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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. | 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 [[Orwellismic temperaments #Triskaidekic|Triskaidekic]], [[Octagar temperaments #Tridecatonic|tridecatonic]], [[Ragismic microtemperaments #Trideci|trideci]] and [[aluminium]] temperaments. | ||
==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable" | ||
|+ | |||
!Nonet | |||
!Period | |||
!Notes | |||
|- | |- | ||
|1/1 | |||
|''92.308'' | |||
|Soft Phrygian mode begins | |||
|- | |- | ||
|25\24 | |||
|''96.154'' | |||
| | |||
|- | |- | ||
| | |24\23 | ||
| | |96.321 | ||
| | |||
| | |- | ||
| | |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 | |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 | |||
| | |109.091 | ||
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins | |||
| | |||
|- | |- | ||
|19\16 | |||
|109.615 | |||
| | |||
|- | |- | ||
| | |6\5 | ||
|110.769 | |110.769 | ||
|Ultrapyth Intense Aeolian mode ends | |||
|}Golden/Pyrite Tunings±13¢ | |||
{| class="wikitable" | |||
|- | |- | ||
! rowspan="4" |Degrees | |||
! colspan="2" rowspan="3" |Octatonic | |||
! colspan="2" |Soft Phrygian | |||
! colspan="4" |Phrygian | |||
| | |||
| | |||
|- | |- | ||
| | ! rowspan="3" |Min-Med | ||
| | ! rowspan="3" |Min-Max/Med-Max | ||
! colspan="2" |Thirdtone | |||
! colspan="2" |Semitone | |||
|- | |- | ||
! rowspan="2" | | ! rowspan="2" |Min-Med/Min-Max | ||
! rowspan="2" | | ! rowspan="2" |Med-Max | ||
! | ! rowspan="2" |Min-Med/Min-Max | ||
! | ! rowspan="2" |Med-Max | ||
|- | |- | ||
! | !Natural | ||
! | !Subset of 26edn | ||
|- | |- | ||
| |1 | | |1 | ||
| |G#/Ab | | |G#/Ab | ||
|G#v/Ab^ | |||
|95.389-97.389 | |95.389-97.389 | ||
|95.578-97.578 | |95.578-97.578 | ||
| | |95.957-98.345 | ||
| | |96.785-98.844 | ||
|98.359-100. | |98.359-100.709 | ||
|99.058-101.523 | |||
|- | |- | ||
| |2 | | |2 | ||
| |A | | colspan="2" |A | ||
|190.778-194.778 | |190.778-194.778 | ||
|191.155-195.155 | |191.155-195.155 | ||
|193. | |191.914-196.689 | ||
| | |193.569-197.688 | ||
| | |196.719-201.417 | ||
|198.1165-203.046 | |||
|- | |- | ||
| |3 | | |3 | ||
| |A#/Bb | | |A#/Bb | ||
|A#v/Bb^ | |||
|286.1665-292.1665 | |286.1665-292.1665 | ||
|286.733-292.733 | |286.733-292.733 | ||
|290. | |287.871-295.034 | ||
| | |290.354-296.531 | ||
| | |295.078-302.126 | ||
|297.175-304.569 | |||
|- | |- | ||
| |4 | | |4 | ||
| |B | | colspan="2" |B | ||
|381.555-389.555 | |381.555-389.555 | ||
|382.3105-390.3105 | |382.3105-390.3105 | ||
|387. | |383.828-393.378 | ||
| | |387.138-395.375 | ||
| | |393.4375-402.835 | ||
|396.233-406.092 | |||
|- | |- | ||
| |5 | | |5 | ||
| |C | | |C | ||
|B#v/Cb^ | |||
|476.944-486.944 | |476.944-486.944 | ||
|477.888-487.888 | |477.888-487.888 | ||
| | |479.785-491.723 | ||
| | |483.923-494.219 | ||
|491.797- | |491.797-503.544 | ||
|495.291-507.615 | |||
|- | |- | ||
| |6 | | |6 | ||
| |C#/Qb | | |C#/Qb | ||
|C | |||
|572.333-584.333 | |572.333-584.333 | ||
|573.466-585.466 | |573.466-585.466 | ||
| | |575.742-590.068 | ||
| | |580.707-593.063 | ||
|590.156- | |590.156-604.253 | ||
