User:Moremajorthanmajor/9edX: Difference between revisions

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|-
|-
|1
|1
|155.556-160
|155.{{Overline|5}}-160
|161.905
|161.905
| colspan="2" |158.5185-167.407
| colspan="2" |158.{{Overline|518}}-167.{{Overline|407}}
|164.103
|164.103
| colspan="2" |162.222-171.111
| colspan="2" |162.{{Overline|2}}-171.{{Overline|1}}
|168.889
|168.889
| colspan="2" |165.2525-174.141
| colspan="2" |165.2525-174.141
|170.37
|170.{{Overline|370}}
|171.429-175.873
|171.429-175.873
|-
|-
|2
|2
|311.111-320
|311.{{Overline|1}}-320
|323.8095
|323.8095
| colspan="2" |317.037-334.814
| colspan="2" |317.{{Overline|037}}-334.{{Overline|814}}
|328.205
|328.205
| colspan="2" |324.444-342.222
| colspan="2" |324.{{Overline|4}}-342.{{Overline|2}}
|337.778
|337.{{Overline|7}}
| colspan="2" |330.505-348.283
| colspan="2" |330.505-348.283
|340.741
|340.{{Overline|740}}
|342.857-351.746
|342.857-351.746
|-
|-
|3
|3
|466.667-480
|466.{{Overline|6}}-480
|485.714
|485.714
| colspan="2" |475.556-502.222
| colspan="2" |475.{{Overline|5}}-502.{{Overline|2}}
|492.308
|492.308
| colspan="2" |486.667-513.333
| colspan="2" |486.{{Overline|6}}-513.{{Overline|3}}
|506.667
|506.{{Overline|6}}
| colspan="2" |495.758-522.424
| colspan="2" |495.758-522.424
|511.111
|511.{{Overline|1}}
|514.286-527.619
|514.286-527.619
|-
|-
|4
|4
|622.222-640
|622.{{Overline|2}}-640
|647.619
|647.619
| colspan="2" |634.074-669.63
| colspan="2" |634.{{Overline|074}}-669.{{Overline|629}}
|656.41
|656.41
| colspan="2" |648.889-684.444
| colspan="2" |648.{{Overline|8}}-684.{{Overline|4}}
|675.556
|675.{{Overline|5}}
| colspan="2" |661.01-696.566
| colspan="2" |661.01-696.566
|681.4815
|681.{{Overline|481}}
|685.714-703.492
|685.714-703.492
|-
|-
|5
|5
|777.778-800
|777.{{Overline|7}}-800
|809.524
|809.524
| colspan="2" |792.593-837.037
| colspan="2" |792.{{Overline|592}}-837.{{Overline|037}}
|820.512
|820.512
| colspan="2" |811.111-855.556
| colspan="2" |811.{{Overline|1}}-855.{{Overline|5}}
|844.444
|844.{{Overline|4}}
| colspan="2" |826.263-870.707
| colspan="2" |826.263-870.707
|851.852
|851.{{Overline|851}}
|857.143-878.365
|857.143-878.365
|-
|-
|6
|6
|943.333-960
|943.{{Overline|3}}-960
|971.429
|971.429
| colspan="2" |951.111-1004.444
| colspan="2" |951.{{Overline|1}}-1004.{{Overline|4}}
|984.615
|984.615
| colspan="2" |973.333-1026.667
| colspan="2" |973.{{Overline|3}}-1026.{{Overline|6}}
|1013.333
|1013.{{Overline|3}}
| colspan="2" |988.515-1044.848
| colspan="2" |988.515-1044.848
|1022.222
|1022.{{Overline|2}}
|1028.571-1055.238
|1028.571-1055.238
|-
|-
|7
|7
|1088.889-1120
|1088.{{Overline|8}}-1120
|1133.333
|1133.{{Overline|3}}
| colspan="2" |1109.63-1171.852
| colspan="2" |1109.{{Overline|629}}-1171.{{Overline|851}}
|1148.718
|1148.718
| colspan="2" |1135.556-1197.778
| colspan="2" |1135.{{Overline|5}}-1197.{{Overline|7}}
|1182.222
|1182.{{Overline|2}}
| colspan="2" |1156.768-1218.99
| colspan="2" |1156.768-1218.99
|1192.593
|1192.{{Overline|592}}
|1200-1231.111
|1200-1231.{{Overline|1}}
|-
|-
|8
|8
|1244.444-1280
|1244.{{Overline|4}}-1280
|1295.238
|1295.238
| colspan="2" |1238.148-1339.259
| colspan="2" |1238.{{Overline|148}}-1339.{{Overline|259}}
|1312.8205
|1312.8205
| colspan="2" |1297.778-1368.889
