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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== | ||
{| 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 | |||
| | |||
|- | |||
|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 | |||
|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" |Min-Med/Min-Max | |||
! rowspan="2" |Med-Max | |||
! rowspan="2" |Min-Med/Min-Max | |||
! rowspan="2" |Med-Max | |||
|- | |||
!Natural | |||
!Subset of 26edn | |||
|- | |- | ||
| |1 | | |1 | ||
| | | | |G#/Ab | ||
| | |G#v/Ab^ | ||
|95.389-97.389 | |||
|95. | |95.578-97.578 | ||
|95.957-98.345 | |||
|96.785-98.844 | |||
| | |98.359-100.709 | ||
|99.058-101.523 | |||
| | |||
| | |||
|98. | |||
|- | |- | ||
| |2 | | |2 | ||
| | | | colspan="2" |A | ||
| | |190.778-194.778 | ||
|191.155-195.155 | |||
|191. | |191.914-196.689 | ||
|193.569-197.688 | |||
|196.719-201.417 | |||
|198.1165-203.046 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |3 | | |3 | ||
| | | | |A#/Bb | ||
| | |A#v/Bb^ | ||
|286.1665-292.1665 | |||
|286. | |286.733-292.733 | ||
|287.871-295.034 | |||
|290.354-296.531 | |||
| | |295.078-302.126 | ||
|297.175-304.569 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |4 | | |4 | ||
| | | | colspan="2" |B | ||
| | |381.555-389.555 | ||
|382.3105-390.3105 | |||
|382. | |383.828-393.378 | ||
|387.138-395.375 | |||
|393.4375-402.835 | |||
|396.233-406.092 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |5 | | |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 | | |6 | ||
| | | | |C#/Qb | ||
| | |C | ||
| | |572.333-584.333 | ||
|573. | |573.466-585.466 | ||
|575.742-590.068 | |||
|580.707-593.063 | |||
|590.156-604.253 | |||
|594.349-609.138 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |7 | | |7 | ||
| | | | |Q | ||
| | |Db | ||
| | |667.722-681.722 | ||
|669. | |669.043-683.043 | ||
|671.699-688.412 | |||
|677.492-691.907 | |||
|688.516-704.962 | |||
|693.408-710.661 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |8 | | |8 | ||
| | | | |D | ||
| | |Q# | ||
| | |763.111-781.111 | ||
|764. | |764.621-780.621 | ||
|767.656-786.757 | |||
|774.2765-790.75 | |||
|786.875-805.67 | |||
|792.466-812.184 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |9 | | |9 | ||
| | | | |D#/Eb | ||
| | |Eb | ||
| | |858.5-876.5 | ||
|860. | |860.199-878.199 | ||
|863.613-885.1015 | |||
|871.061-889.594 | |||
|885.234-906.379 | |||
|891.524-913.707 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |10 | | |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 | | |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 | | |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 | | |13 | ||
| | | | colspan="2" |G | ||
| | |1240.055-1266.055 | ||
|1242.506-1268.509 | |||
|1242. | |1247.441-1278.48 | ||
|1258.199-1284.969 | |||
|1278.672-1309.2145 | |||
| | |1287.757-1319.799 | ||
| | |||
| | |||
| | |||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
|- | |- | ||
! | | ! rowspan="3" |Degrees | ||
! | ! colspan="4" rowspan="2" |Octatonic | ||
! | ! colspan="2" |Intense Phrygian | ||
! | | ! colspan="2" |Intense Phrygian-Soft Aeolian | ||
! | ! colspan="2" |Soft Aeolian | ||
|- | |||
! | ! rowspan="2" |Min-Med/Min-Max | ||
! | | ! rowspan="2" |Med-Max | ||
! | ! rowspan="2" |Min-Med/Min-Max | ||
! | ! rowspan="2" |Med-Max | ||
! | | ! rowspan="2" |Min-Med/Min-Max | ||
! rowspan="2" |Med-Max | |||
! | |- | ||
! colspan="2" |Natural | |||
! colspan="2" |Subset of 26edn | |||
! | | |||
! | | |||
|- | |- | ||
| |1 | | |1 | ||
| |F#/Gb | | |F#/Gb | ||
| | |G#/Ab | ||
| | |F#v/Gb^ | ||
| | |G#v/Ab^ | ||
| | |100.905-102.905 | ||
|101.1465-103.1465 | |||
| | |102.019-104.019 | ||
|102. | |102.32-104.32 | ||
|103.425-105.425 | |||
|102. | |103.812-105.812 | ||
