User:Moremajorthanmajor/19edX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! colspan="2" rowspan="5" |Enneatonic
! colspan="8" |Minor mode Middletown temperament
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Major mode Middletown temperament
|-
|-
! | Degrees
! colspan="2" rowspan="3" |Aeolian-Dorian
! | Enneatonic
! colspan="6" |Dorian
! | Minimum
! colspan="2" rowspan="3" |Dorian-Mixolydian
! | ed(7/3)
! colspan="8" |Mixolydian
! | Mean/Median
! colspan="2" rowspan="3" |Mixolydian-Ionian
! | Golden
! | Maximum
|-
|-
| | 1
! colspan="2" rowspan="2" |Subpental
| | Gb
! colspan="2" rowspan="2" |Pental
| | 75.7895
! colspan="2" rowspan="2" |Superpental
| | 77.204
! colspan="2" rowspan="2" |Subpental
| | 82.105
! colspan="2" rowspan="2" |Pental
| | 83.596
! colspan="4" |Superpental
| | 88.421
|-
|-
| | 2
! colspan="2" |Soft
| | F#
! colspan="2" |Intense
| | 151.579
| | 154.407'5
| | 164.210'5
| | 167.197
| | 176.842
|-
|-
| | 3
! |Minimum
| | G
! |Maximum
| | 227.368
!Minimum
| | 231.611
!Maximum
| | 246.316
!Minimum
| | 250.789
!Maximum
| | 265.263
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| | 4
| |1
| | H
| colspan="2" |Gb
| | 303.158
| |75.7895
| | 308.815
| colspan="2" |77.193
| | 328.421
| colspan="2" |78.947
| | 334.385
| colspan="2" |80.383
| | 353.684
| colspan="2" |81.203
| colspan="2" |82.105
| colspan="2" |82.895
| colspan="2" |84.2105
| colspan="2" |84.9365
| colspan="2" |87.114
| |88.421
|-
|-
| | 5
| |2
| | Jb
| colspan="2" |F#
| | 378.947
| |151.579
| | 386.019
| colspan="2" |154.386
| | 410.526
| colspan="2" |157.895
| | 417.981
| colspan="2" |160.766
| | 442.105
| colspan="2" |162.406
| colspan="2" |164.2105
| colspan="2" |165.7896
| colspan="2" |168.421
| colspan="2" |169.873
| colspan="2" |174.229
| |176.842
|-
|-
| | 6
| |3
| | H#
| colspan="2" |G
| | 454.737
| |227.368
| | 463.222
| colspan="2" |231.579
| | 492.632
| colspan="2" |236.842
| | 501.577
| colspan="2" |241.148
| | 530.526
| colspan="2" |243.609
| colspan="2" |246.316
| colspan="2" |248.684
| colspan="2" |252.632
| colspan="2" |254.809
| colspan="2" |261.343
| |265.263
|-
|-
| | 7
| |4
| | J
|J
| | 530.526
|''A''
| | 540.426
| |303.158
| | 574.737
| colspan="2" |308.772
| | 585.173'5
| colspan="2" |315.7895
| | 618.947
| colspan="2" |321.531
| colspan="2" |324.812
| colspan="2" |328.421
| colspan="2" |331.579
| colspan="2" |336.842
| colspan="2" |339.746
| colspan="2" |348.457
| |353.684
|-
|-
| | 8
| |5
| | A
|Ab
| | 606.316
|''Bb''
| | 617.63
| |378.947
| | 656.842
| colspan="2" |385.965
| | 668.768
| colspan="2" |394.737
| | 707.368
| colspan="2" |401.914
| colspan="2" |406.015
| colspan="2" |410.526
| colspan="2" |414.474
| colspan="2" |421.053
| colspan="2" |424.682
| colspan="2" |435.527
| |442.105
|-
|-
| | 9
| |6
| | Bb
|J#
| | 682.105
|''A#''
| | 694.834
| |454.737
| | 738.947
| colspan="2" |463.158
| | 752.366
| colspan="2" |473.684
| | 795.789'5
| colspan="2" |482.297
| colspan="2" |487.218
| colspan="2" |492.632
| colspan="2" |497.368
| colspan="2" |505.263
| colspan="2" |509.619
| colspan="2" |522.686
| |530.526
|-
|-
| | 10
| |7
| | A#
|A
| | 757.895
|''B''
| | 772.037
| |530.526
| | 821.053
| colspan="2" |540.351
| | 835.962
| colspan="2" |552.632