| colspan="2" |1297.{{Overline|7}}-1368.{{Overline|8}}
|1351.111
|1351.{{Overline|1}}
| colspan="2" |1321.02-1392.131
| colspan="2" |1321.02-1392.131
|1362.963
|1362.{{Overline|962}}
|1371.429-1406.984
|1371.429-1406.984
|}
|}
Line 123: Line 123:
|1
|1
|166.984-171.429
|166.984-171.429
| colspan="2" |''172.222''
| colspan="2" |''172.{{Overline|2}}''
| colspan="2" |168.105-176.9935
| colspan="2" |168.105-176.9935
|172.8395
|172.8395
|173.333-177.778
|173.{{Overline|3}}-177.{{Overline|7}}
|-
|-
|2
|2
|333.968-342.857
|333.968-342.857
| colspan="2" |''344.444''
| colspan="2" |''344.{{Overline|4}}''
| colspan="2" |336.209-353.987
| colspan="2" |336.209-353.987
|345.679
|345.679
|346.667-355.556
|346.{{Overline|6}}-355.{{Overline|5}}
|-
|-
|3
|3
|500.952-514.286
|500.952-514.286
| colspan="2" |''516.667''
| colspan="2" |''516.{{Overline|6}}''
| colspan="2" |504.314-530.98
| colspan="2" |504.314-530.98
|518.5185
|518.{{Overline|518}}
|520-533.333
|520-533.{{Overline|3}}
|-
|-
|4
|4
|667.9365-685.714
|667.9365-685.714
| colspan="2" |''688.889''
| colspan="2" |''688.{{Overline|8}}''
| colspan="2" |672.418-707.974
| colspan="2" |672.418-707.974
|691.358
|691.358
|693.333-711.111
|693.{{Overline|3}}-711.{{Overline|1}}
|-
|-
|5
|5
|834.921-857.143
|834.921-857.143
| colspan="2" |''861.111''
| colspan="2" |''861.{{Overline|1}}''
| colspan="2" |840.523-885.967
| colspan="2" |840.523-885.967
|864.1975
|864.1975
|866.667-888.889
|866.{{Overline|6}}-888.{{Overline|8}}
|-
|-
|6
|6
|1001.904-1028.571
|1001.904-1028.571
| colspan="2" |''1033.333''
| colspan="2" |''1033.{{Overline|3}}''
| colspan="2" |1008.6275-1062.961
| colspan="2" |1008.6275-1062.961
|1037.037
|1037.{{Overline|037}}
|1040-1066.667
|1040-1066.{{Overline|6}}
|-
|-
|7
|7
|1168.889-1200
|1168.{{Overline|8}}-1200
| colspan="2" |''1205.556''
| colspan="2" |''1205.{{Overline|5}}''
| colspan="2" |1176.732-1239.954
| colspan="2" |1176.732-1239.954
|1209.8765
|1209.8765
|1213.333-1244.444
|1213.{{Overline|3}}-1244.{{Overline|4}}
|-
|-
|8
|8
|1335.873-1371.429
|1335.873-1371.429
| colspan="2" |''1377.778''
| colspan="2" |''1377.{{Overline|7}}''
| colspan="2" |1344.837-1416.948
| colspan="2" |1344.837-1416.948
|1382.716
|1382.716
|1386.667-1422.222
|1386.{{Overline|6}}-1422.{{Overline|2}}
|}
|}
{| class="wikitable"
{| class="wikitable"
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|-
|-
| |1
| |1
|168.889-173.333
|168.{{Overline|8}}-173.{{Overline|3}}
|174.359
|174.359
| colspan="2" |170.556-179.444
| colspan="2" |170.{{Overline|5}}-179.{{Overline|4}}
|175.439
|175.439
| colspan="2" |173.333-182.222
| colspan="2" |173.{{Overline|3}}-182.{{Overline|2}}
|179.167
|179.1{{Overline|6}}
| colspan="2" |174.866-183.755
| colspan="2" |174.866-183.755
|181.609
|181.609
| colspan="2" |179.464-188.3525
| colspan="2" |179.464-188.3525
|184.314
|184.314
| |186.667-191.111
| |186.{{Overline|6}}-191.{{Overline|1}}
|-
|-
| |2
| |2
|337.778-346.667
|337.{{Overline|7}}-346.{{Overline|6}}
|348.718
|348.718
| colspan="2" |341.111-358.889
| colspan="2" |341.{{Overline|1}}-358.{{Overline|8}}
|350.877
|350.877
| colspan="2" |346.667-364.444
| colspan="2" |346.{{Overline|6}}-364.{{Overline|4}}
|358.333
|358.{{Overline|3}}
| colspan="2" |349.732-367.51
| colspan="2" |349.732-367.51
|363.218
|363.218
