User:Moremajorthanmajor/9edX: Difference between revisions

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| colspan="2" |1471.264
| colspan="2" |1471.264
|1493.333
|1493.333
|}Most harmonic tunings
{| class="wikitable"
|-
! rowspan="2" |Degrees
!Minor mode Middletown temperament
!Neutral mode Middletown temperament
!Major mode Middletown temperament
|-
!7/3±13¢
!22/9±13¢
!5/2±13¢
|-
| |1
|161.541-164.43
|170.49-173.379
|174.813-177.7015
|-
| |2
|323.082-328.86
|340.9795-346.757
|349.625-355.403
|-
| |3
|484.624-493.29
|511.469-520.136
|524.438-533.105
|-
| |4
|646.165-657.72
|681.959-693.515
|699.2505-710.806
|-
| |5
|807.706-822.1505
|852.489-866.893
|874.063-888.508
|-
| |6
|969.247-986.581
|1022.939-1040.272
|1048.876-1066.5425
|-
| |7
|1130.7885-1151.011
|1193.428-1215.651
|1223.688-1244.466
|-
|8
|1292.33-1315.441
|1363.918-1387.293
|1398.4501-1422.391
|}Golden tunings
|}Golden tunings
Minor mode Middletown temperament
{| class="wikitable"
{| class="wikitable"
|+
|+
! rowspan="4" |Degrees
! rowspan="3" |Degrees
! colspan="4" |Minor mode Middletown temperament
! colspan="3" |Aeolian-Dorian
!Neutral mode Middletown temperament
! colspan="9" |Dorian
! colspan="5" |Major mode Middletown temperament
|-
! rowspan="3" |Aeolian-Dorian
! colspan="3" |Dorian
! rowspan="3" |Dorian-Mixolydian
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
! rowspan="2" |-13¢
! rowspan="2" |Pental
! rowspan="2" |Mean
! rowspan="2" |Superpental
! rowspan="2" |-13¢ (s5D)
! rowspan="2" |Subpental
! colspan="3" |Subpental
! rowspan="2" |Pental
! colspan="3" |Pental
! colspan="2" |Superpental
! colspan="3" |Superpental
|-
|-
!Soft
!+13¢ (A-D)
!Intense
!Mean
!+13¢
!-13¢
!-13¢ (S5)
!Mean
!Mean
!+13¢ (5)
!-13¢ (D-M)
|-
|-
|1
|1
|160.761
|162.206
|162.206
|162.317
|163.65
|163.761
|163.761
|165.2055
|167.6965
|168.741
|169.141
|169.141
|170.186
|170.186
|170.585
|171.314
|-
|2
|321.522
|324.411
|364.633
|327.3
|327.522
|330.411
|335.393
|337.483
|338.282
|340.3715
|341.171
|342.617
|-
|3
|482.284
|486.617
|486.95
|490.95
|491.283
|495.617
|503.089
|506.224
|507.423
|510.557
|511.756
|513.941
|-
|4
|643.045
|648.823
|649.2665
|654.6
|655.044
|660.822
|670.786
|674.965
|676.564
|680.743
|682.341
|685.255
|-
|5
|803.806
|811.028
|811.583
|818.25
|818.805
|826.028
|838.482
|843.707
|845.7045
|850.928
|852.927
|856.568
|-
|6
|964.567
|973.234
|973.9
|981.9
|982.5665
|991.233
|1006.179
|1012.448
|1014.8455
|1021.115
|1023.512
|1027.882
|-
|7
|1125.328
|1135.4395
|1136.216
|1145.55
|1146.3275
|1156.439
|1173.875
|1181.189
|1183.986
|1191.3
|1194.0975
|1199.196
|-
|8
|1286.09
|1297.645
|1278.2435
|1309.2
|1310.089
|1321.644
|1341.572
|1349.9305
|1353.127
|1361.486
|1343.36
|1349.095
|}
Neutral (Dorian-Mixolydian) mode Middletown temperament
{| class="wikitable"
