User:Moremajorthanmajor/17edX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! colspan="4" 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
| | Bb
! colspan="2" rowspan="2" |Pental
| | 84.706
! colspan="2" rowspan="2" |Superpental
| | 86.2865
! colspan="2" rowspan="2" |Subpental
| | 91.765
! colspan="2" rowspan="2" |Pental
| | 93.431
! colspan="4" |Superpental
| | 98.8235
|-
|-
| | 2
! colspan="2" |Soft
| | A#
! colspan="2" |Intense
| | 169.412
| | 172.573
| | 183.528
| | 186.862
| | 197.647
|-
|-
| | 3
! |Minimum
| | B
! |Maximum
| | 254.118
!Minimum
| | 258.859
!Maximum
| | 275.294
!Minimum
| | 280.293
!Maximum
| | 296.471
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| | 4
| |1
| | C
| colspan="2" |G
| | 338.823'5
| colspan="2" |Gb
| | 345.147
| |84.706
| | 367.059
| colspan="2" |86.2745
| | 373.724
| colspan="2" |88.235
| | 395.294
| colspan="2" |89.84
| colspan="2" |90.756
| colspan="2" |91.765
| colspan="2" |92.647
| colspan="2" |94.118
| colspan="2" |94.929
| colspan="2" |97.363
| |98.8235
|-
|-
| | 5
| |2
| | Db
|J\\
| | 423.529
|''A\\''
| | 431.433
| colspan="2" |F#
| | 458.823'5
| |169.412
| | 467.155
| colspan="2" |172.549
| | 494.118
| colspan="2" |176.471
| colspan="2" |179.679
| colspan="2" |181.513
| colspan="2" |183.528
| colspan="2" |185.294
| colspan="2" |188.235
| colspan="2" |189.858
| colspan="2" |194.726
| |197.647
|-
|-
| | 6
| |3
| | C#
| colspan="2" |Gp
| | 508.235
| colspan="2" |G
| | 517.719
| |254.118
| | 550.588
| colspan="2" |258.8235
| | 560.586
| colspan="2" |264.706
| | 592.941
| colspan="2" |269.519
| colspan="2" |272.268
| colspan="2" |275.294
| colspan="2" |277.941
| colspan="2" |282.353
| colspan="2" |284.787
| colspan="2" |292.089
| |296.471
|-
|-
| | 7
| |4
| | D
|J
| | 592.941
|A
| | 604.006
|J
| | 642.353
|''A''
| | 654.017'5
| |338.823'5
| | 691.765
| colspan="2" |345.098
| colspan="2" |352.941
| colspan="2" |359.358
| colspan="2" |363.025
| colspan="2" |367.059
| colspan="2" |370.588
| colspan="2" |376.471
| colspan="2" |379.716
| colspan="2" |389.452
| |395.294
|-
|-
| | 8
| |5
| | E
|A
| | 677.647
|''B''
| | 690.212
|Ab
| | 734.118
|''Bb''
| | 747.448'5
| |423.529
| | 790.588
| colspan="2" |431.3725
| colspan="2" |441.1765
| colspan="2" |449.198
| colspan="2" |453.7815
| colspan="2" |458.8235
| colspan="2" |463.235
| colspan="2" |470.588
| colspan="2" |474.645
| colspan="2" |486.815
| |494.118
|-
|-
| | 9
| |6
| | Fb
|B\\
| | 762.653
|''H\\''
| | 776.579
|J#
| | 825.882
|''A#''
| | 840.88
| |508.235
| | 889.412
| colspan="2" |517.647
| colspan="2" |529.412
| colspan="2" |539.037
| colspan="2" |544.538
| colspan="2" |550.588
| colspan="2" |555.882
| colspan="2" |564.706
| colspan="2" |569.574
| colspan="2" |584.1785
| |592.941
|-
|-
| | 10
| |7
| | E#
|Ap
| | 847.059
|''Bp''
| | 862.865
|A
| | 917.647
|''B''
| | 934.31
| |592.941
| | 988.235
| colspan="2" |603.921
| colspan="2" |617.647
