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This is the neutral scale of the Middletown temperament family.
This is the neutral scale of the Middletown temperament family. It also gives the period of the 9th-decade White Oak temperament family.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="5" |Degrees
|+
! colspan="8" |Minor mode Middletown temperament
!Decade
! colspan="2" |Neutral mode Middletown temperament
!Period
! colspan="10" |Major mode Middletown temperament
!Notes
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|6\5
! colspan="6" |Dorian
|''160.000''
! colspan="2" rowspan="3" |Dorian-Mixolydian
|Intense Aeolian-Subpental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|29\24
! colspan="2" rowspan="2" |Pental
|''161.111''
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|23\19
! colspan="2" |Intense
|161.404
|
|-
|-
! |Minimum
|17\14
! |Maximum
|161.905
!Minimum
|
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|11\9
| |160
|162.962
| colspan="2" |162.963
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| 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
|27\22
| |320
|163.636
| 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
|16\13
| |480
|164.103
| 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
|21\17
| |640
|164.706
| 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
|26\21
| |800
|165.079
| 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
|}Most harmonic tunings
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|5\4
!Minor mode Middletown temperament
| ''166.667''
!Neutral mode Middletown temperament
|Subpental Dorian mode ends, Pental Dorian mode begins
!Major mode Middletown temperament
|-
|-
!7/3±13¢
|34\27
!22/9±13¢
|167.901
!5/2±13¢
|
|-
|-
| |1
|29\23
|161.541-164.43
|168.116
|170.49-173.379
|
|174.813-177.7015
|-
|-
| |2
|24\19
|323.082-328.86
|168.421
|340.9795-346.757
|
|349.625-355.403
|-
|-
| |3
|19\15
|484.624-493.29
|168.889
|511.469-520.136
|
|524.438-533.105
|-
|-
| |4
|14\11
|646.165-657.72
|169.697
|681.959-693.515
|Pental Dorian mode ends, Superpental Dorian mode begins
|699.2505-710.806
|-
|-
| |5
|23\18
|807.706-822.1505
|170.370
|852.489-866.893
|
|874.063-888.508
|-
|-
| |6
|9\7
|969.247-986.581
|171.429
|1022.939-1040.272
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|1048.876-1066.5425
|-
|-
| |7
|31\24
|1130.7885-1151.011
|172.222
|1193.428-1215.651
|
|1223.688-1244.466
|-
|-
|8
|22\17
|1292.33-1315.441
|172.549
|1363.918-1387.293
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|1398.4501-1422.391
|}Golden tunings
 
Minor mode Middletown temperament
{| class="wikitable"
|+
! rowspan="3" |Degrees
! colspan="3" |Aeolian-Dorian
! colspan="9" |Dorian
|-
|-
! rowspan="2" |-13¢
|35\27
! rowspan="2" |Mean
|172.840
! rowspan="2" |-13¢ (s5D)
|
! colspan="3" |Subpental
! colspan="3" |Pental
! colspan="3" |Superpental
|-
|-
!+13¢ (A-D)
|13\10
!Mean
|173.333
!+13¢
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
!-13¢
!-13¢ (S5)
!Mean
!Mean
!+13¢ (5)
!-13¢ (D-M)
|-
|-
|1
|17\13
|160.761
|174.358
|162.206
|
|162.317
|163.65
|163.761
|165.2055
|167.6965
|168.741
|169.141
|170.186
|170.585
|171.314
|-
|-
|2
|21\16
|321.522
|175.000
|324.411
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|364.633
|327.3
|327.522
|330.411
|335.393
|337.483
|338.282
|340.3715
|341.171
|342.617
|-
|-
|3
|25\19
|482.284
|175.439
|486.617
|
|486.95
|490.95
|491.283
|495.617
|503.089
|506.224
|507.423
|510.557
|511.756
|513.941
|-
|-
|4
|29\22
|643.045
|175.758
|648.823
|
|649.2665
|654.6
|655.044
|660.822
|670.786
|674.965
|676.564
|680.743
|682.341
|685.255
|-
|-
|5
|33\25
|803.806
|176.000
|811.028
|
|811.583
|818.25
|818.805
|826.028
|838.482
|843.707
|845.7045
|850.928
|852.927
|856.568
|-
|-
|6
|4\3
|964.567
|''177.778''
|973.234
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|973.9
|981.9
|982.5665
|991.233
|1006.179
|1012.448
|1014.8455
|1021.115
|1023.512
|1027.882
|-
|-
|7
|51\38
|1125.328
|178.947
|1135.4395
|
|1136.216
|1145.55
|1146.3275
|1156.439
|1173.875
|1181.189
|1183.986
|1191.3
|1194.0975
|1199.196
|-
|-
|8
|47\35
|1286.09
|179.048
|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
|43\32
!+13¢ (S5D)
|179.167
!Mean
|
!-13¢ (s5M)
|-
|-
|1
|39\29
|171.63
|179.310
|172.758
|
|173.091
|-
|-
|2
|35\26
|343.36
|179.417
|345.516
|
|346.182
|-
|-
|3
|31\23
|514.891
|179.710
|518.274
|
|519.2735
|-
|-
|4
|27\20
|686.521
|180.000
|691.0325
|
|692.365
|-
|-
|5
|23\17
|858.151
|180.392
|863.791
|
|965.456
|-
|-
|6
|19\14
|1029.781
|180.952
|1036.549
|
|1038.547
|-
|-
|7
|15\11
|1201.411
|181.818
|1209.307
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|1211.638
|-
|-
|8
|26\19
|1373.042
|182.456
|1382.065
|
|1384.729
|}
Major mode Middletown temperament
{| class="wikitable"
|-
|-
! rowspan="4" |Degrees
| 11\8
! colspan="13" |Mixolydian
|''183.333''
! colspan="2" |Mixolydian-Ionian
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|-
! colspan="3" |Subpental
|18\13
! colspan="4" |Pental
|184.615
! colspan="6" |Superpental
|
! rowspan="3" |Mean
! rowspan="3" |+13¢
|-
|-
! rowspan="2" |-13¢ (5)
|25\18
! rowspan="2" |+13¢ (D-M)
|185.185
! 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)
|7\5
!-13¢
|186.667
!Mean
|Mixolydian-Ionian mode ends
!-13¢ (M-I)
|}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.
!+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|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.


[[Category:EdX]]
==See also==
*[[9ed5/2]] - equal division of the classic major tenth
* [[9ed7/3]] - equal division of the septimal minor tent
Retrieved from "https://en.xen.wiki/w/User:Moremajorthanmajor/9edX"