|-
!Degrees
!+13¢ (S5D)
!Mean
!-13¢ (s5M)
|-
|1
|171.63
|172.758
|172.758
|173.091
|-
|2
|343.36
|345.516
|346.182
|-
|3
|514.891
|518.274
|519.2735
|-
|4
|686.521
|691.0325
|692.365
|-
|5
|858.151
|863.791
|965.456
|-
|6
|1029.781
|1036.549
|1038.547
|-
|7
|1201.411
|1209.307
|1211.638
|-
|8
|1373.042
|1382.065
|1384.729
|}
Major mode Middletown temperament
{| class="wikitable"
|-
! rowspan="4" |Degrees
! colspan="13" |Mixolydian
! colspan="2" |Mixolydian-Ionian
|-
! colspan="3" |Subpental
! colspan="4" |Pental
! colspan="6" |Superpental
! rowspan="3" |Mean
! rowspan="3" |+13¢
|-
! rowspan="2" |-13¢ (5)
! rowspan="2" |+13¢ (D-M)
! rowspan="2" |Mean
! rowspan="2" |Mean
! rowspan="2" |+13¢ (s5)
! rowspan="2" |+13¢
! rowspan="2" |-13¢ (Soft S5)
! rowspan="2" |Soft
! colspan="5" |Intense
|-
!+13¢ (Soft s5)
!-13¢
!Mean
!-13¢ (M-I)
!+13¢
|-
|1
|173.844
|174.203
|174.536
|174.536
|175.2885
|175.2885
|175.98
|176.733
|177.774
|179.218
|179.218
|180.663
|180.707
|182.152
|182.152
|182.729
|183.596
|184.174
|184.174
|185.618
|-
|-
|2
|2
|324.411
|347.688
|327.522
|348.405
|338.282
|340.3715
|345.516
|349.071
|349.071
|351.577
|351.577
|351.96
|353.466
|355.548
|358.4365
|358.4365
|361.325
|361.415
|364.304
|364.304
|365.4585
|367.193
|368.347
|368.347
|371.236
|-
|-
|3
|3
|486.617
|521.532
|491.283
|522.608
|507.423
|510.557
|518.274
|523.607
|523.607
|525.865
|525.865
|527.94
|530.199
|533.321
|537.655
|537.655
|541.988
|542.122
|546.456
|546.456
|548.188
|550.789
|552.521
|552.521
|556.854
|-
|-
|4
|4
|648.823
|695.376
|655.044
|696.81
|676.564
|680.743
|691.0325
|698.142
|698.142
|701.154
|701.154
|703.92
|706.932
|711.095
|716.873
|716.873
|722.651
|722.83
|728.6075
|728.6075
|730.917
|734.385
|736.695
|736.695
|742.4725
|-
|-
|5
|5
|811.028
|869.22
|818.805
|871.012
|845.7045
|850.928
|863.791
|872.678
|872.678
|876.442
|876.442
|879.9
|883.6645
|888.896
|896.091
|896.091
|903.3135
|903.537
|910.759
|910.759
|913.646
|917.982
|920.8685
|920.8685
|928.091
|-
|-
|6
|6
|973.234
|1043.064
|982.5665
|1045.2155
|1014.8455
|1021.115
|1036.549
|1047.214
|1047.214
|1051.731
|1051.731
|1055.88
|1060.3975
|1033.634
|1075.3095
|1075.3095
|1083.976
|1084.245
|1092.911
|1092.911
|1096.3755
|1101.578
|1105.042
|1105.042
|1113.709
|-
|-
|7
|7
|1135.4395
|1216.908
|1146.3275
|1219.418
|1183.986
|1191.3
|1209.307
|1221.749
|1221.749
|1227.019
|1227.019
|1231.86
|1237.13
|1244.417
|1254.528
|1254.528
|1264.639
|1264.952
|1275.063
|1275.063
|1279.105
|1285.174
|1289.215
|1289.215
|1299.327
|-
|-
|8
|8
|1297.645
|1390.752
|1310.089
|1393.621
|1353.127
|1361.486
|1382.065
|1396.285
|1396.285
|1402.308
|1402.308
|1407.84
|1413.863
|1422.19
|1433.746
|1433.746
|1445.3015
|1445.6595
|1457.215
|1457.215
|1461.834
|1445.821
|1473.3895
|1473.3895
|1484.945
|}
|}