| colspan="2" |628.877
| colspan="2" |635.394
| colspan="2" |642.353
| colspan="2" |648.529
| colspan="2" |658.8235
| colspan="2" |664.503
| colspan="2" |681.542
| |691.765
|-
|-
| | 11
|8
| | F
|B
| | 931.765
|''H''
| | 949.152
|B
| | 1009.412
|''H''
| | 1027.742
|677.647
| | 1087.059
| colspan="2" |690.169
| colspan="2" |705.882
| colspan="2" |718.717
| colspan="2" |726.05
| colspan="2" |734.118
| colspan="2" |741.1765
| colspan="2" |752.941
| colspan="2" |759.432
| colspan="2" |778.905
|790.588
|-
|-
| | 12
|9
| | G
|H
| | 1016.471
|''C''
| | 1035.438
|Hb
| | 1101.1765
|''Cb''
| | 1121.173
|762.653
| | 1185.882
| colspan="2" |776.471
| colspan="2" |794.118
| colspan="2" |808.556
| colspan="2" |816.806
| colspan="2" |825.882
| colspan="2" |833.8235
| colspan="2" |847.059
| colspan="2" |854.361
| colspan="2" |876.268
|889.412
|-
|-
| | 13
|10
| | Hb
|C\\
| | 1101.1765
|''D\\''
| | 1121.725
|B#
| | 1192.941
|''H#''
| | 1214.604
|847.059
| | 1284.706
| colspan="2" |862.745
| colspan="2" |882.353
| colspan="2" |898.396
| colspan="2" |907.563
| colspan="2" |917.647
| colspan="2" |926.471
| colspan="2" |941.1765
| colspan="2" |949.29
| colspan="2" |973.631
|988.235
|-
|-
| | 14
|11
| | G#
|Hp
| | 1185.882
|''Cp''
| | 1208.011
|H
| | 1284.706
|''C''
| | 1308.035
|931.765
| | 1383.529
| colspan="2" |949.02
| colspan="2" |970.588
| colspan="2" |988.235
| colspan="2" |998.319
| colspan="2" |1009.412
| colspan="2" |1019.118
| colspan="2" |1035.294
| colspan="2" |1044.219
| colspan="2" |1070.994
|1087.059
|-
|-
| | 15
|12
| | H
|C
| | 1270.588
|''D''
| | 1294.298
|C
| | 1376.471
|''D''
| | 1401.466
|1016.471
| | 1482.352
| colspan="2" |1035.294
| colspan="2" |1058.8235
| colspan="2" |1078.075
| colspan="2" |1089.076
| colspan="2" |1101.1765
| colspan="2" |1111.765
| colspan="2" |1129.412
| colspan="2" |1139.148
| colspan="2" |1168.357
|1185.882
|-
|-
| | 16
|13
| | J
|D
| | 1355.294
|''S''
| | 1380.584
|Db
| | 1468.235
|''Sb''
| | 1494.897
|1101.1765
| | 1581.1765
| colspan="2" |1121.569
| colspan="2" |1147.059
| colspan="2" |1167.914
| colspan="2" |1179.832
| colspan="2" |1192.941
| colspan="2" |1204.412
| colspan="2" |1223.529
| colspan="2" |1234.077
| colspan="2" |1265.72
|1284.706
|-
|-
| | 17
|14
| | A
| colspan="2" |E
| | 1440
|C#
| | 1466.871
|''D#''
| | 1560
|1185.882
| | 1588.238
| colspan="2" |1027.843
| | 1680
| colspan="2" |1235.294
| colspan="2" |1257.754
| colspan="2" |1270.588
| colspan="2" |1284.706
| colspan="2" |1297.059
| colspan="2" |1317.647
| colspan="2" |1329.006
| colspan="2" |1363.083
|1383.529
|-
|15
| colspan="2" |F\\
|D
|''S''
|1270.588
| colspan="2" |1294.118
| colspan="2" |1323.529
| colspan="2" |1347.594
| colspan="2" |1361.3445
| colspan="2" |1376.471
| colspan="2" |1389.706
| colspan="2" |1411.765
| colspan="2" |1423.935
| colspan="2" |1460.446
|1482.352
|-
|16
| colspan="2" |Ep
| colspan="2" |E
|1355.294
| colspan="2" |1380.392