|103. | |||
|- | |- | ||
| |2 | | |2 | ||
| |G | | |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 | | |3 | ||
| |G#/Ab | | |G#/Ab | ||
| | | |A#/Bb | ||
| | |G#v/Ab^ | ||
| | |A#v/Bb^ | ||
|302.715-308.715 | |||
| | |303.44-309.44 | ||
|306.056-312.056 | |||
|306. | |306.961-312.961 | ||
|310.274-316.274 | |||
| | |311.4365-317.4365 | ||
|311. | |||
|- | |- | ||
| |4 | | |4 | ||
| |A | | |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 | | |5 | ||
| |B | | |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 | | |6 | ||
| |B#/Hb | | |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 | | |7 | ||
| |H | | |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 | | |8 | ||
| |C | | |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 | | |9 | ||
| |C#/Db | | |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 | | |10 | ||
| |D | | |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 | | |11 | ||
| |D#/Eb | | |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 | | |12 | ||
| |E | | |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 | | |13 | ||
| |F | | |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 | |||
| | |||
| | |||
| | |||
| | |||
|} | |} | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan=" | ! rowspan="4" |Degrees | ||
! rowspan=" | ! colspan="2" rowspan="3" |Octatonic | ||
! colspan=" | ! colspan="4" |Aeolian | ||
! 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 | ||
| |105. | |F#v/Gb^ | ||
|105.256-107.256 | |||
| | | | colspan="2" |105.625-108.015 | ||
| | |106.156-108.156 | ||
|107.435-109.435 | |||
|107.738-109.738 | |||
|108.459-110.459 | |||
|108. | |108.802-110.802 | ||
|108. | |||
|- | |- | ||
| |2 | | |2 | ||
| |G | | colspan="2" |G | ||
|210.511-214.511 | |||
| colspan="2" |211.25-216.03 | |||
| | | |212.313-216.313 | ||
| | |214.8705-218.8705 | ||
|215.4765-219.4765 | |||
|216.918-220.918 | |||
|217.604-221.604 | |||
|216. | |||
|217. | |||
|- | |- | ||
| |3 | | |3 | ||
| |G#/Ab | | |G#/Ab | ||
| | |G#v/Ab^ | ||
| | |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 | ||
|326.4065-332.4065 | |||
| | |||
| | |||
| | |||
| | |||
|- | |- | ||
| |4 | | |4 | ||
| |A | | colspan="2" |A | ||
|421.022-429.022 | |||
| colspan="2" |422.501-432.059 | |||
| | | |424.626-432.626 | ||
| | |429.741-437.741 | ||
|430.953-438.953 | |||
| | |433.836-437.836 | ||
|435.209-443.209 | |||
| | |||
|435. | |||
|- | |- | ||
| |5 | | |5 | ||
| |B | | |B | ||
| | | |A#v/Bb^ | ||
|526.278-536.278 | |||
| | | | colspan="2" |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 | | |6 | ||
| |B#/Hb | | |B#/Hb | ||
| | | |B | ||
|631.534-643.534 | |||
| | | | colspan="2" |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 | | |7 | ||
| |H | | |H | ||
| | | |Cb | ||
|736.789-750.789 | |||
| | | | colspan="2" |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 | | |8 | ||
| |C | | |C | ||
| | | |H# | ||
|842.045-858.045 | |||
| | | | colspan="2" |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 | | |9 | ||
| |C#/Db | | |C#/Db | ||
| | | |Db | ||
|947.3-965.3 | |||
| | | | colspan="2" |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 | | |10 | ||
| |D | | |D | ||
| | | |C# | ||
|1052.556-1072.556 | |||
| | | | colspan="2" |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 | | |11 | ||
| |D#/Eb | | |D#/Eb | ||
| | | |Eb | ||
|1157.8115-1179.8115 | |||
| | | | colspan="2" |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 | | |12 | ||
| |E | | |E | ||
| | | |D# | ||
|1264.067-1287.067 | |||
| | | | colspan="2" |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 | | |13 | ||
| |F | | colspan="2" |F | ||
| | |1368.323-1394.323 | ||
| colspan="2" |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 | |||