User:Moremajorthanmajor/14edIX: Difference between revisions
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==Intervals== | ==Intervals== | ||
{| class="wikitable" | {| class="wikitable" | ||
! rowspan=" | ! rowspan="3" |Degrees | ||
! rowspan=" | ! rowspan="3" |Octatonic | ||
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) | ! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) | ||
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) | ! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) | ||
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor) | ! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor) | ||
|- | |- | ||
!Absolute Minimum | ! rowspan="2" |Absolute Minimum | ||
!Minimum | ! rowspan="2" |Minimum | ||
!Median | ! rowspan="2" |Median | ||
!Maximum | ! rowspan="2" |Maximum | ||
! |Minimum | ! colspan="3"|Intense Phrygian | ||
!Median | ! colspan="3" |Intense Phrygian-Soft Aeolian | ||
!Maximum | ! colspan="3" |Soft Aeolian | ||
! rowspan="2" |Minimum | |||
! rowspan="2" |Median | |||
! rowspan="2" |Maximum | |||
|- | |||
!Minimum | !Minimum | ||
!Median | !Median | ||
Revision as of 18:19, 2 December 2018
This scale, a Long Common Practice minor mode,occurs in 12edo, where it is the equal division of the major ninth. It has the Macroshrutis 6L 2s MOS with a 2:1 ratio of large against small.
Intervals
| Degrees | Octatonic | Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) | Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) | Aeolian Mode Neapolitan Temperament (melodic/harmonic minor) | |||||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Absolute Minimum | Minimum | Median | Maximum | Intense Phrygian | Intense Phrygian-Soft Aeolian | Soft Aeolian | Minimum | Median | Maximum | ||||||||
| Minimum | Median | Maximum | Minimum | Median | Maximum | Minimum | Median | Maximum | |||||||||
| 1 | F#/Gb | 85.714 | 89.143 | 91.429 | 94.286 | 94.737 | 95.238 | 95.798 | 96.429 | 97.143 | 97.959 | 100 | 102.857 | ||||
| 2 | G | 171.429 | 178.286 | 182.857 | 188.571 | 189.473 | 190.476 | 191.597 | 192.857 | 194.286 | 195.918 | 200 | 205.714 | ||||
| 3 | G#/Ab | 257.143 | 267.429 | 274.286 | 282.857 | 284.2105 | 285.714 | 287.395 | 289.286 | 291.429 | 293.878 | 300 | 308.571 | ||||
| 4 | A | 342.857 | 356.571 | 365.714 | 377.143 | 378.947 | 380.952 | 383.193 | 385.714 | 388.571 | 391.836 | 400 | 411.429 | ||||
| 5 | A#/Bb | 428.571 | 445.714 | 467.143 | 471.429 | 473.684 | 476.1905 | 478.992 | 482.143 | 485.714 | 489.796 | 500 | 514.286 | ||||
| 6 | B | 514.286 | 534.857 | 548.571 | 565.714 | 568.421 | 571.429 | 574.79 | 578.571 | 582.857 | 587.755 | 600 | 617.143 | ||||
| 7 | H | 600 | 624 | 640 | 660 | 663.158 | 666.667 | 670.588 | 675 | 680 | 685.714 | 700 | 720 | ||||
| 8 | H#/Cb | 685.714 | 713.143 | 731.429 | 754.286 | 757.894 | 761.905 | 766.387 | 771.429 | 777.143 | 783.6735 | 800 | 822.857 | ||||
| 9 | C | 771.429 | 802.286 | 822.857 | 848.571 | 853.632 | 857.143 | 862.185 | 867.857 | 874.286 | 881.633 | 900 | 925.714 | ||||
