User:Moremajorthanmajor/9edX: Difference between revisions

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|1
|1
|156.667-160
|155.556-160
|161.905
|161.905
| colspan="2" |159.63-166.297
| colspan="2" |158.5185-167.407
|164.103
|164.103
| colspan="2" |163.333-170
| colspan="2" |162.222-171.111
|168.889
|168.889
| colspan="2" |166.364-173.03
| colspan="2" |165.2525-174.141
|170.37
|170.37
|171.429-174.762
|171.429-175.873
|-
|-
|2
|2
|313.333-320
|311.111-320
|323.8095
|323.8095
| colspan="2" |319.26-333.593
| colspan="2" |317.037-334.814
|328.205
|328.205
| colspan="2" |326.667-340
| colspan="2" |324.444-342.222
|337.778
|337.778
| colspan="2" |332.727-346.06
| colspan="2" |330.505-348.283
|340.741
|340.741
|342.857-349.524
|342.857-351.746
|-
|-
|3
|3
|470-480
|466.667-480
|485.714
|485.714
| colspan="2" |478.889-498.889
| colspan="2" |475.556-502.222
|492.308
|492.308
| colspan="2" |490-510
| colspan="2" |486.667-513.333
|506.667
|506.667
| colspan="2" |499.091-519.091
| colspan="2" |495.758-522.424
|511.111
|511.111
|514.286-524.286
|514.286-527.619
|-
|-
|4
|4
|626.666-640
|622.222-640
|647.619
|647.619
| colspan="2" |638.5185-665.185
| colspan="2" |634.074-669.63
|656.41
|656.41
| colspan="2" |653.333-680
| colspan="2" |648.889-684.444
|675.556
|675.556
| colspan="2" |665.4545-682.121
| colspan="2" |661.01-696.566
|681.4815
|681.4815
|685.714-699.048
|685.714-703.492
|-
|-
|5
|5
|783.333-800
|777.778-800
|809.524
|809.524
| colspan="2" |798.148-831.4815
| colspan="2" |792.593-837.037
|820.512
|820.512
| colspan="2" |816.667-850
| colspan="2" |811.111-855.556
|844.444
|844.444
| colspan="2" |831.818-851.1515
| colspan="2" |826.263-870.707
|851.852
|851.852
|857.143-873.81
|857.143-878.365
|-
|-
|6
|6
|940-960
|943.333-960
|971.429
|971.429
| colspan="2" |957.778-997.778
| colspan="2" |951.111-1004.444
|984.615
|984.615
| colspan="2" |980-1020
| colspan="2" |973.333-1026.667
|1013.333
|1013.333
| colspan="2" |998.182-1038.182
| colspan="2" |988.515-1044.848
|1022.222
|1022.222
|1028.571-1048.571
|1028.571-1055.238
|-
|-
|7
|7
|1096.667-1120
|1088.889-1120
|1133.333
|1133.333
| colspan="2" |1117.407-1164.074
| colspan="2" |1109.63-1171.852
|1148.718
|1148.718
| colspan="2" |1143.333-1190
| colspan="2" |1135.556-1197.778
|1182.222
|1182.222
| colspan="2" |1164.5455-1211.212
| colspan="2" |1156.768-1218.99
|1192.593
|1192.593
|1200-1223.333
|1200-1231.111
|-
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|8
|8
|1253.333-1280
|1244.444-1280
|1295.238
|1295.238
| colspan="2" |1277.037-1310.33
| colspan="2" |1238.148-1339.259
|1312.8205
|1312.8205
| colspan="2" |1306.667-1360
| colspan="2" |1297.778-1368.889
|1351.111
|1351.111
| colspan="2" |1330.909-1384.242
| colspan="2" |1321.02-1392.131
|1362.963
|1362.963
|1371.429-1398.095
|1371.429-1406.984
|}
|}
{| class="wikitable" style="text-align: center"
{| class="wikitable" style="text-align: center"
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|-
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|1
|1
|168.095-171.429
|166.984-171.429
| colspan="2" |''172.222''
| colspan="2" |''172.222''
| colspan="2" |169.216-175.883
| colspan="2" |168.105-176.9935
|172.8395
|172.8395
|173.333-176.667
|173.333-177.778
|-
|-
|2
|2
|336.19-342.857
|333.968-342.857
| colspan="2" |''344.444''
| colspan="2" |''344.444''
| colspan="2" |338.431-351.765
| colspan="2" |336.209-353.987
|345.679
|345.679
|346.667-353.333
|346.667-355.556
|-
|-
|3
|3
|504.286-514.286
|500.952-514.286
| colspan="2" |''516.667''
| colspan="2" |''516.667''
| colspan="2" |507.647-527.647
| colspan="2" |504.314-530.98
|518.5185
|518.5185
|520-530
|520-533.333
|-
|-
|4
|4
|672.381-685.714
|667.9365-685.714
| colspan="2" |''688.889''
| colspan="2" |''688.889''
| colspan="2" |676.863-703.529
| colspan="2" |672.418-707.974
|691.358
|691.358
|693.333-706.667
|693.333-711.111
|-
|-
|5
|5
|843.476-857.143
|834.921-857.143
| colspan="2" |''861.111''
| colspan="2" |''861.111''
| colspan="2" |846.078-879.412
| colspan="2" |840.523-885.967
|864.1975
|864.1975
|866.667-883.333
|866.667-888.889
|-
|-
|6
|6
|1008.571-1028.571
