User:Moremajorthanmajor/13edIX
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This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small. It also gives the wide values for the period of the Greater Triskaidekic, tridecatonic, trideci and aluminium temperaments.
Intervals
| Nonet | Period | Notes |
|---|---|---|
| 1/1 | 92.308 | Soft Phrygian mode begins |
| 23\22 | 96.503 | |
| 22\21 | 96.703 | Soft Phrygian mode ends, Thirdtone Phrygian mode begins |
| 21\20 | 96.923 | |
| 20\19 | 97.166 | |
| 19\18 | 97.436 | |
| 37\35 | 97.582 | |
| 18\17 | 97.738 | |
| 17\16 | 98.077 | |
| 16\15 | 98.462 | Thirdtone Phrygian mode ends |
| 15\14 | 98.901 | Semitone Phrygian mode begins |
| 14\13 | 99.408 | |
| 27\25 | 99.692 | |
| 13\12 | 100.000 | |
| 12\11 | 100.699 | |
| 11\10 | 101.538 | Semitone Phrygian mode ends, Intense Phrygian mode begins |
| 21\19 | 102.024 | |
| 10\9 | 102.564 | Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins |
| 19\17 | 103.167 | |
| 9\8 | 103.846 | Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins |
| 17\15 | 104.615 | |
| 8\7 | 105.495 | Soft Aeolian mode ends, Flattone Aeolian mode begins |
| 15\13 | 106.509 | |
| 22\19 | 106.883 | Flattone Aeolian mode ends, Meantone Aeolian mode begins |
| 29\25 | 107.077 | |
| 7\6 | 107.692 | Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins |
| 20\17 | 108.597 | |
| 13\11 | 109.09 | Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins |
| 19\16 | 109.615 | |
| 6\5 | 110.769 | Ultrapyth Intense Aeolian mode ends |
Golden/Pyrite Tunings±13¢
| Degrees | Octatonic | Soft Phrygian | Phrygian | |||||
|---|---|---|---|---|---|---|---|---|
| Min-Med | Min-Max/Med-Max | Thirdtone | Semitone | |||||
| Min-Med/Min-Max | Med-Max | Min-Med/Min-Max | Med-Max | |||||
| Natural | Subset of 26edn | |||||||
| 1 | G#/Ab | G#v/Ab^ | 95.389-97.389 | 95.578-97.578 | 95.957-98.345 | 96.785-98.844 | 98.359-100.709 | 99.058-101.523 |
| 2 | A | 190.778-194.778 | 191.155-195.155 | 191.914-196.689 | 193.569-197.688 | 196.719-201.417 | 198.1165-203.046 | |
| 3 | A#/Bb | A#v/Bb^ | 286.1665-292.1665 | 286.733-292.733 | 287.871-295.034 | 290.354-296.531 | 295.078-302.126 | 297.175-304.569 |
| 4 | B | 381.555-389.555 | 382.3105-390.3105 | 383.828-393.378 | 387.138-395.375 | 393.4375-402.835 | 396.233-406.092 | |
| 5 | C | B#v/Cb^ | 476.944-486.944 | 477.888-487.888 | 479.785-491.723 | 483.923-494.219 | 491.797-503.544 | 495.291-507.615 |
| 6 | C#/Qb | C | 572.333-584.333 | 573.466-585.466 | 575.742-590.068 | 580.707-593.063 | 590.156-604.253 | 594.349-609.138 |
| 7 | Q | Db | 667.722-681.722 | 669.043-683.043 | 671.699-688.412 | 677.492-691.907 | 688.516-704.962 | 693.408-710.661 |
