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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 | |||
| | |||
|96. | |||
| | |||
|- | |- | ||
| | |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¢ | |||
|} | |||
Golden/Pyrite Tunings±13¢ | |||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! rowspan=" | ! rowspan="4" |Degrees | ||
! rowspan="3" |Octatonic | ! colspan="2" rowspan="3" |Octatonic | ||
! colspan="2" |Soft Phrygian | ! colspan="2" |Soft Phrygian | ||
! colspan="4" |Phrygian | ! colspan="4" |Phrygian | ||
|- | |- | ||
! rowspan=" | ! rowspan="3" |Min-Med | ||
! rowspan=" | ! rowspan="3" |Min-Max/Med-Max | ||
! colspan="2" |Thirdtone | ! colspan="2" |Thirdtone | ||
! colspan="2" |Semitone | ! colspan="2" |Semitone | ||
|- | |- | ||
!Min-Med/Min-Max | ! rowspan="2" |Min-Med/Min-Max | ||
!Med-Max | ! rowspan="2" |Med-Max | ||
!Min-Med/Min-Max | ! rowspan="2" |Min-Med/Min-Max | ||
!Med-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 | ||
| Line 578: | Line 166: | ||
|- | |- | ||
| |2 | | |2 | ||
| |A | | colspan="2" |A | ||
|190.778-194.778 | |190.778-194.778 | ||
|191.155-195.155 | |191.155-195.155 | ||
| Line 588: | Line 176: | ||
| |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 | ||
| Line 596: | Line 185: | ||
|- | |- | ||
| |4 | | |4 | ||
| |B | | colspan="2" |B | ||
|381.555-389.555 | |381.555-389.555 | ||
|382.3105-390.3105 | |382.3105-390.3105 | ||
| Line 606: | Line 195: | ||
| |5 | | |5 | ||
| |C | | |C | ||
|B#v/Cb^ | |||
|476.944-486.944 | |476.944-486.944 | ||
|477.888-487.888 | |477.888-487.888 | ||
| Line 615: | Line 205: | ||
| |6 | | |6 | ||
| |C#/Qb | | |C#/Qb | ||
|C | |||
|572.333-584.333 | |572.333-584.333 | ||
|573.466-585.466 | |573.466-585.466 | ||
| Line 624: | Line 215: | ||
| |7 | | |7 | ||
| |Q | | |Q | ||
|Db | |||
|667.722-681.722 | |667.722-681.722 | ||
|669.043-683.043 | |669.043-683.043 | ||
| Line 633: | Line 225: | ||
| |8 | | |8 | ||
| |D | | |D | ||
|Q# | |||
|763.111-781.111 | |763.111-781.111 | ||
|764.621-780.621 | |764.621-780.621 | ||
| Line 642: | Line 235: | ||
| |9 | | |9 | ||
| |D#/Eb | | |D#/Eb | ||
|Eb | |||
|858.5-876.5 | |858.5-876.5 | ||
|860.199-878.199 | |860.199-878.199 | ||
| Line 651: | Line 245: | ||
| |10 | | |10 | ||
| |E | | |E | ||
|D# | |||
|953.8885-973.8885 | |953.8885-973.8885 | ||
|955.776-975.776 | |955.776-975.776 | ||
| Line 660: | Line 255: | ||
| |11 | | |11 | ||
| |E#/Fb | | |E#/Fb | ||
|Fb | |||
|1049.277-1071.277 | |1049.277-1071.277 | ||
|1051.354-1073.354 | |1051.354-1073.354 | ||
| Line 669: | Line 265: | ||
| |12 | | |12 | ||
| |F | | |F | ||
|E# | |||
|1144.666-1168.666 | |1144.666-1168.666 | ||
|1146.932-1170.932 | |1146.932-1170.932 | ||
| Line 677: | Line 274: | ||
|- | |- | ||
| |13 | | |13 | ||
| |G | | colspan="2" |G | ||
|1240.055-1266.055 | |1240.055-1266.055 | ||
|1242.506-1268.509 | |1242.506-1268.509 | ||
| Line 688: | Line 285: | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! rowspan=" | ! rowspan="3" |Degrees | ||
! colspan=" | ! colspan="4" rowspan="2" |Octatonic | ||
! colspan="2" |Intense Phrygian | ! colspan="2" |Intense Phrygian | ||
! colspan=" | ! colspan="2" |Intense Phrygian-Soft Aeolian | ||
! colspan=" | ! colspan="2" |Soft Aeolian | ||
|- | |- | ||
!Min-Med/Min-Max | ! rowspan="2" |Min-Med/Min-Max | ||
!Med-Max | ! rowspan="2" |Med-Max | ||
!Min-Med/Min- | ! rowspan="2" |Min-Med/Min-Max | ||
! rowspan="2" |Med-Max | |||
!Med- | ! rowspan="2" |Min-Med/Min-Max | ||
! rowspan="2" |Med-Max | |||
|- | |||
!Min-Med/Min- | ! 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 | ||