| | 884.210'5
| colspan="2" |592.679
| colspan="2" |568.421
| colspan="2" |574.737
| colspan="2" |580.263
| colspan="2" |589.474
| colspan="2" |594.555
| colspan="2" |609.8
| |618.947
|-
|-
| | 11
|8
| | B
|B
| | 833.654
|''H''
| | 849.241
|606.316
| | 903.158
| colspan="2" |617.544
| | 919.558
| colspan="2" |631.579
| | 972.632
| colspan="2" |643.062
| colspan="2" |647.624
| colspan="2" |656.842
| colspan="2" |663.158
| colspan="2" |673.684
| colspan="2" |679.491
| colspan="2" |696.915
|707.368
|-
|-
| | 12
|9
| | C
|Hb
| | 909.474
|''Cb''
| | 926.445
|682.105
| | 985.263
| colspan="2" |694.737
| | 1003.155
| colspan="2" |710.526
| | 1061.053
| colspan="2" |723.445
| colspan="2" |730.827
| colspan="2" |738.947
| colspan="2" |746.053
| colspan="2" |757.895
| colspan="2" |764.418
| colspan="2" |784.029
|795.7895
|-
|-
| | 13
|10
| | Db
|B#
| | 985.263
|''H#''
| | 1003.6485
|757.895
| | 1067.368
| colspan="2" |771.93
| | 1086.751
| colspan="2" |789.474
| | 1149.474
| colspan="2" |803.828
| colspan="2" |812.03
| colspan="2" |821.053
| colspan="2" |828.947
| colspan="2" |842.105
| colspan="2" |849.365
| colspan="2" |871.143
|884.2105
|-
|-
| | 14
|11
| | C#
|H
| | 1061.053
|''C''
| | 1008.852
|833.654
| | 1149.474
| colspan="2" |849.123
| | 1170.347
| colspan="2" |868.421
| | 1237.895
| colspan="2" |884.2105
| colspan="2" |893.233
| colspan="2" |903.158
| colspan="2" |911.843
| colspan="2" |926.316
| colspan="2" |934.302
| colspan="2" |958.258
|972.632
|-
|-
| | 15
|12
| | D
|C
| | 1136.842
|''D''
| | 1158.056
|909.474
| | 1231.579
| colspan="2" |926.326
| | 1253.943
| colspan="2" |947.378
| | 1326.316
| colspan="2" |964.593
| colspan="2" |974.436
| colspan="2" |985.263
| colspan="2" |994.737
| colspan="2" |1010.526
| colspan="2" |1019.238
| colspan="2" |1045.372
|1061.053
|-
|-
| | 16
|13
| | Eb
|Db
| | 1212.632
|''Sb''
| | 1235.26
|985.263
| | 1313.684
| colspan="2" |1003.509
| | 1337.539'5
| colspan="2" |1026.316
| | 1414.737
| colspan="2" |1044.976
| colspan="2" |1055.639
| colspan="2" |1067.368
| colspan="2" |1077.612
| colspan="2" |1094.737
| colspan="2" |1104.172
| colspan="2" |1132.486
|1149.474
|-
|-
| | 17
|14
| | D#
|C#
| | 1288.421
|''D#''
| | 1312.463
|1061.053
| | 1395.7895
| colspan="2" |1080.702
| | 1421.136
| colspan="2" |1105.263
| | 1503.158
| colspan="2" |1125.359
| colspan="2" |1136.842
| colspan="2" |1149.474
| colspan="2" |1160.526
| colspan="2" |1178.947
| colspan="2" |1189.111
| colspan="2" |1220.601
|1237.895
|-
|-
| | 18
|15
| | E
|D
| | 1364.2105
|''S''
| | 1289.667
|1136.842
| | 1477.895
| colspan="2" |1107.895
| | 1504.732
| colspan="2" |1184.2105
| | 1591.579
| colspan="2" |1205.742
| colspan="2" |1218.045
| colspan="2" |1231.579
| colspan="2" |1243.421
| colspan="2" |1263.158
| colspan="2" |1274.047
| colspan="2" |1306.715
|1326.316
|-
|-
| | 19
|16
| | F
| colspan="2" |Eb
| | 1440
|1212.632
| | 1466.871
| colspan="2" |1235.088
| | 1560
| colspan="2" |1363.156
| | 1588.238
| colspan="2" |1286.124
| | 1680
| colspan="2" |1299.248
| colspan="2" |1313.684
| colspan="2" |1326.316
| colspan="2" |1347.378
| colspan="2" |1359.984
| colspan="2" |1393.829
|1414.737
|-
|17
|D#
|''S#''
|1288.421
| colspan="2" |1312.181
| colspan="2" |1042.105