Revision as of 01:01, 6 November 2018

This is the neutral scale of the Middletown temperament family.

Intervals

Degrees Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
Aeolian-Dorian Dorian Dorian-Mixolydian Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Subpental Pental Superpental
Soft Intense
Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum Minimum Maximum
1 160 162.963 166.667 169.697 171.429 173.333 175 177.778 179.31 183.908 186.667
2 320 325.926 333.333 339.394 342.857 246.667 350 355.556 358.621 367.816 373.333
3 480 488.889 500 509.091 514.286 520 525 533.333 537.931 551.724 560
4 640 651.852 666.667 678.788 685.714 693.333 700 711.111 717.241 735.632 846.667
5 800 814.815 833.333 848.485 857.143 866.667 875 888.889 896.552 919.54 1033.333
6 960 977.778 1000 1018.182 1028.571 1040 1050 1066.667 1075.862 1103.448 1120
7 1120 1140.741 1166.666 1187.879 1200 1213.333 1225 1244.444 1255.172 1287.356 1306.667
8 1280 1303.704 1333.333 1357.576 1371.429 1386.667 1400 1422.222 1434.483 1471.264 1493.333

Most harmonic tunings

Degrees Minor mode Middletown temperament Neutral mode Middletown temperament Major mode Middletown temperament
7/3±13¢ 22/9±13¢ 5/2±13¢
1 161.541-164.43 170.49-173.379 174.813-177.7015
2 323.082-328.86 340.9795-346.757 349.625-355.403
3 484.624-493.29 511.469-520.136 524.438-533.105
4 646.165-657.72 681.959-693.515 699.2505-710.806
5 807.706-822.1505 852.489-866.893 874.063-888.508
6 969.247-986.581 1022.939-1040.272 1048.876-1066.5425
7 1130.7885-1151.011 1193.428-1215.651 1223.688-1244.466
8 1292.33-1315.441 1363.918-1387.293 1398.4501-1422.391

Golden tunings

Minor mode Middletown temperament

Degrees Aeolian-Dorian Dorian
-13¢ Mean -13¢ (s5D) Subpental Pental Superpental
+13¢ (A-D) Mean +13¢ -13¢ -13¢ (S5) Mean Mean +13¢ (5) -13¢ (D-M)
1 160.761 162.206 162.317 163.65 163.761 165.2055 167.6965 168.741 169.141 170.186 170.585 171.314
2 321.522 324.411 364.633 327.3 327.522 330.411 335.393 337.483 338.282 340.3715 341.171 342.617
3 482.284 486.617 486.95 490.95 491.283 495.617 503.089 506.224 507.423 510.557 511.756 513.941
4 643.045 648.823 649.2665 654.6 655.044 660.822 670.786 674.965 676.564 680.743 682.341 685.255
5 803.806 811.028 811.583 818.25 818.805 826.028 838.482 843.707 845.7045 850.928 852.927 856.568
6 964.567 973.234 973.9 981.9 982.5665 991.233 1006.179 1012.448 1014.8455 1021.115 1023.512 1027.882
7 1125.328 1135.4395 1136.216 1145.55 1146.3275 1156.439 1173.875 1181.189 1183.986 1191.3 1194.0975 1199.196
8 1286.09 1297.645 1278.2435 1309.2 1310.089 1321.644 1341.572 1349.9305 1353.127 1361.486 1343.36 1349.095

Neutral (Dorian-Mixolydian) mode Middletown temperament

Degrees +13¢ (S5D) Mean -13¢ (s5M)
1 171.63 172.758 173.091
2 343.36 345.516 346.182
3 514.891 518.274 519.2735
4 686.521 691.0325 692.365
5 858.151 863.791 965.456
6 1029.781 1036.549 1038.547
7 1201.411 1209.307 1211.638
8 1373.042 1382.065 1384.729

Major mode Middletown temperament

Degrees Mixolydian Mixolydian-Ionian
Subpental Pental Superpental Mean +13¢
-13¢ (5) +13¢ (D-M) Mean Mean +13¢ (s5) +13¢ -13¢ (Soft S5) Soft Intense
+13¢ (Soft s5) -13¢ Mean -13¢ (M-I) +13¢
1 173.844 174.203 174.536 175.2885 175.98 176.733 177.774 179.218 180.663 180.707 182.152 182.729 183.596 184.174 185.618
2 347.688 348.405 349.071 351.577 351.96 353.466 355.548 358.4365 361.325 361.415 364.304 365.4585 367.193 368.347 371.236
3 521.532 522.608 523.607 525.865 527.94 530.199 533.321 537.655 541.988 542.122 546.456 548.188 550.789 552.521 556.854
4 695.376 696.81 698.142 701.154 703.92 706.932 711.095 716.873 722.651 722.83 728.6075 730.917 734.385 736.695 742.4725
5 869.22 871.012 872.678 876.442 879.9 883.6645 888.896 896.091 903.3135 903.537 910.759 913.646 917.982 920.8685 928.091
6 1043.064 1045.2155 1047.214 1051.731 1055.88 1060.3975 1033.634 1075.3095 1083.976 1084.245 1092.911 1096.3755 1101.578 1105.042 1113.709
7 1216.908 1219.418 1221.749 1227.019 1231.86 1237.13 1244.417 1254.528 1264.639 1264.952 1275.063 1279.105 1285.174 1289.215 1299.327
8 1390.752 1393.621 1396.285 1402.308 1407.84 1413.863 1422.19 1433.746 1445.3015 1445.6595 1457.215 1461.834 1445.821 1473.3895 1484.945

By a surprising coincidence, the 9ed of the Golden tenth (7*phi+6)\(5*phi^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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