| colspan="2" |368.927-376.705
| colspan="2" |368.927-376.705
|368.6275
|368.6275
| |373.333-382.222
| |373.{{Overline|3}}-382.{{Overline|2}}
|-
|-
| |3
| |3
|506.667-520
|506.{{Overline|6}}-520
|523.077
|523.077
| colspan="2" |511.667-538.333
| colspan="2" |511.{{Overline|6}}-538.{{Overline|3}}
|526.316
|526.316
| colspan="2" |520-546.667
| colspan="2" |520-546.{{Overline|6}}
|537.5
|537.5
| colspan="2" |524.598-551.264
| colspan="2" |524.598-551.264
Line 239: Line 239:
| colspan="2" |538.391-565.0575
| colspan="2" |538.391-565.0575
|552.941
|552.941
| |560-573.333
| |560-573.{{Overline|3}}
|-
|-
| |4
| |4
|675.556-693.333
|675.{{Overline|5}}-693.{{Overline|3}}
|697.436
|697.436
| colspan="2" |682.222-717.778
| colspan="2" |682.{{Overline|2}}-717.{{Overline|7}}
|701.754
|701.754
| colspan="2" |693.333-728.889
| colspan="2" |693.{{Overline|3}}-728.{{Overline|8}}
|716.667
|716.{{Overline|6}}
| colspan="2" |699.464-735.019
| colspan="2" |699.464-735.019
|726.437
|726.437
| colspan="2" |717.854-753.41
| colspan="2" |717.854-753.41
|737.255
|737.255
| |746.667-764.444
| |746.{{Overline|6}}-764.{{Overline|4}}
|-
|-
| |5
| |5
|844.444-866.667
|844.{{Overline|4}}-866.{{Overline|6}}
|871.795
|871.795
| colspan="2" |852.778-897.222
| colspan="2" |852.{{Overline|7}}-897.{{Overline|2}}
|877.193
|877.193
| colspan="2" |866.667-911.111
| colspan="2" |866.{{Overline|6}}-911.{{Overline|1}}
|895.833
|895.8{{Overline|3}}
| colspan="2" |874.3295-918.774
| colspan="2" |874.3295-918.774
|908.046
|908.046
| colspan="2" |897.318-942.7625
| colspan="2" |897.318-942.7625
|921.569
|921.569
| |933.333-955.556
| |933.{{Overline|3}}-955.{{Overline|5}}
|-
|-
| |6
| |6
|1013.333-1040
|1013.{{Overline|3}}-1040
|1046.154
|1046.154
| colspan="2" |1023.333-1076.667
| colspan="2" |1023.{{Overline|3}}-1076.{{Overline|6}}
|1052.632
|1052.632
| colspan="2" |1040-1093.333
| colspan="2" |1040-1093.{{Overline|3}}
|1075
|1075
| colspan="2" |1049.195-1102.529
| colspan="2" |1049.195-1102.529
Line 278: Line 278:
| colspan="2" |1076.782-1130.115
| colspan="2" |1076.782-1130.115
|1105.882
|1105.882
| |1120-1146.667
| |1120-1146.{{Overline|6}}
|-
|-
| |7
| |7
|1182.222-1213.333
|1182.{{Overline|2}}-1213.{{Overline|3}}
|1220.513
|1220.513
| colspan="2" |1193.889-1256.111
| colspan="2" |1193.{{Overline|8}}-1256.{{Overline|1}}
|1228.07
|1228.07
| colspan="2" |1213.333-1275.556
| colspan="2" |1213.{{Overline|3}}-1275.{{Overline|5}}
|1254.167
|1254.1{{Overline|6}}
| colspan="2" |1224.061-1286.2835
| colspan="2" |1224.061-1286.2835
|1271.264
|1271.264
| colspan="2" |1256.245-1318.457
| colspan="2" |1256.245-1318.457
|1290.196
|1290.196
| |1306.667-1337.778
| |1306.{{Overline|6}}-1337.{{Overline|7}}
|-
|-
|8
|8
|1351.111-1386.667
|1351.{{Overline|1}}-1386.{{Overline|6}}
|1394.872
|1394.872
| colspan="2" |1364.444-1435.556
| colspan="2" |1364.{{Overline|4}}-1435.{{Overline|5}}
|1403.509
|1403.509
| colspan="2" |1386.667-1457.778
| colspan="2" |1386.{{Overline|6}}-1457.{{Overline|7}}
|1433.333
|1433.{{Overline|3}}
| colspan="2" |1398.927-1470.038
| colspan="2" |1398.927-1470.038
|1452.874
|1452.874
| colspan="2" |1438.709-1506.82
| colspan="2" |1438.709-1506.82
|1474.51
|1474.51
|1493.333-1528.889
|1493.{{Overline|3}}-1528.{{Overline|8}}
|}Relative cents
|}Relative cents