| colspan="2" |1411.765
| colspan="2" |1437.433
| colspan="2" |1452.101
| colspan="2" |1468.235
| colspan="2" |1482.353
| colspan="2" |1505.882
| colspan="2" |1518.864
| colspan="2" |1557.809
|1581.1765
|-
|17
| colspan="2" |F
| 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="4" 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" |G
| colspan="2" |Gb
|85.874
|86.697
|89.545
|90.098
|91.46
|92.401
|92.8
|94.88
|96.433
|97.504
|-
|2
|J\\
|''A\\''
| colspan="2" |F#
|171.747
|173.394
|179.09
|180.197
|182.92
|184.802
|185.6
|189.7605
|192.867
|195.007
|-
|3
| colspan="2" |Gp
| colspan="2" |G
|257.621
|260.091
|268.636
|270.295
|274.381
|277.204
|278.399
|284.641
|289.3
|292.511
|-
|4
|J
|A
|J
|''A''
|343.494
|346.788
|358.181
|360.393
|365.841
|369.605
|371.199
|379.521
|385.733
|390.015
|-
|5
|A
|''B''
|Ab
|''Bb''
|429.368
|433.485
|447.726
|450.492
|457.301
|462.006
|463.999
|474.401
|482.167
|487.519
|-
|6
|B\\
|''H\\''
|J#
|''A#''
|515.2415
|520.182
|537.271
|540.59
|548.761
|554.407
|556.799
|569.2815
|578.6
|585.022
|-
|7
|Ap
|''Bp''
|A
|''B''
|601.115
|606.879
|626.516
|630.688
|640.221
|646.808
|649.598
|664.162
|675.033
|682.526
|-
|8
|B
|''H''
|B
|''H''
|686.989
|693.576
|716.3615
|720.787
|731.6815
|739.21
|742.398
|759.042
|771.467
|780.03
|-
|9
|H
|''C''
|Hb
|''Cb''
|772.862
|780.273
|805.907
|810.885
|823.142
|831.611
|835.198
|853.922
|867.9
|877.5335
|-
|10
|C\\
|''D\\''
|B#
|''H#''
|858.736
|866.97
|895.452
|900.983
|914.602
|924.012
|927.998
|948.8025
|964.3335
|975.037
|-
|11
|Hp
|''Cp''
|H
|''C''
|944.609
|953.667
|984.997
|991.082
|1006.062
|1016.413
|1020.7975
|1043.683
|1060.767
|1072.541
|-
|12
|C
|''D''
|C
|''D''
|1030.483
|1040.3645
|1074.542
|1081.18
|1097.522
|1108.814
|1113.567
|1138.563
|1157.2
|1170.045
|-
|13
|D
|''S''
|Db
|''Sb''
|1116.3565
|1127.0615
|1164.087
|1171.2785
|1188.982
|1201.216
|1206.397
|1233.443
|1253.6335
|1267.548
|-
|14
| colspan="2" |E
|C#
|''D#''
|1202.23
|1213.759
|1253.633
|1261.377
|1280.443
|1293.617
|1299.197
|1328.3235
|1350.067
|13565.052
|-
|15
| colspan="2" |F\\
|D
|''S''
|1288.104
|1300.456
|1343.178
|1351.475
|1371.903
|1386.018
|1391.997
|1423.204
|1446.5
|1462.556
|-
|16
| colspan="2" |Ep
| colspan="2" |E
|1373.977
|1387.153
|1432.723
|1441.5735
|1463.363
|1478.419
|1454.796
|1518.083
|1542.934
|1560.0595
|-
|17
| colspan="2" |F
| 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 01:48, 24 October 2018

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 G Gb 84.706 86.2745 88.235 89.84 90.756 91.765 92.647 94.118 94.929 97.363 98.8235
2 J\\ A\\ F# 169.412 172.549 176.471 179.679 181.513 183.528 185.294 188.235 189.858 194.726 197.647
3 Gp G 254.118 258.8235 264.706 269.519 272.268 275.294 277.941 282.353 284.787 292.089 296.471
4 J A J A 338.823'5 345.098 352.941 359.358 363.025 367.059 370.588 376.471 379.716 389.452 395.294