| 10 | C#/Db | 857.143 | 891.429 | 914.286 | 942.857 | 947.368 | 952.381 | 957.983 | 964.286 | 971.429 | 979.592 | 1000 | 1028.571 | ||||
| 11 | D | 942.857 | 980.571 | 1005.714 | 1037.143 | 1042.105 | 1047.619 | 1053.7815 | 1060.714 | 1068.571 | 1077.551 | 1100 | 1131.429 | ||||
| 12 | D#/Eb | 1028.571 | 1069.714 | 1097.143 | 1131.429 | 1136.842 | 1142.857 | 1149.58 | 1157.143 | 1165.714 | 1175.51 | 1200 | 1234.286 | ||||
| 13 | E | 1114.286 | 1158.857 | 1188.571 | 1225.714 | 1231.579 | 1238.095 | 1245.378 | 1253.571 | 1262.857 | 1273.469 | 1300 | 1337.143 | ||||
| 14 | F | 1200 | 1268.571 | 1280 | 1320 | 1326.316 | 1333.333 | 1341.1765 | 1350 | 1360 | 1371.429 | 1400 | 1440 | ||||
Most harmonic tunings
| Degrees | Octatonic | Phrygian Mode (natural minor) | Phrygian-Aeolian Mode (intermediate minor) | Aeolian Mode (melodic/harmonic minor) |
|---|---|---|---|---|
| 15/7±13¢ | 11/5±13¢ | 9/4±13¢ | ||
| 1 | F#/Gb | 93.317-95.1745 | 96.572-98.429 | 99.351-101.208 |
| 2 | G | 186.635-190.349 | 193.1435-196.858 | 198.701-202.416 |
| 3 | G#/Ab | 279.952-285.5235 | 289.715-295.287 | 298.052-303.624 |
| 4 | A | 373.269-380.698 | 386.287-393.7155 | 397.403-404.831 |
| 5 | A#/Bb | 466.587-475.872 | 482.859-492.144 | 496.754-506.039 |
| 6 | B | 559.904-571.047 | 579.43-590.573 | 596.104-607.247 |
| 7 | H | 653.224-666.221 | 676.002-689.002 | 695.455-708.455 |
| 8 | H#/Cb | 746.539-761.396 | 772.574-787.431 | 794.805-809.663 |
| 9 | C | 839.856-856.57 | 869.146-885.86 | 894.156-910.871 |
| 10 | C#/Db | 933.173-951.745 | 965.717-984.289 | 993.507-1012.079 |
| 11 | D | 1026.491-1046.919 | 1062.289-1082.718 | 1092.858-1113.286 |
| 12 | D#/Eb | 1119.808-1142.094 | 1158.861-1181.1465 | 1192.209-1214.494 |
| 13 | E | 1213.1255-1237.268 | 1255.4325-1279.575 | 1291.559-1315.702 |
| 14 | F | 1306.443-1332.443 | 1352.004-1378.004 | 1390.91-1416.91 |
Golden Tunings
Phrygian Mode (natural minor)
| Degrees | Octatonic | Min-Med±13¢ | Min-Max±13¢ | Med-Max±13¢ |
|---|---|---|---|---|
| 1 | F#/Gb | 89.855-91.712 | 90.235-92.092 | 91.234-93.191 |
| 2 | G | 179.709-183.4235 | 180.47-184.184 | 182.667-186.382 |
| 3 | G#/Ab | 269.564-275.135 | 270.705-276.276 | 274.001-279.5725 |
| 4 | A | 359.4185-366.847 | 360.94-368.3685 | 365.335-372.763 |
| 5 | A#/Bb | 449.273-458.559 | 451.175-460.461 | 456.6685-465.954 |
| 6 | B | 539.128-550.271 | 541.41-552.553 | 548.002-559.145 |
| 7 | H | 628.982-641.982 | 631.645-644.645 | 639.335-652.335 |
| 8 | H#/Cb | 718.837-733.694 | 721.88-736.737 | 730.67-745.257 |
| 9 | C | 808.692-825.406 | 812.115-828.829 | 822.003-838.718 |
| 10 | C#/Db | 898.546-917.118 | 902.35-920.921 | 913.337-931.908 |
| 11 | D | 988.401-1008.829 | 992.585-1013.013 | 1007.671-1025.099 |
| 12 | D#/Eb | 1078.255-1100.541 | 1082.82-1105.106 | 1096.004-1118.29 |
| 13 | E | 1168.11-1192.253 | 1173.055-1197.198 | 1187.338-1211.481 |
| 14 | F | 1257.965-1283.965 | 1263.29-1289.29 | 1278.672-1304.672 |
Phrygian-Aeolian Mode (intermediate minor)