| 8 | D | Q# | 763.111-781.111 | 764.621-780.621 | 767.656-786.757 | 774.2765-790.75 | 786.875-805.67 | 792.466-812.184 |
| 9 | D#/Eb | Eb | 858.5-876.5 | 860.199-878.199 | 863.613-885.1015 | 871.061-889.594 | 885.234-906.379 | 891.524-913.707 |
| 10 | E | D# | 953.8885-973.8885 | 955.776-975.776 | 959.57-983.446 | 967.846-988.438 | 983.594-1007.088 | 990.582-1015.23 |
| 11 | E#/Fb | Fb | 1049.277-1071.277 | 1051.354-1073.354 | 1055.527-1081.791 | 1064.63-1087.282 | 1081.953-1107.797 | 1089.641-1116.75 |
| 12 | F | E# | 1144.666-1168.666 | 1146.932-1170.932 | 1151.484-1180.135 | 1161.415-1186.126 | 1180.312-1208.506 | 1188.699-1218.276 |
| 13 | G | 1240.055-1266.055 | 1242.506-1268.509 | 1247.441-1278.48 | 1258.199-1284.969 | 1278.672-1309.2145 | 1287.757-1319.799 | |
| Degrees | Octatonic | Intense Phrygian | Intense Phrygian-Soft Aeolian | Soft Aeolian | ||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Min-Med/Min-Max | Med-Max | Min-Med/Min-Max | Med-Max | Min-Med/Min-Max | Med-Max | |||||
| Natural | Subset of 26edn | |||||||||
| 1 | F#/Gb | G#/Ab | F#v/Gb^ | G#v/Ab^ | 100.905-102.905 | 101.1465-103.1465 | 102.019-104.019 | 102.32-104.32 | 103.425-105.425 | 103.812-105.812 |
| 2 | G | A | G | A | 201.81-205.81 | 202.293-206.293 | 204.037-208.037 | 204.641-208.641 | 206.849-210.849 | 207.624-211.624 |
| 3 | G#/Ab | A#/Bb | G#v/Ab^ | A#v/Bb^ | 302.715-308.715 | 303.44-309.44 | 306.056-312.056 | 306.961-312.961 | 310.274-316.274 | 311.4365-317.4365 |
| 4 | A | B | A | B | 403.62-411.62 | 404.586-412.586 | 408.075-416.075 | 409.281-417.281 | 413.699-421.699 | 415.249-423.249 |
| 5 | B | C | A#v/Bb^ | B#v/Cb^ | 504.525-514.525 | 505.733-515.733 | 510.093-520.093 | 511.602-521.602 | 517.123-527.123 | 519.061-529.061 |
| 6 | B#/Hb | C#/Qb | B | C | 605.43-617.43 | 606.879-618.879 | 612.112-624.112 | 613.922-625.922 | 620.548-632.548 | 622.873-634.873 |
| 7 | H | Q | Cb | Db | 706.335-720.335 | 708.026-722.026 | 714.131-728.131 | 716.242-730.242 | 723.973-737.973 | 726.685-740.685 |
| 8 | C | D | H# | Q# | 807.24-823.24 | 809.172-825.172 | 816.1495-832.1495 | 818.563-834.563 | 827.3975-843.3975 | 830.497-846.497 |
| 9 | C#/Db | D#/Eb | Db | Eb | 908.145-926.145 | 910.319-928.319 | 918.168-936.168 | 920.883-938.883 | 930.822-948.822 | 934.309-952.309 |
| 10 | D | E | C# | D# | 1009.0505-1029.0505 | 1011.465-1031.465 | 1020.186-1040.186 | 1023.2035-1043.2035 | 1034.247-1054.2547 | 1038.122-1058.122 |
| 11 | D#/Eb | E#/Fb | Eb | Fb | 1109.9555-1131.9555 | 1112.61-1134.612 | 1122.2055-1143.2055 | 1125.524-1147.524 | 1137.672-1159.672 | 1141.934-1163.934 |
| 12 | E | F | D# | E# | 1210.861-1234.861 | 1213.758-1227.758 | 1224.224-1248.224 | 1225.844-1249.884 | 1241.096-1265.096 | 1245.746-1269.746 |