|102.019-104.019 | |102.019-104.019 | ||
|102.32-104.32 | |102.32-104.32 | ||
|103.425-105.425 | |103.425-105.425 | ||
|103.812-105.812 | |103.812-105.812 | ||
|- | |- | ||
| |2 | | |2 | ||
| |G | | |G | ||
|A | |||
|G | |||
|A | |A | ||
|201.81-205.81 | |201.81-205.81 | ||
|202.293-206.293 | |202.293-206.293 | ||
|204.037-208.037 | |204.037-208.037 | ||
|204.641-208.641 | |204.641-208.641 | ||
|206.849-210.849 | |206.849-210.849 | ||
|207.624-211.624 | |207.624-211.624 | ||
|- | |- | ||
| |3 | | |3 | ||
| |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 | ||
|306.056-312.056 | |306.056-312.056 | ||
|306.961-312.961 | |306.961-312.961 | ||
|310.274-316.274 | |310.274-316.274 | ||
|311.4365-317.4365 | |311.4365-317.4365 | ||
|- | |- | ||
| |4 | | |4 | ||
| |A | | |A | ||
|B | |||
|A | |||
|B | |B | ||
|403.62-411.62 | |403.62-411.62 | ||
|404.586-412.586 | |404.586-412.586 | ||
|408.075-416.075 | |408.075-416.075 | ||
|409.281-417.281 | |409.281-417.281 | ||
|413.699-421.699 | |413.699-421.699 | ||
|415.249-423.249 | |415.249-423.249 | ||
|- | |- | ||
| |5 | | |5 | ||
| |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 | ||
|510.093-520.093 | |510.093-520.093 | ||
|511.602-521.602 | |511.602-521.602 | ||
|517.123-527.123 | |517.123-527.123 | ||
|519.061-529.061 | |519.061-529.061 | ||
|- | |- | ||
| |6 | | |6 | ||
| |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 | ||
|612.112-624.112 | |612.112-624.112 | ||
|613.922-625.922 | |613.922-625.922 | ||
|620.548-632.548 | |620.548-632.548 | ||
|622.873-634.873 | |622.873-634.873 | ||
|- | |- | ||
| |7 | | |7 | ||
| |H | | |H | ||
|Q | |Q | ||
|Cb | |||
|Db | |||
|706.335-720.335 | |706.335-720.335 | ||
|708.026-722.026 | |708.026-722.026 | ||
|714.131-728.131 | |714.131-728.131 | ||
|716.242-730.242 | |716.242-730.242 | ||
|723.973-737.973 | |723.973-737.973 | ||
|726.685-740.685 | |726.685-740.685 | ||
|- | |- | ||
| |8 | | |8 | ||
| |C | | |C | ||
|D | |D | ||
|H# | |||
|Q# | |||
|807.24-823.24 | |807.24-823.24 | ||
|809.172-825.172 | |809.172-825.172 | ||
|816.1495-832.1495 | |816.1495-832.1495 | ||
|818.563-834.563 | |818.563-834.563 | ||
|827.3975-843.3975 | |827.3975-843.3975 | ||
|830.497-846.497 | |830.497-846.497 | ||
|- | |- | ||
| |9 | | |9 | ||
| |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 | ||
|918.168-936.168 | |918.168-936.168 | ||
|920.883-938.883 | |920.883-938.883 | ||
|930.822-948.822 | |930.822-948.822 | ||
|934.309-952.309 | |934.309-952.309 | ||
|- | |- | ||
| |10 | | |10 | ||
| |D | | |D | ||
|E | |E | ||
|C# | |||
|D# | |||
|1009.0505-1029.0505 | |1009.0505-1029.0505 | ||
|1011.465-1031.465 | |1011.465-1031.465 | ||
|1020.186-1040.186 | |1020.186-1040.186 | ||
|1023.2035-1043.2035 | |1023.2035-1043.2035 | ||
|1034.247-1054.2547 | |1034.247-1054.2547 | ||
|1038.122-1058.122 | |1038.122-1058.122 | ||
|- | |- | ||
| |11 | | |11 | ||
| |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 | ||
|1122.2055-1143.2055 | |1122.2055-1143.2055 | ||
|1125.524-1147.524 | |1125.524-1147.524 | ||
|1137.672-1159.672 | |1137.672-1159.672 | ||
|1141.934-1163.934 | |1141.934-1163.934 | ||
|- | |- | ||
| |12 | | |12 | ||
| |E | | |E | ||
|F | |F | ||
|D# | |||
|E# | |||
|1210.861-1234.861 | |1210.861-1234.861 | ||
|1213.758-1227.758 | |1213.758-1227.758 | ||
|1224.224-1248.224 | |1224.224-1248.224 | ||
|1225.844-1249.884 | |1225.844-1249.884 | ||
|1241.096-1265.096 | |1241.096-1265.096 | ||
|1245.746-1269.746 | |1245.746-1269.746 | ||
|- | |- | ||
| |13 | | |13 | ||
| |F | | |F | ||
|G | |||
|F | |||