5 A B Ab Bb 423.529 431.3725 441.1765 449.198 453.7815 458.8235 463.235 470.588 474.645 486.815 494.118
6 B\\ H\\ J# A# 508.235 517.647 529.412 539.037 544.538 550.588 555.882 564.706 569.574 584.1785 592.941
7 Ap Bp A B 592.941 603.921 617.647 628.877 635.394 642.353 648.529 658.8235 664.503 681.542 691.765
8 B H B H 677.647 690.169 705.882 718.717 726.05 734.118 741.1765 752.941 759.432 778.905 790.588
9 H C Hb Cb 762.653 776.471 794.118 808.556 816.806 825.882 833.8235 847.059 854.361 876.268 889.412
10 C\\ D\\ B# H# 847.059 862.745 882.353 898.396 907.563 917.647 926.471 941.1765 949.29 973.631 988.235
11 Hp Cp H C 931.765 949.02 970.588 988.235 998.319 1009.412 1019.118 1035.294 1044.219 1070.994 1087.059
12 C D C D 1016.471 1035.294 1058.8235 1078.075 1089.076 1101.1765 1111.765 1129.412 1139.148 1168.357 1185.882
13 D S Db Sb 1101.1765 1121.569 1147.059 1167.914 1179.832 1192.941 1204.412 1223.529 1234.077 1265.72 1284.706
14 E C# D# 1185.882 1027.843 1235.294 1257.754 1270.588 1284.706 1297.059 1317.647 1329.006 1363.083 1383.529
15 F\\ D S 1270.588 1294.118 1323.529 1347.594 1361.3445 1376.471 1389.706 1411.765 1423.935 1460.446 1482.352
16 Ep E 1355.294 1380.392 1411.765 1437.433 1452.101 1468.235 1482.353 1505.882 1518.864 1557.809 1581.1765
17 F 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 G Gb 85.874 86.697 89.545 90.098 91.46 92.401 92.8 94.88 96.433 97.504
2 J\\ A\\ F# 171.747 173.394 179.09 180.197 182.92 184.802 185.6 189.7605 192.867 195.007
3 Gp G 257.621 260.091 268.636 270.295 274.381 277.204 278.399 284.641 289.3 292.511
4 J A J A 343.494 346.788 358.181 360.393 365.841 369.605 371.199 379.521 385.733 390.015
5 A B Ab Bb 429.368 433.485 447.726 450.492 457.301 462.006 463.999 474.401 482.167 487.519
6 B\\ H\\ J# A# 515.2415 520.182 537.271 540.59 548.761 554.407 556.799 569.2815 578.6 585.022
7 Ap Bp A B 601.115 606.879 626.516 630.688 640.221 646.808 649.598 664.162 675.033 682.526
8 B H B H 686.989 693.576 716.3615 720.787 731.6815 739.21 742.398 759.042 771.467 780.03
9 H C Hb Cb 772.862 780.273 805.907 810.885 823.142 831.611 835.198 853.922 867.9 877.5335
10 C\\ D\\ B# H# 858.736 866.97 895.452 900.983 914.602 924.012 927.998 948.8025 964.3335 975.037
11 Hp Cp H C 944.609 953.667 984.997 991.082 1006.062 1016.413 1020.7975 1043.683 1060.767 1072.541
12 C D C D 1030.483 1040.3645 1074.542 1081.18 1097.522 1108.814 1113.567 1138.563 1157.2 1170.045
13 D S Db Sb 1116.3565 1127.0615 1164.087 1171.2785 1188.982 1201.216 1206.397 1233.443 1253.6335 1267.548
14 E C# D# 1202.23 1213.759 1253.633 1261.377 1280.443 1293.617 1299.197 1328.3235 1350.067 13565.052
15 F\\ D S 1288.104 1300.456 1343.178 1351.475 1371.903 1386.018 1391.997 1423.204 1446.5 1462.556
16 Ep E 1373.977 1387.153 1432.723 1441.5735 1463.363 1478.419 1454.796 1518.083 1542.934 1560.0595
17 F 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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