| Degrees | Octatonic | Intense Phrygian | Intense Phrygian-Soft Aeolian | Soft Aeolian | |||
|---|---|---|---|---|---|---|---|
| Min-Med/Min-Max±13¢ | Med-Max±13¢ | Min-Med/Min-Max±13¢ | Med-Max±13¢ | Min-Med/Min-Max±13¢ | Med-Max±13¢ | ||
| 1 | F#/Gb | 93.6975-95.555 | 93.922-95.779 | 94.732-96.589 | 95.012-96.869 | 96.037-97.894 | 96.397-98.254 |
| 2 | G | 187.395-191.109 | 187.844-191.558 | 189.463-193.178 | 190.0235-193.738 | 192.074-195.789 | 192.794-196.508 |
| 3 | G#/Ab | 281.093-286.664 | 281.765-287.337 | 284.195-289.766 | 285.035-290.607 | 288.112-293.683 | 289.191-294.7625 |
| 4 | A | 374.79-382.219 | 375.687-383.116 | 378.9265-386.219 | 380.047-387.476 | 384.149-391.577 | 385.588-393.017 |
| 5 | A#/Bb | 468.488-477.773 | 469.609-478.895 | 473.658-482.944 | 475.059-484.3445 | 480.186-489.472 | 481.985-491.271 |
| 6 | B | 562.185-573.328 | 563.531-574.674 | 568.39-579.533 | 570.0705-581.213 | 576.223-587.366 | 578.382-589.525 |
| 7 | H | 655.883-668.883 | 657.4525-670.4525 | 663.121-676.121 | 665.082-678.082 | 672.2605-685.2605 | 674.779-687.779 |
| 8 | H#/Cb | 749.58-764.4375 | 751.374-766.231 | 757.853-772.71 | 760.094-774.951 | 768.298-783.155 | 771.176-786.033 |
| 9 | C | 843.278-859.992 | 845.296-862.01 | 852.585-869.299 | 855.105-871.82 | 864.335-881.049 | 867.573-884.2875 |
| 10 | C#/Db | 936.975-955.5546 | 939.218-957.789 | 947.316-965.887 | 950.1175-968.689 | 960.372-978.9435 | 963.97-982.542 |
| 11 | D | 1030.672-1051.101 | 1033.101-1053.568 | 1042.048-1062.477 | 1045.129-1065.558 | 1056.409-1076.838 | 1060.367-1080.796 |
| 12 | D#/Eb | 1124.3705-1146.656 | 1127.061-1149.347 | 1136.78-1159.065 | 1140.141-1162.427 | 1152.4465-1174.732 | 1156.764-1179.05 |
| 13 | E | 1218.068-1242.211 | 1220.983-1245.126 | 1231.511-1255.654 | 1235.153-1259.295 | 1248.484-1272.626 | 1253.161-1227.304 |
| 14 | F | 1311.767-1337.767 | 1314.905-1340.905 | 1326.243-1352.243 | 1330.1645-1356.1645 | 1344.521-1370.521 | 1349.558-1375.558 |
Aeolian Mode (melodic/harmonic minor)
| Degrees | Octatonic | Min-Med±13¢ | Min-Max±13¢ | Med-Max±13¢ |
|---|---|---|---|---|
| 1 | F#/Gb | 97.737-99.5945 | 98.531-100.388 | 100.043-101.9 |
| 2 | G | 195.475-199.189 | 197.061-200.776 | 200.085-203.8 |
| 3 | G#/Ab | 293.212-298.783 | 295.592-301.163 | 300.128-305.6995 |
| 4 | A | 390.949-398.378 | 394.123-401.551 | 400.171-407.599 |
| 5 | A#/Bb | 488.687-497.972 | 492.653-501.939 | 500.2135-509.499 |
| 6 | B | 586.424-597.567 | 591.184-602.327 | 600.256-611.399 |
| 7 | H | 684.161-697.161 | 689.7145-702.7145 | 700.299-713.299 |
| 8 | H#/Cb | 781.899-796.756 | 788.245-803.102 | 800.342-815.199 |
| 9 | C | 879.636-896.35 | 886.776-903.49 | 900.384-917.099 |
| 10 | C#/Db | 977.373-995.945 | 985.306-1003.878 | 1000.427-1018.9985 |
| 11 | D | 1075.111-1095.539 | 1083.837-1104.266 | 1100.47-1120.898 |
| 12 | D#/Eb | 1172.848-1195.134 | 1182.368-1204.653 | 1200.512-1222.798 |
| 13 | E | 1270.585-1294.728 | 1280.898-1305.041 | 1300.555-1324.698 |
| 14 | F | 1368.322-1394.322 | 1379.429-1405.429 | 1400.598-1426.598 |