| colspan="2" |1366.507
| colspan="2" |1380.451
| colspan="2" |1395.7895
| colspan="2" |1408.2105
| colspan="2" |1431.579
| colspan="2" |1443.98
| colspan="2" |1480.944
|1503.158
|-
|18
| colspan="2" |E
|1364.2105
| colspan="2" |1389.474
| colspan="2" |1421.053
| colspan="2" |1446.89
| colspan="2" |1461.654
| colspan="2" |1477.895
| colspan="2" |1491.105
| colspan="2" |1515.7895
| colspan="2" |1526.8275
| colspan="2" |1568.058
|1591.579
|-
|19
| colspan="2" |F
|1440
| colspan="2" |1466.667
| colspan="2" |1500
| colspan="2" |1527.273
| colspan="2" |1542.857
| colspan="2" |1560
| colspan="2" |1575
| colspan="2" |1600
| colspan="2" |1613.793
| colspan="2" |1655.172
|1680
|}Golden tunings
{| class="wikitable"
|+
! rowspan="4" |Degrees
! colspan="2" rowspan="4" |Enneatonic
! colspan="4" |Minor mode Middletown temperament
!Neutral mode Middletown temperament
! 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" |Pental
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
!Soft
!Intense
|-
|1
| colspan="2" |Gb
|76.834
|77.571
|80.119
|80.614
|81.833
|82.675
|83.031
|84.893
|86.2825
|87.24
|-
|2
| colspan="2" |F#
|153.6685
|155.142
|160.239
|161.229
|163.666
|165.3495
|166.063
|169.786
|172.565
|174.48
|-
|3
| colspan="2" |G
|230.503
|232.713
|240.358
|241.843
|245.498
|248.024
|249.094
|254.679
|258.847
|261.7205
|-
|4
|J
|''A''
|307.337
|310.284
|320.4775
|322.457
|327.331
|330.7
|332.1255
|339.571
|345.13
|348.961
|-
|5
|Ab
|''Bb''
|384.171
|387.855
|400.597
|403.3715
|409.164
|413.374
|415.157
|424.464
|431.412
|436.201
|-
|6
|J#
|''A#''
|491.055
|465.426
|480.716
|483.686
|490.997
|496.0485
|498.188
|509.357
|517.695
|523.441
|-
|7
|A
|''B''
|537.84
|542.997
|560.836
|564.3
|572.83
|578.723
|581.22
|594.25
|603.977
|610.681
|-
|8
|B
|''H''
|614.074
|620.568
|640.955
|644.9145
|654.662
|661.398
|664.251
|679.143
|690.26
|697.921
|-
|9
|Hb
|''Cb''
|691.508
|698.139
|721.074
|725.529
|736.495
|744.073
|747.282
|764.036
|776.542
|785.1615
|-
|10
|B#
|''H#''
|768.3425
|775.71
|801.194
|806.143
|818.327
|826.748
|830.314
|848.9285
|862.825
|872.402
|-
|11
|H
|''C''
|845.177
|853.281
|881.313
|886.757
|900.161
|909.422
|913.345
|933.821
|949.107
|959.642
|-
|12
|C
|''D''
|922.011
|930.852
|964.4325
|967.372
|981.994
|992.097
|996.3765
|1018.714
|1035.39
|1046.882
|-
|13
|Db
|''Sb''
|998.845
|1008.4235
|1041.552
|1047.986
|1063.826
|1074.772
|1079.408
|1103.607
|1121.672
|1134.122
|-
|14
|C#
|''D#''
|1075.68
|1085.9945
|1121.671
|1128.6
|1145.659
|1157.44
|1162.439
|1188.5
|1207.955
|1221.362
|-
|15
|D
|''S''
|1152.514
|1163.566
|1201.791
|1209.215
|1227.492
|1240.121
|1245.471
|1273.392
|1294.237
|1308.6025
|-
|16
| colspan="2" |Eb
|1229.348
|1241.137
|1281.91
|1289.829
|1309.325
|1322.796
|1328.502
|1358.286
|1380.5195
|1395.843
|-
|17
|D#
|''S#''
|1306.182
|1318.708
|1362.029
|1370.443
|1391.158
|1405.471
|1411.533
|1443.1785
|1466.802
|1483.083
|-
|18
| colspan="2" |E
|1383.017
|1396.279
|1442.149
|1451.0575
|1472.99
|1488.149
|1494.565
|1528.071
|1553.0845
|1570.323
|-
|19
| colspan="2" |F
|1459.851
|1473.85
|1522.268
|1531.672
|1554.823
|1570.82
|1577.596
|1612.964
|1639.367
|1657.563
|}
|}

Revision as of 20:22, 25 October 2018

Explanation needed for what this is. See edX maybe?

