.069 | 672 | |||||||||
| 7 | B | H | 672 | 684.444 | 700 | 712.727 | 720 | 728 | 735 | 746.667 | 753.103 | 772.414 | 784 | |||||||||
| 8 | B#/Hb | H#/Cb | 768 | 782.822 | 800 | 814.5455 | 822.857 | 832 | 845 | 853.333 | 860.69 | 882.759 | 896 | |||||||||
| 9 | H | C | 864 | 880 | 900 | 916.364 | 925.714 | 936 | 940 | 960 | 968.276 | 993.103 | 1008 | |||||||||
| 10 | C | D | 960 | 977.778 | 1000 | 1018.182 | 1028.571 | 1040 | 1050 | 1066.667 | 1075.862 | 1103.448 | 1120 | |||||||||
| 11 | C#/Db | D#/Sb | 1056 | 1075.556 | 1100 | 1120 | 1131.429 | 1144 | 1155 | 1173.333 | 1183.448 | 1213.379 | 1232 | |||||||||
| 12 | D | S | 1152 | 1173.333 | 1200 | 1221.818 | 1234.286 | 1248 | 1260 | 1280 | 1291.034 | 1324.138 | 1344 | |||||||||
| 13 | D#/Eb | S#/Eb | 1248 | 1271.111 | 1300 | 1323.636 | 1337.143 | 1352 | 1365 | 1386.667 | 1398.621 | 1424.483 | 1456 | |||||||||
| 14 | E | 1344 | 1368.889 | 1400 | 1425.4545 | 1440 | 1456 | 1470 | 1493.333 | 1506.207 | 1544.827 | 1568 | ||||||||||
| 15 | F | 1440 | 1466.667 | 1500 | 1527.273 | 1542.857 | 1560 | 1575 | 1600 | 1613.793 | 1655.172 | 1680 | ||||||||||
Golden tunings
| Degrees | Enneatonic | Minor mode Middletown temperament | Neutral mode Middletown temperament | Major mode Middletown temperament | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Aeolian-Dorian | Dorian | Dorian-Mixolydian | Mixolydian | Mixolydian-Ionian | ||||||||
| Subpental | Pental | Superpental | Subpental | Pental | Superpental | |||||||
| Soft | Intense | |||||||||||
| 1 | F#/Gb | 97.323 | 98.257 | 101.4845 | 102.1115 | 103.655 | 104.721 | 105.173 | 107.531 | 109.291 | 110.504 | |
| 2 | G | 194.647 | 196.513 | 202.969 | 204.223 | 207.31 | 209.443 | 210.346 | 215.032 | 218.582 | 221.008 | |
| 3 | G#/Jb | G#/Ab | 291.97 | 294.77 | 304.454 | 306.334 | 310.965 | 314.164 | 315.519 | 322.593 | 327.873 | 331.613 |
| 4 | J | A | 389.294 | 394.027 | 405.938 | 408.446 | 414.6195 | 418.885 | 420.639 | 430.124 | 437.1345 | 442.017 |
| 5 | A | B | 486.617 | 491.283 | 507.423 | 510.557 | 518.274 | 523.607 | 525.865 | 537.655 | 546.456 | 552.521 |
| 6 | A#/Bb | B#/Hb | 583.94 | 589.54 | 608.907 | 612.669 | 621.929 | 628.328 | 631.0385 | 645.186 | 655.747 | 663.025 |
| 7 | B | H | 681.364 | 687.7965 | 710.392 | 714.78 | 725.584 | 733.0495 | 736.212 | 752.717 | 765.038 | 773.5235 |
| 8 | B#/Hb | H#/Cb | 778.587 | 786.053 | 811.877 | 816.892 | 829.239 | 837.771 | 841.385 | 860.248 | 874.329 | 884.033 |
| 9 | H | C | 875.9105 | 884.31 | 913.361 | 919.003 | 932.893 | 942.492 | 946.558 | 967.7785 | 983.62 | 994.538 |
| 10 | C | D | 973.234 | 982.5665 | 1014.8455 | 1021.115 | 1036.549 | 1047.214 | 1051.731 | 1075.3095 | 1092.911 | 1105.042 |
| 11 | C#/Db | D#/Sb | 1070.557 | 1080.823 | 1116.33 | 1123.226 | 1140.204 | 1151.935 | 1156.904 | 1182.84 | 1202.202 | 1215.546 |
| 12 | D | S | 1167.881 | 1179.08 | 1217.8145 | 1225.3375 | 1243.859 | 1256.656 | 1262.077 | 1290.371 | 1311.4935 | 1326.051 |
| 13 | D#/Eb | S#/Eb | 1265.204 | 1277.336 | 1319.299 | 1327.449 | 1347.513 | 1361.378 | 1367.25 | 1397.902 | 1420.785 | 1436.555 |
| 14 | E | 1362.527 | 1375.593 | 1420.783 | 1429.56 | 1451.168 | 1466.099 | 1472.423 | 1505.433 | 1530.076 | 1547.059 | |
| 15 | F | 1459.851 | 1473.85 | 1522.268 | 1531.672 | 1554.823 | 1570.82 | 1577.596 | 1612.964 | 1639.366 | 1657.563 | |
By a surprising coincidence, the 15ed of the Golden tenth (7φ+6)\(5φ^2)edo is almost exactly every third degree of 34edo. Additionally, those of the modal Golden tenths are almost exactly +1/28-syntonic comma 4ed(5/4) (Aeolian-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), -1/20-septimal comma 4ed(9/7)/-1/28-syntonic comma 14ed(12/5)/9ed(7/4) (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.