|594.349-609.138 | |||
|- | |- | ||
| |7 | | |7 | ||
| |Q | | |Q | ||
|Db | |||
|667.722-681.722 | |667.722-681.722 | ||
|669.043-683.043 | |669.043-683.043 | ||
|677. | |671.699-688.412 | ||
| | |677.492-691.907 | ||
| | |688.516-704.962 | ||
|693.408-710.661 | |||
|- | |- | ||
| |8 | | |8 | ||
| |D | | |D | ||
|Q# | |||
|763.111-781.111 | |763.111-781.111 | ||
|764.621-780.621 | |764.621-780.621 | ||
|774. | |767.656-786.757 | ||
| | |774.2765-790.75 | ||
| | |786.875-805.67 | ||
|792.466-812.184 | |||
|- | |- | ||
| |9 | | |9 | ||
| |D#/Eb | | |D#/Eb | ||
|Eb | |||
|858.5-876.5 | |858.5-876.5 | ||
|860.199-878.199 | |860.199-878.199 | ||
| | |863.613-885.1015 | ||
| | |871.061-889.594 | ||
|885.234- | |885.234-906.379 | ||
|891.524-913.707 | |||
|- | |- | ||
| |10 | | |10 | ||
| |E | | |E | ||
|D# | |||
|953.8885-973.8885 | |953.8885-973.8885 | ||
|955.776-975.776 | |955.776-975.776 | ||
| | |959.57-983.446 | ||
| | |967.846-988.438 | ||
|983.594- | |983.594-1007.088 | ||
|990.582-1015.23 | |||
|- | |- | ||
| |11 | | |11 | ||
| |E#/Fb | | |E#/Fb | ||
|Fb | |||
|1049.277-1071.277 | |1049.277-1071.277 | ||
|1051.354-1073.354 | |1051.354-1073.354 | ||
| | |1055.527-1081.791 | ||
| | |1064.63-1087.282 | ||
|1081.953- | |1081.953-1107.797 | ||
|1089.641-1116.75 | |||
|- | |- | ||
| |12 | | |12 | ||
| |F | | |F | ||
|E# | |||
|1144.666-1168.666 | |1144.666-1168.666 | ||
|1146.932-1170.932 | |1146.932-1170.932 | ||
| | |1151.484-1180.135 | ||
| | |1161.415-1186.126 | ||
|1180.312- | |1180.312-1208.506 | ||
|1188.699-1218.276 | |||
|- | |- | ||
| |13 | | |13 | ||
| |G | | colspan="2" |G | ||
|1240.055-1266.055 | |1240.055-1266.055 | ||
|1242.506-1268.509 | |1242.506-1268.509 | ||
| | |1247.441-1278.48 | ||
| | |1258.199-1284.969 | ||
|1278.672- | |1278.672-1309.2145 | ||
|1287.757-1319.799 | |||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! rowspan=" | ! rowspan="3" |Degrees | ||
! colspan=" | ! colspan="4" rowspan="2" |Octatonic | ||
! colspan="2" |Intense Phrygian | ! colspan="2" |Intense Phrygian | ||
! colspan="2" |Intense Phrygian-Soft Aeolian | ! colspan="2" |Intense Phrygian-Soft Aeolian | ||
! colspan="2" |Soft Aeolian | ! colspan="2" |Soft Aeolian | ||
|- | |- | ||
!Min-Med/Min- | ! rowspan="2" |Min-Med/Min-Max | ||
!Med- | ! rowspan="2" |Med-Max | ||
!Min-Med/Min- | ! rowspan="2" |Min-Med/Min-Max | ||
!Med- | ! rowspan="2" |Med-Max | ||
!Min-Med/Min- | ! rowspan="2" |Min-Med/Min-Max | ||
!Med- | ! rowspan="2" |Med-Max | ||
|- | |||
! colspan="2" |Natural | |||
! colspan="2" |Subset of 26edn | |||
|- | |- | ||
| |1 | | |1 | ||
| |F#/Gb | | |F#/Gb | ||
|G#/Ab | |G#/Ab | ||
|F#v/Gb^ | |||
|G#v/Ab^ | |||
|100.905-102.905 | |100.905-102.905 | ||
|101.1465-103.1465 | |101.1465-103.1465 | ||
| Line 589: | Line 315: | ||
| |2 | | |2 | ||
| |G | | |G | ||
|A | |||
|G | |||
|A | |A | ||
|201.81-205.81 | |201.81-205.81 | ||
| Line 600: | Line 328: | ||
| |G#/Ab | | |G#/Ab | ||
|A#/Bb | |A#/Bb | ||
|G#v/Ab^ | |||
|A#v/Bb^ | |||
|302.715-308.715 | |302.715-308.715 | ||
|303.44-309.44 | |303.44-309.44 | ||
| Line 609: | Line 339: | ||
| |4 | | |4 | ||