Line 315: Line 315:
|-
|-
|1
|1
|161.111
|161.{{Overline|1}}
|166.667
|166.{{Overline|6}}
|177.778
|177.{{Overline|7}}
|183.333
|183.{{Overline|3}}
|-
|-
|2
|2
|322.222
|322.{{Overline|2}}
|333.333
|333.{{Overline|3}}
|355.556
|355.{{Overline|5}}
|366.667
|366.{{Overline|6}}
|-
|-
|3
|3
|483.333
|483.{{Overline|3}}
|500
|500
|533.333
|533.{{Overline|3}}
|550
|550
|-
|-
|4
|4
|644.444
|644.{{Overline|4}}
|666.667
|666.{{Overline|6}}
|711.111
|711.{{Overline|1}}
|733.333
|733.{{Overline|3}}
|-
|-
|5
|5
|805.556
|805.{{Overline|5}}
|833.333
|833.{{Overline|3}}
|888.889
|888.{{Overline|8}}
|916.667
|916.{{Overline|6}}
|-
|-
|6
|6
|966.667
|966.{{Overline|6}}
|1000
|1000
|1066.667
|1066.{{Overline|6}}
|1100
|1100
|-
|-
|7
|7
|1127.778
|1127.{{Overline|7}}
|1166.666
|1166.{{Overline|6}}
|1244.444
|1244.{{Overline|4}}
|1283.333
|1283.{{Overline|3}}
|-
|-
|8
|8
|1288.889
|1288.{{Overline|8}}
|1333.333
|1333.{{Overline|3}}
|1422.222
|1422.{{Overline|2}}
|1466.667
|1466.{{Overline|6}}
|}Golden/Pyrite Tunings±13¢
|}Golden/Pyrite Tunings±13¢