Intervals

Degrees Enneatonic 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 Gb 75.7895 77.193 78.947 80.383 81.203 82.105 82.895 84.2105 84.9365 87.114 88.421
2 F# 151.579 154.386 157.895 160.766 162.406 164.2105 165.7896 168.421 169.873 174.229 176.842
3 G 227.368 231.579 236.842 241.148 243.609 246.316 248.684 252.632 254.809 261.343 265.263
4 J A 303.158 308.772 315.7895 321.531 324.812 328.421 331.579 336.842 339.746 348.457 353.684
5 Ab Bb 378.947 385.965 394.737 401.914 406.015 410.526 414.474 421.053 424.682 435.527 442.105
6 J# A# 454.737 463.158 473.684 482.297 487.218 492.632 497.368 505.263 509.619 522.686 530.526
7 A B 530.526 540.351 552.632 592.679 568.421 574.737 580.263 589.474 594.555 609.8 618.947
8 B H 606.316 617.544 631.579 643.062 647.624 656.842 663.158 673.684 679.491 696.915 707.368
9 Hb Cb 682.105 694.737 710.526 723.445 730.827 738.947 746.053 757.895 764.418 784.029 795.7895
10 B# H# 757.895 771.93 789.474 803.828 812.03 821.053 828.947 842.105 849.365 871.143 884.2105
11 H C 833.654 849.123 868.421 884.2105 893.233 903.158 911.843 926.316 934.302 958.258 972.632
12 C D 909.474 926.326 947.378 964.593 974.436 985.263 994.737 1010.526 1019.238 1045.372 1061.053
13 Db Sb 985.263 1003.509 1026.316 1044.976 1055.639 1067.368 1077.612 1094.737 1104.172 1132.486 1149.474
14 C# D# 1061.053 1080.702 1105.263 1125.359 1136.842 1149.474 1160.526 1178.947 1189.111 1220.601 1237.895
15 D S 1136.842 1107.895 1184.2105 1205.742 1218.045 1231.579 1243.421 1263.158 1274.047 1306.715 1326.316
16 Eb 1212.632 1235.088 1363.156 1286.124 1299.248 1313.684 1326.316 1347.378 1359.984 1393.829 1414.737
17 D# S# 1288.421 1312.181 1042.105 1366.507 1380.451 1395.7895 1408.2105 1431.579 1443.98 1480.944 1503.158
18 E 1364.2105 1389.474 1421.053 1446.89 1461.654 1477.895 1491.105 1515.7895 1526.8275 1568.058 1591.579
19 F 1440 1466.667 1500 1527.273 1542.857 1560 1575 1600 1613.793 1655.172 1680

Golden tunings

Degrees Enneatonic 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
1 Gb 76.834 77.571 80.119 80.614 81.833 82.675 83.031 84.893 86.2825 87.24
2 F# 153.6685 155.142 160.239 161.229 163.666 165.3495 166.063 169.786 172.565 174.48
3 G 230.503 232.713 240.358 241.843 245.498 248.024 249.094 254.679 258.847 261.7205
4 J A 307.337 310.284 320.4775 322.457 327.331 330.7 332.1255 339.571 345.13 348.961
5 Ab Bb 384.171 387.855 400.597 403.3715 409.164 413.374 415.157 424.464 431.412 436.201
6 J# A# 491.055 465.426 480.716 483.686 490.997 496.0485 498.188 509.357 517.695 523.441
7 A B 537.84 542.997 560.836 564.3 572.83 578.723 581.22 594.25 603.977 610.681
8 B H 614.074 620.568 640.955 644.9145 654.662 661.398 664.251 679.143 690.26 697.921
9 Hb Cb 691.508 698.139 721.074 725.529 736.495 744.073 747.282 764.036 776.542 785.1615
10 B# H# 768.3425 775.71 801.194 806.143 818.327 826.748 830.314 848.9285 862.825 872.402
11 H C 845.177 853.281 881.313 886.757 900.161 909.422 913.345 933.821 949.107 959.642
12 C D 922.011 930.852 964.4325 967.372 981.994 992.097 996.3765 1018.714 1035.39 1046.882
13 Db Sb 998.845 1008.4235 1041.552 1047.986 1063.826 1074.772 1079.408 1103.607 1121.672 1134.122
14 C# D# 1075.68 1085.9945 1121.671 1128.6 1145.659 1157.44 1162.439 1188.5 1207.955 1221.362
15 D S 1152.514 1163.566 1201.791 1209.215 1227.492 1240.121 1245.471 1273.392 1294.237 1308.6025
16 Eb 1229.348 1241.137 1281.91 1289.829 1309.325 1322.796 1328.502 1358.286 1380.5195 1395.843
17 D# S# 1306.182 1318.708 1362.029 1370.443 1391.158 1405.471 1411.533 1443.1785 1466.802 1483.083
18 E 1383.017 1396.279 1442.149 1451.0575 1472.99 1488.149 1494.565 1528.071 1553.0845 1570.323
19 F 1459.851 1473.85 1522.268 1531.672 1554.823 1570.82 1577.596 1612.964 1639.367 1657.563
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