| |A | | |A | ||
|B | |||
|A | |||
|B | |B | ||
|403.62-411.62 | |403.62-411.62 | ||
| Line 620: | Line 352: | ||
| |B | | |B | ||
|C | |C | ||
|A#v/Bb^ | |||
|B#v/Cb^ | |||
|504.525-514.525 | |504.525-514.525 | ||
|505.733-515.733 | |505.733-515.733 | ||
| Line 630: | Line 364: | ||
| |B#/Hb | | |B#/Hb | ||
|C#/Qb | |C#/Qb | ||
|B | |||
|C | |||
|605.43-617.43 | |605.43-617.43 | ||
|606.879-618.879 | |606.879-618.879 | ||
| Line 640: | Line 376: | ||
| |H | | |H | ||
|Q | |Q | ||
|Cb | |||
|Db | |||
|706.335-720.335 | |706.335-720.335 | ||
|708.026-722.026 | |708.026-722.026 | ||
| Line 650: | Line 388: | ||
| |C | | |C | ||
|D | |D | ||
|H# | |||
|Q# | |||
|807.24-823.24 | |807.24-823.24 | ||
|809.172-825.172 | |809.172-825.172 | ||
| Line 660: | Line 400: | ||
| |C#/Db | | |C#/Db | ||
|D#/Eb | |D#/Eb | ||
|Db | |||
|Eb | |||
|908.145-926.145 | |908.145-926.145 | ||
|910.319-928.319 | |910.319-928.319 | ||
| Line 670: | Line 412: | ||
| |D | | |D | ||
|E | |E | ||
|C# | |||
|D# | |||
|1009.0505-1029.0505 | |1009.0505-1029.0505 | ||
|1011.465-1031.465 | |1011.465-1031.465 | ||
| Line 680: | Line 424: | ||
| |D#/Eb | | |D#/Eb | ||
|E#/Fb | |E#/Fb | ||
|Eb | |||
|Fb | |||
|1109.9555-1131.9555 | |1109.9555-1131.9555 | ||
|1112.61-1134.612 | |1112.61-1134.612 | ||
| Line 690: | Line 436: | ||
| |E | | |E | ||
|F | |F | ||
|D# | |||
|E# | |||
|1210.861-1234.861 | |1210.861-1234.861 | ||
|1213.758-1227.758 | |1213.758-1227.758 | ||
| Line 699: | Line 447: | ||
| |13 | | |13 | ||
| |F | | |F | ||
|G | |||
|F | |||
|G | |G | ||
|1311.767-1337.767 | |1311.767-1337.767 | ||
| Line 707: | Line 457: | ||
|1349.558-1375.558 | |1349.558-1375.558 | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan=" | ! rowspan="4" |Degrees | ||
! rowspan=" | ! colspan="2" rowspan="3" |Octatonic | ||
! colspan=" | ! colspan="4" |Aeolian | ||
! colspan=" | ! colspan="4" |Intense Aeolian | ||
|- | |||
! colspan="2" |Flattone | |||
! colspan="2" |Meantone | |||
! colspan="2" |Superpyth | |||
! colspan="2" |Ultrapyth | |||
|- | |||
! rowspan="2" |Min-Med | |||
! rowspan="2" |Med-Max~Min-Max | |||
! rowspan="2" |Min-Med/Min-Max | |||
! rowspan="2" |Med-Max | |||
! rowspan="2" |Min-Med | |||
! rowspan="2" |Min-Max/Med-Max | |||
! rowspan="2" |Min-Med/Min-Max | |||
! rowspan="2" |Med-Max | |||
|- | |- | ||
! | !Natural | ||
! | !Subset of 26edn | ||
|- | |- | ||
| |1 | | |1 | ||
| |F#/Gb | | |F#/Gb | ||
|F#v/Gb^ | |||
|105.256-107.256 | |105.256-107.256 | ||
|105. | | colspan="2" |105.625-108.015 | ||
|106.156-108.156 | |||
|107.435-109.435 | |||
|107.738-109.738 | |107.738-109.738 | ||
|108.459-110.459 | |108.459-110.459 | ||
|108.802-110.802 | |||
|- | |- | ||
| |2 | | |2 | ||
| |G | | colspan="2" |G | ||
|210.511-214.511 | |210.511-214.511 | ||
|211. | | colspan="2" |211.25-216.03 | ||
|215. | |212.313-216.313 | ||
|214.8705-218.8705 | |||
|215.4765-219.4765 | |||
|216.918-220.918 | |216.918-220.918 | ||
|217.604-221.604 | |||
|- | |- | ||
| |3 | | |3 | ||
| |G#/Ab | | |G#/Ab | ||
|G#v/Ab^ | |||
|315.767-321.767 | |315.767-321.767 | ||
| | | colspan="2" |316.875-324.044 | ||
| | |318.469-324.469 | ||