Revision as of 18:27, 9 May 2023

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
1 155.5-160 161.905 158.518-167.407 164.103 162.2-171.1 168.889 165.2525-174.141 170.370 171.429-175.873
2 311.1-320 323.8095 317.037-334.814 328.205 324.4-342.2 337.7 330.505-348.283 340.740 342.857-351.746
3 466.6-480 485.714 475.5-502.2 492.308 486.6-513.3 506.6 495.758-522.424 511.1 514.286-527.619
4 622.2-640 647.619 634.074-669.629 656.41 648.8-684.4 675.5 661.01-696.566 681.481 685.714-703.492
5 777.7-800 809.524 792.592-837.037 820.512 811.1-855.5 844.4 826.263-870.707 851.851 857.143-878.365
6 943.3-960 971.429 951.1-1004.4 984.615 973.3-1026.6 1013.3 988.515-1044.848 1022.2 1028.571-1055.238
7 1088.8-1120 1133.3 1109.629-1171.851 1148.718 1135.5-1197.7 1182.2 1156.768-1218.99 1192.592 1200-1231.1
8 1244.4-1280 1295.238 1238.148-1339.259 1312.8205 1297.7-1368.8 1351.1 1321.02-1392.131 1362.962 1371.429-1406.984
Degrees Mohajira Beatles
Min-comma r¢ Med Max+comma~Min-comma Med Max+comma
1 166.984-171.429 172.2 168.105-176.9935 172.8395 173.3-177.7
2 333.968-342.857 344.4 336.209-353.987 345.679 346.6-355.5
3 500.952-514.286 516.6 504.314-530.98 518.518 520-533.3
4 667.9365-685.714 688.8 672.418-707.974 691.358 693.3-711.1
5 834.921-857.143 861.1 840.523-885.967 864.1975 866.6-888.8
6 1001.904-1028.571 1033.3 1008.6275-1062.961 1037.037 1040-1066.6
7 1168.8-1200 1205.5 1176.732-1239.954 1209.8765 1213.3-1244.4
8 1335.873-1371.429 1377.7 1344.837-1416.948 1382.716 1386.6-1422.2
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
1 168.8-173.3 174.359 170.5-179.4 175.439 173.3-182.2 179.16 174.866-183.755 181.609 179.464-188.3525 184.314 186.6-191.1
2 337.7-346.6 348.718 341.1-358.8 350.877 346.6-364.4 358.3 349.732-367.51 363.218 368.927-376.705 368.6275 373.3-382.2
3 506.6-520 523.077 511.6-538.3 526.316 520-546.6 537.5 524.598-551.264 544.828 538.391-565.0575 552.941 560-573.3
4 675.5-693.3 697.436 682.2-717.7 701.754 693.3-728.8 716.6 699.464-735.019 726.437 717.854-753.41 737.255 746.6-764.4
5 844.4-866.6 871.795 852.7-897.2 877.193 866.6-911.1 895.83 874.3295-918.774 908.046 897.318-942.7625 921.569 933.3-955.5
6 1013.3-1040 1046.154 1023.3-1076.6 1052.632 1040-1093.3 1075 1049.195-1102.529 1089.655 1076.782-1130.115 1105.882 1120-1146.6
7 1182.2-1213.3 1220.513 1193.8-1256.1 1228.07 1213.3-1275.5 1254.16 1224.061-1286.2835 1271.264 1256.245-1318.457 1290.196 1306.6-1337.7
8 1351.1-1386.6 1394.872 1364.4-1435.5 1403.509 1386.6-1457.7 1433.3 1398.927-1470.038 1452.874 1438.709-1506.82 1474.51 1493.3-1528.8

Relative cents

Degrees Intense Aeolian-Subpental Dorian Dorian Subpental-Soft Superpental Mixolydian Intense Superpental Mixolydian ~ Mixolydian-Ionian
1 161.1 166.6 177.7 183.3
2 322.2 333.3 355.5 366.6
3 483.3 500 533.3 550
4 644.4 666.6 711.1 733.3
5 805.5 833.3 888.8 916.6
6 966.6 1000 1066.6 1100
7 1127.7 1166.6 1244.4 1283.3
8 1288.8 1333.3 1422.2 1466.6

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.

See also

  • 9ed5/2 - equal division of the classic major tenth
  • 9ed7/3 - equal division of the septimal minor tenth
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