User:Moremajorthanmajor/9edX: Difference between revisions

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This is the neutral scale of the Middletown temperament family.
This is the neutral scale of the Middletown temperament family.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
! colspan="8" |Minor mode Middletown temperament
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Major mode Middletown temperament
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
! colspan="6" |Dorian
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="2" rowspan="2" |Superpental
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
! colspan="2" |Soft
! colspan="2" |Intense
|-
! |Minimum
! |Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
| |1
| |160
| colspan="2" |162.963
| colspan="2" |166.667
| colspan="2" |169.697
| colspan="2" |171.429
| colspan="2" |173.333
| colspan="2" |175
| colspan="2" |177.778
| colspan="2" |179.31
| colspan="2" |183.908
| |186.667
|-
| |2
| |320
| colspan="2" |325.926
| colspan="2" |333.333
| colspan="2" |339.394
| colspan="2" |342.857
| colspan="2" |246.667
| colspan="2" |350
| colspan="2" |355.556
| colspan="2" |358.621
| colspan="2" |367.816
| |373.333
|-
| |3
| |480
| colspan="2" |488.889
| colspan="2" |500
| colspan="2" |509.091
| colspan="2" |514.286
| colspan="2" |520
| colspan="2" |525
| colspan="2" |533.333
| colspan="2" |537.931
| colspan="2" |551.724
| |560
|-
| |4
| |640
| colspan="2" |651.852
| colspan="2" |666.667
| colspan="2" |678.788
| colspan="2" |685.714
| colspan="2" |693.333
| colspan="2" |700
| colspan="2" |711.111
| colspan="2" |717.241
| colspan="2" |735.632
| |846.667
|-
| |5
| |800
| colspan="2" |814.815
| colspan="2" |833.333
| colspan="2" |848.485
| colspan="2" |857.143
| colspan="2" |866.667
| colspan="2" |875
| colspan="2" |888.889
| colspan="2" |896.552
| colspan="2" |919.54
| |1033.333
|-
| |6
| |960
| colspan="2" |977.778
| colspan="2" |1000
| colspan="2" |1018.182
| colspan="2" |1028.571
| colspan="2" |1040
| colspan="2" |1050
| colspan="2" |1066.667
| colspan="2" |1075.862
| colspan="2" |1103.448
| |1120
|-
| |7
| |1120
| colspan="2" |1140.741
| colspan="2" |1166.666
| colspan="2" |1187.879
| colspan="2" |1200
| colspan="2" |1213.333
| colspan="2" |1225
| colspan="2" |1244.444
| colspan="2" |1255.172
| colspan="2" |1287.356
| |1306.667
|-
|8
|1280
| colspan="2" |1303.704
| colspan="2" |1333.333
| colspan="2" |1357.576
| colspan="2" |1371.429
| colspan="2" |1386.667
| colspan="2" |1400
| colspan="2" |1422.222
| colspan="2" |1434.483
| colspan="2" |1471.264
|1493.333
|}Golden tunings
{| class="wikitable"
|+
! rowspan="4" |Degrees
! 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
|-
|-
! | Degrees
!Soft
! | Minimum
!Intense
! | ed(7/3)
! | Mean/Median
! | Golden
! | Maximum
|-
|-
| | 1
|1
| | 160
|162.206
| | 162.986
|163.761
| | 173.333
|169.141
| | 176.481
|170.186
| | 193.333
|172.758
|174.536
|175.2885
|179.218
|182.152
|184.174
|-
|-
| | 2
|2
| | 320
|324.411
| | 325.971
|327.522
| | 346.667
|338.282
| | 352.961
|340.3715
| | 386.667
|345.516
|349.071
|351.577
|358.4365
|364.304
|368.347
|-
|-
| | 3
|3
| | 480
|486.617
| | 488.957
|491.283
| | 520
|507.423
| | 529.443
|510.557
| | 560
|518.274
|523.607
|525.865
|537.655
|546.456
|552.521
|-
|-
| | 4
|4
| | 640
|648.823
| | 651.943
|655.044
| | 693.333
|676.564
| | 705.924
|680.743
| | 753.333
|691.0325
|698.142
|701.154
|716.873
|728.6075
|736.695
|-
|-
| | 5
|5
| | 800
|811.028
| | 814.928
|818.805
| | 866.667
|845.7045
| | 882.404'5
|850.928
| | 886.667
|863.791
|872.678
|876.442
|896.091
|910.759
|920.8685
|-
|-
| | 6
|6
| | 960
|973.234
| | 977.913
|982.5665
| | 1040
|1014.8455
| | 1058.885
|1021.115
| | 1120
|1036.549
|1047.214
|1051.731
|1075.3095
|1092.911
|1105.042
|-
|-
| | 7
|7
| | 1120
|1135.4395
| | 1140.9
|1146.3275
| | 1213.333
|1183.986
| | 1235.366
|1191.3
| | 1313.333
|1209.307
|1221.749
|1227.019
|1254.528
|1275.063
|1289.215
|-
|-
| | 8
|8
| | 1280
|1297.645
| | 1303.885
|1310.089
| | 1386.667
|1353.127
| | 1411.847
|1361.486
| | 1506.667
|1382.065
|1396.285
|1402.308
|1433.746
|1457.215
|1473.3895
|}
|}


By a surprising coincidence, the Golden tuning of this edX is almost exactly every fifth degree of [[34edo|34edo]].
By a surprising coincidence, the edX of the Golden tenth (7*phi+6)\(5*phi^2)edo is almost exactly every fifth degree of [[34edo|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.

Revision as of 22:31, 22 October 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

Golden tunings

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
1 162.206 163.761 169.141 170.186 172.758 174.536 175.2885 179.218 182.152 184.174
2 324.411 327.522 338.282 340.3715 345.516 349.071 351.577 358.4365 364.304 368.347
3 486.617 491.283 507.423 510.557 518.274 523.607 525.865 537.655 546.456 552.521
4 648.823 655.044 676.564 680.743 691.0325 698.142 701.154 716.873 728.6075 736.695
5 811.028 818.805 845.7045 850.928 863.791 872.678 876.442 896.091 910.759 920.8685
6 973.234 982.5665 1014.8455 1021.115 1036.549 1047.214 1051.731 1075.3095 1092.911 1105.042
7 1135.4395 1146.3275 1183.986 1191.3 1209.307 1221.749 1227.019 1254.528 1275.063 1289.215
8 1297.645 1310.089 1353.127 1361.486 1382.065 1396.285 1402.308 1433.746 1457.215 1473.3895

By a surprising coincidence, the edX 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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