|321.306-329.306 | |||
|322.215-330.215 | |||
|325.377-331.377 | |325.377-331.377 | ||
|326.4065-332.4065 | |||
|- | |- | ||
| |4 | | |4 | ||
| |A | | colspan="2" |A | ||
|421.022-429.022 | |421.022-429.022 | ||
| | | colspan="2" |422.501-432.059 | ||
|424.626-432.626 | |||
|429.741-437.741 | |||
|430.953-438.953 | |430.953-438.953 | ||
|433.836-437.836 | |433.836-437.836 | ||
|435.209-443.209 | |||
|- | |- | ||
| |5 | | |5 | ||
| |B | | |B | ||
|A#v/Bb^ | |||
|526.278-536.278 | |526.278-536.278 | ||
|528. | | colspan="2" |528.126-540.074 | ||
|530.782-540.782 | |||
|547.176-547.176 | |||
|538.6915-548.6915 | |538.6915-548.6915 | ||
|542.295-552.295 | |542.295-552.295 | ||
|544.011-554.011 | |||
|- | |- | ||
| |6 | | |6 | ||
| |B#/Hb | | |B#/Hb | ||
|B | |||
|631.534-643.534 | |631.534-643.534 | ||
| | | colspan="2" |633.751-648.089 | ||
|636.9385-648.9385 | |||
|644.611-656.611 | |||
|646.43-658.43 | |646.43-658.43 | ||
|650.754-666.754 | |650.754-666.754 | ||
|652.813-664.813 | |||
|- | |- | ||
| |7 | | |7 | ||
| |H | | |H | ||
|Cb | |||
|736.789-750.789 | |736.789-750.789 | ||
| | | colspan="2" |739.376-756.104 | ||
|743.095-757.095 | |||
|752.047-766.047 | |||
|754.168-768.168 | |754.168-768.168 | ||
|759.213-773.213 | |759.213-773.213 | ||
|761.615-775.615 | |||
|- | |- | ||
| |8 | | |8 | ||
| |C | | |C | ||
|H# | |||
|842.045-858.045 | |842.045-858.045 | ||
| | | colspan="2" |845.001-864.1185 | ||
|849.251-865.521 | |||
|859.482-875.482 | |||
|861.906-877.906 | |861.906-877.906 | ||
|867.672-883.672 | |867.672-883.672 | ||
|870.417-886.417 | |||
|- | |- | ||
| |9 | | |9 | ||
| |C#/Db | | |C#/Db | ||
|Db | |||
|947.3-965.3 | |947.3-965.3 | ||
| | | colspan="2" |950.626-972.133 | ||
|958.408-976.408 | |||
|966.917-984.917 | |||
|969.645-986.645 | |969.645-986.645 | ||
|976.131-994.131 | |976.131-994.131 | ||
|979.219-997.219 | |||
|- | |- | ||
| |10 | | |10 | ||
| |D | | |D | ||
|C# | |||
|1052.556-1072.556 | |1052.556-1072.556 | ||
| | | colspan="2" |1056.2515-1080.148 | ||
|1061.564-1081.564 | |||
|1074.352-1094.352 | |||
|1077.383-1077.383 | |1077.383-1077.383 | ||
|1084.59-1104.59 | |1084.59-1104.59 | ||
|1088.022-1108.022 | |||
|- | |- | ||
| |11 | | |11 | ||
| |D#/Eb | | |D#/Eb | ||
|Eb | |||
|1157.8115-1179.8115 | |1157.8115-1179.8115 | ||
| | | colspan="2" |1161.877-1188.163 | ||
|1167.7205-1189.7205 | |||
|1181.7875-1203.7875 | |||
|1185.121-1207.121 | |1185.121-1207.121 | ||
|1193.049-1215.049 | |1193.049-1215.049 | ||
|1196.824-1218.824 | |||
|- | |- | ||
| |12 | | |12 | ||
| |E | | |E | ||
|D# | |||
|1264.067-1287.067 | |1264.067-1287.067 | ||
| | | colspan="2" |1267.502-1296.178 | ||
|1273.877-1298.877 | |||
|1288.223-1312.223 | |||
|1292.86-1316.86 | |1292.86-1316.86 | ||
|1301.508-1325.508 | |1301.508-1325.508 | ||
|1304.626-1328-626 | |||
|- | |- | ||
| |13 | | |13 | ||
| |F | | colspan="2" |F | ||
|1368. | |1368.323-1394.323 | ||
| | | colspan="2" |1373.127-1404.193 | ||
|1380.033-1406.033 | |||
|1396.658-1422.658 | |||
|1400.598-1426.598 | |1400.598-1426.598 | ||
|1409.967-1435.967 | |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 | |||