|1001.904-1028.571
| colspan="2" |''1033.333''
| colspan="2" |''1033.333''
| colspan="2" |1015.294-1055.294
| colspan="2" |1008.6275-1062.961
|1037.037
|1037.037
|1040-1060
|1040-1066.667
|-
|-
|7
|7
|1176.667-1200
|1168.889-1200
| colspan="2" |''1205.556''
| colspan="2" |''1205.556''
| colspan="2" |1184.51-1231.1765
| colspan="2" |1176.732-1239.954
|1209.8765
|1209.8765
|1213.333-1236.667
|1213.333-1244.444
|-
|-
|8
|8
|1334.762-1371.429
|1335.873-1371.429
| colspan="2" |''1377.778''
| colspan="2" |''1377.778''
| colspan="2" |1353.7255-1407.059
| colspan="2" |1344.837-1416.948
|1382.716
|1382.716
|1386.667-1413.333
|1386.667-1422.222
|}
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| |1
| |1
|170-173.333
|168.889-173.333
|174.359
|174.359
| colspan="2" |171.667-178.333
| colspan="2" |170.556-179.444
|175.439
|175.439
| colspan="2" |174.444-181.111
| colspan="2" |173.333-182.222
|179.167
|179.167
| colspan="2" |157.977-182.644
| colspan="2" |174.866-183.755
|181.609
|181.609
| colspan="2" |180.575-187.241
| colspan="2" |179.464-188.3525
|184.314
|184.314
| |186.667-190
| |186.667-191.111
|-
|-
| |2
| |2
|340-346.667
|337.778-346.667
|348.718
|348.718
| colspan="2" |343.333-356.667
| colspan="2" |341.111-358.889
|350.877
|350.877
| colspan="2" |348.889-362.222
| colspan="2" |346.667-364.444
|358.333
|358.333
| colspan="2" |355.954-365.287
| colspan="2" |349.732-367.51
|363.218
|363.218
| colspan="2" |361.149-374.483
| colspan="2" |368.927-376.705
|368.6275
|368.6275
| |373.333-380
| |373.333-382.222
|-
|-
| |3
| |3
|510-520
|506.667-520
|523.077
|523.077
| colspan="2" |515-535
| colspan="2" |511.667-538.333
|526.316
|526.316
| colspan="2" |523.333-543.333
| colspan="2" |520-546.667
|537.5
|537.5
| colspan="2" |527.931-547.931
| colspan="2" |524.598-551.264
|544.828
|544.828
| colspan="2" |541.724-561.724
| colspan="2" |538.391-565.0575
|552.941
|552.941
| |560-570
| |560-573.333
|-
|-
| |4
| |4
|680-693.333
|675.556-693.333
|697.436
|697.436
| colspan="2" |686.667-713.333
| colspan="2" |682.222-717.778
|701.754
|701.754
| colspan="2" |697.778-724.444
| colspan="2" |693.333-728.889
|716.667
|716.667
| colspan="2" |703.908-730.576
| colspan="2" |699.464-735.019
|726.437
|726.437
| colspan="2" |722.299-748.9655
| colspan="2" |717.854-753.41
|737.255
|737.255
| |746.667-760
| |746.667-764.444
|-
|-
| |5
| |5
|850-866.667
|844.444-866.667
|871.795
|871.795
| colspan="2" |858.333-891.667
| colspan="2" |852.778-897.222
|877.193
|877.193
| colspan="2" |872.222-905.556
| colspan="2" |866.667-911.111
|895.833
|895.833
| colspan="2" |879.885-912.218
| colspan="2" |874.3295-918.774
|908.046
|908.046
| colspan="2" |903.207-936.8735
| colspan="2" |897.318-942.7625
|921.569
|921.569
| |933.333-950
| |933.333-955.556
|-
|-
| |6
| |6
|1020-1040
|1013.333-1040
|1046.154
|1046.154
| colspan="2" |1030-1070
| colspan="2" |1023.333-1076.667
|1052.632
|1052.632
| colspan="2" |1046.667-1086.667
| colspan="2" |1040-1093.333
|1075
|1075
| colspan="2" |1055.862-1095.862
| colspan="2" |1049.195-1102.529
|1089.655
|1089.655
| colspan="2" |1083.448-1123.448
| colspan="2" |1076.782-1130.115
|1105.882
|1105.882
| |1120-1140
| |1120-1146.667
|-
|-
| |7
| |7
|1190-1213.333
|1182.222-1213.333
|1220.513
|1220.513
| colspan="2" |1201.667-1248.333
| colspan="2" |1193.889-1256.111
|1228.07
|1228.07
| colspan="2" |1221.111-1267.778
| colspan="2" |1213.333-1275.556
|1254.167
|1254.167
| colspan="2" |1221.839-1268.506
| colspan="2" |1224.061-1286.2835
|1271.264
|1271.264
| colspan="2" |1264.023-1330.69
| colspan="2" |1256.245-1318.457
|1290.196
|1290.196
| |1306.667-1330
| |1306.667-1337.778
|-
|-
|8
|8
|1360-1386.667
|1351.111-1386.667
|1394.872
|1394.872
| colspan="2" |1373.333-1426.667
| colspan="2" |1364.444-1435.556
|1403.509
|1403.509
| colspan="2" |1395.556-1448.889
| colspan="2" |1386.667-1457.778
|1433.333
|1433.333
| colspan="2" |1407.816-1462.419
| colspan="2" |1398.927-1470.038
|1452.874
|1452.874
| colspan="2" |1444.598-1496.931
| colspan="2" |1438.709-1506.82
|1474.51
|1474.51
|1493.333-1520
|1493.333-1528.889
|}Relative cents
|}Relative cents


