User:Moremajorthanmajor/16edX
This is the scale which occurs as the dominant major edX.
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 | 1#/2b | F#/Gb | 90 | 91.667 | 93.75 | 95.4545 | 96.429 | 97.5 | 98.4375 | 100 | 100.862 | 103.448 | 105 | ||||||||||
| 2 | 2 | G | 180 | 183.333 | 187.5 | 190.909 | 192.857 | 195 | 196.875 | 200 | 201.724 | 206.897 | 210 | ||||||||||
| 3 | 2#/3b | G#/Jb | G#/Ab | 270 | 275 | 281.25 | 286.364 | 289.286 | 292.5 | 295.3125 | 300 | 302.586 | 310.345 | 315 | |||||||||
| 4 | 3 | J | A | 360 | 366.667 | 375 | 381.818 | 385.714 | 390 | 393.75 | 400 | 403.448 | 413.793 | 420 | |||||||||
| 5 | 3#/4b | J#/Ab | A#/Bb | 450 | 458.333 | 468.75 | 477.273 | 482.143 | 487.5 | 492.1875 | 500 | 504.31 | 517.241 | 525 | |||||||||
| 6 | 4 | A | B | 540 | 550 | 562.5 | 572.727 | 578.571 | 585 | 590.625 | 600 | 605.172 | 620.69 | 630 | |||||||||
| 7 | 5 | B | H | 630 | 641.667 | 656.25 | 668.182 | 675 | 682.5 | 689.0625 | 700 | 706.0345 | 724.138 | 735 | |||||||||
| 8 | 5#/6b | B#/Hb | H#/Cb | 720 | 733.333 | 750 | 763.636 | 771.429 | 780 | 787.5 | 800 | 806.897 | 827.586 | 840 | |||||||||
| 9 | 6 | H | C | 810 | 825 | 843.75 | 859.091 | 867.857 | 877.5 | 885.9375 | 900 | 907.759 | 931.0345 | 945 | |||||||||
| 10 | 6#/7b | H#/Cb | C#/Db | 900 | 916.667 | 937.5 | 954.5455 | 964.286 | 975 | 984.375 | 1000 | 1008.621 | 1034.483 | 1050 | |||||||||
| 11 | 7 | C | D | 990 | 1018.333 | 1031.25 | 1050 | 1060.714 | 1072.5 | 1082.8125 | 1100 | 1109.483 | 1137.931 | 1155 | |||||||||
| 12 | 7#/8b | C#/Db | D#/Sb | 1080 | 1100 | 1125 | 1145.4545 | 1157.143 | 1170 | 1181.25 | 1200 | 1210.345 | 1241.379 | 1260 | |||||||||
| 13 | 8 | D | S | 1170 | 1191.667 | 1218.75 | 1240.909 | 1253.571 | 1267.5 | 1279.6875 | 1300 | 1311.207 | 1344.828 | 1365 | |||||||||
| 14 | 8#/9b | D#/Eb | S#/Eb | 1260 | 1283.333 | 1312.5 | 1336.364 | 1350 | 1365 | 1378.125 | 1400 | 1412.069 | 1448.276 | 1470 | |||||||||
| 15 | 9 | E | 1350 | 1375 | 1406.25 | 1431.818 | 1446.429 | 1462.5 | 1476.5625 | 1500 | 1512.931 | 1551.724 | 1575 | ||||||||||
| 16 | 1 | 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 | 1#/2b | F#/Gb | 91.241 | 92.116 | 95.142 | 95.7295 | 97.176 | 98.176 | 98.6 | 100.81 | 102.46 | 103.598 | |
| 2 | 2 | G | 182.481 | 184.231 | 190.2835 | 191.459 | 194.353 | 196.3525 | 197.1995 | 201.6205 | 204.921 | 207.195 | |
| 3 | 2#/3b | G#/Jb | G#/Ab | 273.722 | 276.347 | 285.425 | 287.1885 | 291.529 | 294.529 | 295.799 | 302.431 | 307.381 | 310.793 |
| 4 | 3 | J | A | 364.962 | 368.462 | 380.567 | 382.918 | 388.706 | 392.705 | 394.399 | 403.241 | 409.842 | 414.391 |
| 5 | 3#/4b | J#/Ab | A#/Bb | 456.203 | 460.578 | 475.709 | 478.6475 | 485.882 | 490.881 | 492.999 | 504.051 | 512.302 | 517.9885 |
| 6 | 4 | A | B | 547.444 | 552.694 | 570.851 | 574.377 | 680.235 | 589.058 | 591.599 | 604.862 | 614.763 | 621.586 |
| 7 | 5 | B | H | 638.685 | 644.809 | 665.992 | 670.106 | 725.584 | 687.234 | 690.198 | 705.672 | 717.223 | 725.184 |
| 8 | 5#/6b | B#/Hb | H#/Cb | 729.925 | 736.925 | 761.134 | 765.836 | 777.412 | 785.41 | 788.798 | 806.482 | 819.6835 | 828.781 |
| 9 | 6 | H | C | 821.166 | 829.04 | 856.276 | 861.565 | 874.588 | 883.5865 | 887.398 | 907.292 | 922.144 | 932.379 |
| 10 | 6#/7b | H#/Cb | C#/Db | 912.407 | 921.156 | 951.418 | 957.295 | 971.7645 | 981.763 | 985.998 | 1008.103 | 1024.604 | 1035.977 |
| 11 | 7 | C | D | 1003.6475 | 1013.272 | 1046.559 | 1053.024 | 1068.941 | 1079.939 | 1084.597 | 1108.913 | 1127.065 | 1139.575 |
| 12 | 7#/8b | C#/Db | D#/Sb | 1094.888 | 1105.387 | 1141.701 | 1148.753 | 1166.117 | 1178.115 | 1183.197 | 1209.723 | 1229.525 | 1243.172 |
| 13 | 8 | D | S | 1186.129 | 1197.502 | 1236.843 | 1244.483 | 1263.293 | 1276.292 | 1281.797 | 1310.533 | 1331.986 | 1346.77 |
| 14 | 8#/9b | D#/Eb | S#/Eb | 1277.3965 | 1289.6185 | 1331.985 | 1340.213 | 1360.47 | 1374.468 | 1380.397 | 1411.344 | 1434.446 | 1450.368 |
| 15 | 9 | E | 1368.61 | 1381.734 | 1427.126 | 1435.942 | 1457.645 | 1472.644 | 1478.996 | 1512.154 | 1536.9065 | 1553.9655 | |
| 16 | 1 | 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, neutral 16edX turns out to be a false Pelogic temperament with a very pure 5:4 (mistuned by no more than 3.596 cents), and tuning 5:3 pure creates a tenth almost exactly equal to 38/29edo or almost exactly the Golden Subpental Mixolydian step or every ninth step of 110edo, and tuning 4:3 pure creates an almost exact 43/74edo fifth. Also, the Golden Soft Superpental Mixolydian step is almost exactly (25/24)^(10/7) and tuning 12:7 pure creates almost exactly the Golden Mixolydian-Ionian step.