User:Moremajorthanmajor/9edX: Difference between revisions

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Line 4: Line 4:
! rowspan="3" |Degrees
! rowspan="3" |Degrees
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="10" |Dorian
! colspan="9" |Dorian
|-
|-
! colspan="4" |Subpental
! colspan="3" |Subpental
! colspan="3" |Pental
! colspan="3" |Pental
! colspan="3" |Superpental
! colspan="3" |Superpental
Line 15: Line 15:
!Max
!Max
!Min
!Min
!7/3±13¢
!Golden±13¢
!Golden±13¢
!Max
!Max
Line 30: Line 29:
|''161.111''
|''161.111''
| colspan="2" |162.963
| colspan="2" |162.963
|161.541-164.43
|162.317-165.2055
|162.317-165.2055
| colspan="2" |''166.667''
| colspan="2" |''166.667''
Line 43: Line 41:
|''322.222''
|''322.222''
| colspan="2" |325.926
| colspan="2" |325.926
|323.082-328.86
|364.633-330.411
|364.633-330.411
| colspan="2" |''333.333''
| colspan="2" |''333.333''
Line 56: Line 53:
|''483.333''
|''483.333''
| colspan="2" |488.889
| colspan="2" |488.889
|484.624-493.29
|486.95-495.617
|486.95-495.617
| colspan="2" |''500''
| colspan="2" |''500''
Line 69: Line 65:
|''644.444''
|''644.444''
| colspan="2" |651.852
| colspan="2" |651.852
|646.165-657.72
|649.2665-660.822
|649.2665-660.822
| colspan="2" |''666.667''
| colspan="2" |''666.667''
Line 82: Line 77:
|''805.556''
|''805.556''
| colspan="2" |814.815
| colspan="2" |814.815
|807.706-822.1505
|811.583-826.028
|811.583-826.028
| colspan="2" |''833.333''
| colspan="2" |''833.333''
Line 95: Line 89:
|''966.667''
|''966.667''
| colspan="2" |977.778
| colspan="2" |977.778
|969.247-986.581
|973.9-991.233
|973.9-991.233
| colspan="2" |''1000''
| colspan="2" |''1000''
Line 108: Line 101:
|''1127.778''
|''1127.778''
| colspan="2" |1140.741
| colspan="2" |1140.741
|1130.7885-1151.011
|1136.216-1156.439
|1136.216-1156.439
| colspan="2" |''1166.666''
| colspan="2" |''1166.666''
Line 121: Line 113:
|''1288.889''
|''1288.889''
| colspan="2" |1303.704
| colspan="2" |1303.704
|1292.33-1315.441
|1278.2435-1321.644
|1278.2435-1321.644
| colspan="2" |''1333.333''
| colspan="2" |''1333.333''
Line 132: Line 123:
!Degrees
!Degrees
!Min
!Min
!22/9±13¢
!Golden±13¢
!Golden±13¢
!''r¢''
!''r¢''
Line 139: Line 129:
|1
|1
|171.429
|171.429
|170.49-173.379
|171.314-174.203
|171.314-174.203
|''172.222''
|''172.222''
Line 146: Line 135:
|2
|2
|342.857
|342.857
|340.9795-346.757
|342.617-348.405
|342.617-348.405
|''344.444''
|''344.444''
Line 153: Line 141:
|3
|3
|514.286
|514.286
|511.469-520.136
|513.941-522.608
|513.941-522.608
|''516.667''
|''516.667''
Line 160: Line 147:
|4
|4
|685.714
|685.714
|681.959-693.515
|685.255-696.81
|685.255-696.81
|''688.889''
|''688.889''
Line 167: Line 153:
|5
|5
|857.143
|857.143
|852.489-866.893
|856.568-871.012
|856.568-871.012
|''861.111''
|''861.111''
Line 174: Line 159:
|6
|6
|1028.571
|1028.571
|1022.939-1040.272
|1027.882-1045.2155
|1027.882-1045.2155
|''1033.333''
|''1033.333''
Line 181: Line 165:
|7
|7
|1200
|1200
|1193.428-1215.651
|1199.196-1219.418
|1199.196-1219.418
|''1205.556''
|''1205.556''
Line 188: Line 171:
|8
|8
|1371.429
|1371.429
|1363.918-1387.293
|1370.5095-1393.621
|1370.5095-1393.621
|''1377.778''
|''1377.778''
Line 196: Line 178:
|-
|-
! rowspan="4" |Degrees
! rowspan="4" |Degrees
! colspan="14" |Mixolydian
! colspan="13" |Mixolydian
! colspan="3" rowspan="3" |Mixolydian-Ionian
! colspan="3" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="3" rowspan="2" |Subpental
! colspan="3" rowspan="2" |Subpental
! colspan="4" rowspan="2" |Pental
! colspan="3" rowspan="2" |Pental
! colspan="7" |Superpental
! colspan="7" |Superpental
|-
|-
Line 211: Line 193:
! |Minimum
! |Minimum
!Golden±13¢
!Golden±13¢
!5/2±13¢
!Maximum
!Maximum
!Minimum
!Minimum
Line 229: Line 210:
| colspan="2" |175
| colspan="2" |175
|173.844-176.733
|173.844-176.733
|174.813-177.7015
| colspan="2" |''177.778''
| colspan="2" |''177.778''
|177.774-180.663
|177.774-180.663
Line 244: Line 224:
| colspan="2" |350
| colspan="2" |350
|347.688-353.466
|347.688-353.466
|349.625-355.403
| colspan="2" |''355.556''
| colspan="2" |''355.556''
|355.548-361.325
|355.548-361.325
Line 259: Line 238:
| colspan="2" |525
| colspan="2" |525
|521.532-530.199
|521.532-530.199
|524.438-533.105
| colspan="2" |''533.333''
| colspan="2" |''533.333''
|533.321-541.988
|533.321-541.988
Line 274: Line 252:
| colspan="2" |700
| colspan="2" |700
|695.376-706.932
|695.376-706.932
|699.2505-710.806
| colspan="2" |''711.111''
| colspan="2" |''711.111''
|711.095-722.651
|711.095-722.651
Line 289: Line 266:
| colspan="2" |875
| colspan="2" |875
|869.22-883.6645
|869.22-883.6645
|874.063-888.508
| colspan="2" |''888.889''
| colspan="2" |''888.889''
|888.896-903.3135
|888.896-903.3135
Line 304: Line 280:
| colspan="2" |1050
| colspan="2" |1050
|1043.064-1060.3975
|1043.064-1060.3975
|1048.876-1066.5425
| colspan="2" |''1066.667''
| colspan="2" |''1066.667''
|1033.634-1083.976
|1033.634-1083.976
Line 319: Line 294:
| colspan="2" |1225
| colspan="2" |1225
|1216.908-1237.13
|1216.908-1237.13
|1223.688-1244.466
| colspan="2" |''1244.444''
| colspan="2" |''1244.444''
|1244.417-1264.639
|1244.417-1264.639
Line 334: Line 308:
| colspan="2" |1400
| colspan="2" |1400
|1390.752-1413.863
|1390.752-1413.863
|1398.4501-1422.391
| colspan="2" |''1422.222''
| colspan="2" |''1422.222''
|1422.19-1445.3015
|1422.19-1445.3015