Revision as of 00:15, 11 June 2019

This is the neutral scale of the Middletown temperament family.

Intervals

Degrees Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 155.556-160 161.905 158.5185-167.407 164.103 162.222-171.111 168.889 165.2525-174.141 170.37 171.429-175.873
2 311.111-320 323.8095 317.037-334.814 328.205 324.444-342.222 337.778 330.505-348.283 340.741 342.857-351.746
3 466.667-480 485.714 475.556-502.222 492.308 486.667-513.333 506.667 495.758-522.424 511.111 514.286-527.619
4 622.222-640 647.619 634.074-669.63 656.41 648.889-684.444 675.556 661.01-696.566 681.4815 685.714-703.492
5 777.778-800 809.524 792.593-837.037 820.512 811.111-855.556 844.444 826.263-870.707 851.852 857.143-878.365
6 943.333-960 971.429 951.111-1004.444 984.615 973.333-1026.667 1013.333 988.515-1044.848 1022.222 1028.571-1055.238
7 1088.889-1120 1133.333 1109.63-1171.852 1148.718 1135.556-1197.778 1182.222 1156.768-1218.99 1192.593 1200-1231.111
8 1244.444-1280 1295.238 1238.148-1339.259 1312.8205 1297.778-1368.889 1351.111 1321.02-1392.131 1362.963 1371.429-1406.984
Degrees Mohajira Beatles
Min-comma r¢ Med Max+comma Min-comma Med Max+comma
1 166.984-171.429 172.222 168.105-176.9935 172.8395 173.333-177.778
2 333.968-342.857 344.444 336.209-353.987 345.679 346.667-355.556
3 500.952-514.286 516.667 504.314-530.98 518.5185 520-533.333
4 667.9365-685.714 688.889 672.418-707.974 691.358 693.333-711.111
5 834.921-857.143 861.111 840.523-885.967 864.1975 866.667-888.889
6 1001.904-1028.571 1033.333 1008.6275-1062.961 1037.037 1040-1066.667
7 1168.889-1200 1205.556 1176.732-1239.954 1209.8765 1213.333-1244.444
8 1335.873-1371.429 1377.778 1344.837-1416.948 1382.716 1386.667-1422.222
Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma Min-comma Med Max+comma
1 168.889-173.333 174.359 170.556-179.444 175.439 173.333-182.222 179.167 174.866-183.755 181.609 179.464-188.3525 184.314 186.667-191.111
2 337.778-346.667 348.718 341.111-358.889 350.877 346.667-364.444 358.333 349.732-367.51 363.218 368.927-376.705 368.6275 373.333-382.222
3 506.667-520 523.077 511.667-538.333 526.316 520-546.667 537.5 524.598-551.264 544.828 538.391-565.0575 552.941 560-573.333
4 675.556-693.333 697.436 682.222-717.778 701.754 693.333-728.889 716.667 699.464-735.019 726.437 717.854-753.41 737.255 746.667-764.444
5 844.444-866.667 871.795 852.778-897.222 877.193 866.667-911.111 895.833 874.3295-918.774 908.046 897.318-942.7625 921.569 933.333-955.556
6 1013.333-1040 1046.154 1023.333-1076.667 1052.632 1040-1093.333 1075 1049.195-1102.529 1089.655 1076.782-1130.115 1105.882 1120-1146.667
7 1182.222-1213.333 1220.513 1193.889-1256.111 1228.07 1213.333-1275.556 1254.167 1224.061-1286.2835 1271.264 1256.245-1318.457 1290.196 1306.667-1337.778
8 1351.111-1386.667 1394.872 1364.444-1435.556 1403.509 1386.667-1457.778 1433.333 1398.927-1470.038 1452.874 1438.709-1506.82 1474.51 1493.333-1528.889