|G | |G | ||
|1311.767-1337.767 | |1311.767-1337.767 | ||
|1314.905-1340.905 | |1314.905-1340.905 | ||
|1326.243-1352.243 | |1326.243-1352.243 | ||
|1343.1645-1396.1645 | |1343.1645-1396.1645 | ||
|1344.521-1370.521 | |1344.521-1370.521 | ||
|1349.558-1375.558 | |1349.558-1375.558 | ||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan=" | ! rowspan="4" |Degrees | ||
! rowspan="3" |Octatonic | ! colspan="2" rowspan="3" |Octatonic | ||
! colspan="4" |Aeolian | ! colspan="4" |Aeolian | ||
! colspan="4" |Intense Aeolian | ! colspan="4" |Intense Aeolian | ||
| Line 900: | Line 469: | ||
! colspan="2" |Ultrapyth | ! colspan="2" |Ultrapyth | ||
|- | |- | ||
!Min-Med | ! rowspan="2" |Min-Med | ||
!Med-Max~Min-Max | ! rowspan="2" |Med-Max~Min-Max | ||
!Min-Med/Min-Max | ! rowspan="2" |Min-Med/Min-Max | ||
!Med-Max | ! rowspan="2" |Med-Max | ||
!Min-Med | ! rowspan="2" |Min-Med | ||
!Min-Max/Med-Max | ! rowspan="2" |Min-Max/Med-Max | ||
!Min-Med/Min-Max | ! rowspan="2" |Min-Med/Min-Max | ||
!Med-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 | ||
| colspan="2" |105.625-108.015 | | colspan="2" |105.625-108.015 | ||
| Line 920: | Line 493: | ||
|- | |- | ||
| |2 | | |2 | ||
| |G | | colspan="2" |G | ||
|210.511-214.511 | |210.511-214.511 | ||
| colspan="2" |211.25-216.03 | | colspan="2" |211.25-216.03 | ||
| Line 931: | Line 504: | ||
| |3 | | |3 | ||
| |G#/Ab | | |G#/Ab | ||
|G#v/Ab^ | |||
|315.767-321.767 | |315.767-321.767 | ||
| colspan="2" |316.875-324.044 | | colspan="2" |316.875-324.044 | ||
| Line 940: | Line 514: | ||
|- | |- | ||
| |4 | | |4 | ||
| |A | | colspan="2" |A | ||
|421.022-429.022 | |421.022-429.022 | ||
| colspan="2" |422.501-432.059 | | colspan="2" |422.501-432.059 | ||
| Line 951: | Line 525: | ||
| |5 | | |5 | ||
| |B | | |B | ||
|A#v/Bb^ | |||
|526.278-536.278 | |526.278-536.278 | ||
| colspan="2" |528.126-540.074 | | colspan="2" |528.126-540.074 | ||
| Line 961: | Line 536: | ||
| |6 | | |6 | ||
| |B#/Hb | | |B#/Hb | ||
|B | |||
|631.534-643.534 | |631.534-643.534 | ||
| colspan="2" |633.751-648.089 | | colspan="2" |633.751-648.089 | ||
| Line 971: | Line 547: | ||
| |7 | | |7 | ||
| |H | | |H | ||
|Cb | |||
|736.789-750.789 | |736.789-750.789 | ||
| colspan="2" |739.376-756.104 | | colspan="2" |739.376-756.104 | ||
| Line 981: | Line 558: | ||
| |8 | | |8 | ||
| |C | | |C | ||
|H# | |||
|842.045-858.045 | |842.045-858.045 | ||
| colspan="2" |845.001-864.1185 | | colspan="2" |845.001-864.1185 | ||
| Line 991: | Line 569: | ||
| |9 | | |9 | ||
| |C#/Db | | |C#/Db | ||
|Db | |||
|947.3-965.3 | |947.3-965.3 | ||
| colspan="2" |950.626-972.133 | | colspan="2" |950.626-972.133 | ||
| Line 1,001: | Line 580: | ||
| |10 | | |10 | ||
| |D | | |D | ||
|C# | |||
|1052.556-1072.556 | |1052.556-1072.556 | ||
| colspan="2" |1056.2515-1080.148 | | colspan="2" |1056.2515-1080.148 | ||
| Line 1,011: | Line 591: | ||
| |11 | | |11 | ||
| |D#/Eb | | |D#/Eb | ||
|Eb | |||
|1157.8115-1179.8115 | |1157.8115-1179.8115 | ||
| colspan="2" |1161.877-1188.163 | | colspan="2" |1161.877-1188.163 | ||
| Line 1,021: | Line 602: | ||
| |12 | | |12 | ||
| |E | | |E | ||
|D# | |||
|1264.067-1287.067 | |1264.067-1287.067 | ||
| colspan="2" |1267.502-1296.178 | | colspan="2" |1267.502-1296.178 | ||
| Line 1,030: | Line 612: | ||
|- | |- | ||
| |13 | | |13 | ||
| |F | | colspan="2" |F | ||
|1368.323-1394.323 | |1368.323-1394.323 | ||
| colspan="2" |1373.127-1404.193 | | colspan="2" |1373.127-1404.193 | ||
| Line 1,039: | Line 621: | ||
|1414.428-1440.428 | |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 | |||