| 13 | F | G | F | G | 1311.767-1337.767 | 1314.905-1340.905 | 1326.243-1352.243 | 1343.1645-1396.1645 | 1344.521-1370.521 | 1349.558-1375.558 |
| Degrees | Octatonic | Aeolian | Intense Aeolian | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Flattone | Meantone | Superpyth | Ultrapyth | |||||||
| Min-Med | Med-Max~Min-Max | Min-Med/Min-Max | Med-Max | Min-Med | Min-Max/Med-Max | Min-Med/Min-Max | Med-Max | |||
| Natural | Subset of 26edn | |||||||||
| 1 | F#/Gb | F#v/Gb^ | 105.256-107.256 | 105.625-108.015 | 106.156-108.156 | 107.435-109.435 | 107.738-109.738 | 108.459-110.459 | 108.802-110.802 | |
| 2 | G | 210.511-214.511 | 211.25-216.03 | 212.313-216.313 | 214.8705-218.8705 | 215.4765-219.4765 | 216.918-220.918 | 217.604-221.604 | ||
| 3 | G#/Ab | G#v/Ab^ | 315.767-321.767 | 316.875-324.044 | 318.469-324.469 | 321.306-329.306 | 322.215-330.215 | 325.377-331.377 | 326.4065-332.4065 | |
| 4 | A | 421.022-429.022 | 422.501-432.059 | 424.626-432.626 | 429.741-437.741 | 430.953-438.953 | 433.836-437.836 | 435.209-443.209 | ||
| 5 | B | A#v/Bb^ | 526.278-536.278 | 528.126-540.074 | 530.782-540.782 | 547.176-547.176 | 538.6915-548.6915 | 542.295-552.295 | 544.011-554.011 | |
| 6 | B#/Hb | B | 631.534-643.534 | 633.751-648.089 | 636.9385-648.9385 | 644.611-656.611 | 646.43-658.43 | 650.754-666.754 | 652.813-664.813 | |
| 7 | H | Cb | 736.789-750.789 | 739.376-756.104 | 743.095-757.095 | 752.047-766.047 | 754.168-768.168 | 759.213-773.213 | 761.615-775.615 | |
| 8 | C | H# | 842.045-858.045 | 845.001-864.1185 | 849.251-865.521 | 859.482-875.482 | 861.906-877.906 | 867.672-883.672 | 870.417-886.417 | |
| 9 | C#/Db | Db | 947.3-965.3 | 950.626-972.133 | 958.408-976.408 | 966.917-984.917 | 969.645-986.645 | 976.131-994.131 | 979.219-997.219 | |
| 10 | D | C# | 1052.556-1072.556 | 1056.2515-1080.148 | 1061.564-1081.564 | 1074.352-1094.352 | 1077.383-1077.383 | 1084.59-1104.59 | 1088.022-1108.022 | |
| 11 | D#/Eb | Eb | 1157.8115-1179.8115 | 1161.877-1188.163 | 1167.7205-1189.7205 | 1181.7875-1203.7875 | 1185.121-1207.121 | 1193.049-1215.049 | 1196.824-1218.824 | |
| 12 | E | D# | 1264.067-1287.067 | 1267.502-1296.178 | 1273.877-1298.877 | 1288.223-1312.223 | 1292.86-1316.86 | 1301.508-1325.508 | 1304.626-1328-626 | |
| 13 | F | 1368.323-1394.323 | 1373.127-1404.193 | 1380.033-1406.033 | 1396.658-1422.658 | 1400.598-1426.598 | 1409.967-1435.967 | 1414.428-1440.428 | ||
See also
13ed33/16 - equal division of the harmonic subminor ninth
13ed44/21 - equal division of the Neogothic minor ninth
13ed21/10 - equal division of the septimal chromatic minor ninth
13ed15/7 - equal division of the septimal diatonic minor ninth
13ed11/5 - equal division of the undecimal neutral ninth
13ed9/4 - equal division of the classic major ninth