Relative cents

Degrees Intense Aeolian-Subpental Dorian Dorian Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 161.111 166.667 177.778 183.333
2 322.222 333.333 355.556 366.667
3 483.333 500 533.333 550
4 644.444 666.667 711.111 733.333
5 805.556 833.333 888.889 916.667
6 966.667 1000 1066.667 1100
7 1127.778 1166.666 1244.444 1283.333
8 1288.889 1333.333 1422.222 1466.667

Golden/Pyrite Tunings±13¢

Degrees Intense Aeolian-Subpental Dorian Dorian
Subpental Pental Superpental
1 160.761-163.65 162.317-165.2055 167.6965-170.585 168.741-171.63
2 321.522-327.3 364.633-330.411 335.393-341.171 337.483-343.36
3 482.284-490.95 486.95-495.617 503.089-511.756 506.224-514.891
4 643.045-654.6 649.2665-660.822 670.786-682.341 674.965-686.521
5 803.806-818.25 811.583-826.028 838.482-852.927 843.707-858.151
6 964.567-981.9 973.9-991.233 1006.179-1023.512 1012.448-1029.781
7 1125.328-1145.55 1136.216-1156.439 1173.875-1194.0975 1181.189-1201.411
8 1286.09-1309.2 1278.2435-1321.644 1341.572-1343.36 1349.9305-1373.042
Degrees Mohajira Beatles
1 170.877-173.776 171.314-174.203
2 341.755-347.513 342.627-348.405
3 512.632-521.2985 513.941-522.607
4 683.509-695.065 685.255-696.81
5 854.386-868.831 856.568-870.112
6 1025.264-1042.597 1027.882-1045.215
7 1196.141-1216.363 1199.196-1219.418
8 1367.018-1389.119 1370.5095-1393.621
Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental
Soft Intense
1 173.091-175.98 173.844-176.733 177.774-180.663 180.707-183.596 182.729-185.618
2 346.182-351.96 347.688-353.466 355.548-361.325 361.415-367.193 365.4585-371.236
3 519.2735-527.94 521.532-530.199 533.321-541.988 542.122-550.789 548.188-556.854
4 692.365-703.92 695.376-706.932 711.095-722.651 722.83-734.385 730.917-742.4725
5 865.456-879.9 869.22-883.6645 888.896-903.3135 903.537-917.982 913.646-928.091
6 1038.547-1055.88 1043.064-1060.3975 1033.634-1083.976 1084.245-1101.578 1096.3755-1113.709
7 1211.638-1231.86 1216.908-1237.13 1244.417-1264.639 1264.952-1285.174 1279.105-1299.327
8 1384.729-1407.84 1390.752-1413.863 1422.19-1445.3015 1445.6595-1445.821 1461.834-1484.945

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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