Revision as of 14:15, 7 March 2019

This is the neutral scale of the Middletown temperament family.

Intervals

Degrees Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
Min Golden±13¢ r¢ Max Min Golden±13¢ Max Min Golden±13¢ Max Min Golden±13¢ Max
1 160 160.761-163.65 161.111 162.963 162.317-165.2055 166.667 167.6965-170.585 169.697 168.741-171.63 171.429
2 320 321.522-327.3 322.222 325.926 364.633-330.411 333.333 335.393-341.171 339.394 337.483-343.36 342.857
3 480 482.284-490.95 483.333 488.889 486.95-495.617 500 503.089-511.756 509.091 506.224-514.891 514.286
4 640 643.045-654.6 644.444 651.852 649.2665-660.822 666.667 670.786-682.341 678.788 674.965-686.521 685.714
5 800 803.806-818.25 805.556 814.815 811.583-826.028 833.333 838.482-852.927 848.485 843.707-858.151 857.143
6 960 964.567-981.9 966.667 977.778 973.9-991.233 1000 1006.179-1023.512 1018.182 1012.448-1029.781 1028.571
7 1120 1125.328-1145.55 1127.778 1140.741 1136.216-1156.439 1166.666 1173.875-1194.0975 1187.879 1181.189-1201.411 1200
8 1280 1286.09-1309.2 1288.889 1303.704 1278.2435-1321.644 1333.333 1341.572-1343.36 1357.576 1349.9305-1373.042 1371.429
Degrees Min Golden±13¢ r¢ Max
1 171.429 171.314-174.203 172.222 173.333
2 342.857 342.617-348.405 344.444 246.667
3 514.286 513.941-522.608 516.667 520
4 685.714 685.255-696.81 688.889 693.333
5 857.143 856.568-871.012 861.111 866.667
6 1028.571 1027.882-1045.2155 1033.333 1040
7 1200 1199.196-1219.418 1205.556 1213.333
8 1371.429 1370.5095-1393.621 1377.778 1386.667
Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Minimum Golden±13¢ Maximum Minimum Golden±13¢ Maximum Minimum Golden±13¢ Maximum Minimum Golden±13¢ r¢ Maximum Minimum Golden±13¢ Maximum
1 173.333 173.091-175.98 175 173.844-176.733 177.778 177.774-180.663 179.31 180.707-183.596 183.333 183.908 182.729-185.618 186.667
2 246.667 346.182-351.96 350 347.688-353.466 355.556 355.548-361.325 358.621 361.415-367.193 366.667 367.816 365.4585-371.236 373.333
3 520 519.2735-527.94 525 521.532-530.199 533.333 533.321-541.988 537.931 542.122-550.789 550 551.724 548.188-556.854 560
4 693.333 692.365-703.92 700 695.376-706.932 711.111 711.095-722.651 717.241 722.83-734.385 733.333 735.632 730.917-742.4725 746.667
5 866.667 865.456-879.9 875 869.22-883.6645 888.889 888.896-903.3135 896.552 903.537-917.982 916.667 919.54 913.646-928.091 1033.333
6 1040 1038.547-1055.88 1050 1043.064-1060.3975 1066.667 1033.634-1083.976 1075.862 1084.245-1101.578 1100 1103.448 1096.3755-1113.709 1120
7 1213.333 1211.638-1231.86 1225 1216.908-1237.13 1244.444 1244.417-1264.639 1255.172 1264.952-1285.174 1283.333 1287.356 1279.105-1299.327 1306.667
8 1386.667 1384.729-1407.84 1400 1390.752-1413.863 1422.222 1422.19-1445.3015 1434.483 1445.6595-1445.821 1466.667 1471.264 1461.834-1484.945 1493.333

By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^2)edo is almost exactly every fifth degree of 34edo. Additionally, those of the Golden Subpental Dorian and Pental and Intense Superpental Mixolydian tenths are almost exactly every third step of 22edo, 4edf and equal multiples of 10/9 respectively.

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