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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
| |746.667
|-
|-
| |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
|5\4
| |960
| ''166.667''
| colspan="2" |977.778
|Subpental Dorian mode ends, Pental Dorian mode begins
| 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
|34\27
| |1120
|167.901
| 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
|29\23
|1280
|168.116
| colspan="2" |1303.704
|
| colspan="2" |1333.333
|-
| colspan="2" |1357.576
|24\19
| colspan="2" |1371.429
|168.421
| colspan="2" |1386.667
|
| colspan="2" |1400
|-
| colspan="2" |1422.222
|19\15
| colspan="2" |1434.483
|168.889
| colspan="2" |1471.264
|
|1493.333
|-
|}Most harmonic tunings
|14\11
{| class="wikitable"
|169.697
|Pental Dorian mode ends, Superpental Dorian mode begins
|-
|23\18
|170.370
|
|-
|9\7
|171.429
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|-
|31\24
|172.222
|
|-
|22\17
|172.549
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
|-
|35\27
|172.840
|
|-
|13\10
|173.333
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|-
! rowspan="2" |Degrees
|17\13
!Minor mode Middletown temperament
|174.358
!Neutral mode Middletown temperament
|
!Major mode Middletown temperament
|-
|-
!7/3±13¢
|21\16
!22/9±13¢
|175.000
!5/2±13¢
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|-
| |1
|25\19
|161.541-164.43
|175.439
|170.49-173.379
|
|174.813-177.7015
|-
|-
| |2
|29\22
|323.082-328.86
|175.758
|340.9795-346.757
|
|349.625-355.403
|-
|-
| |3
|33\25
|484.624-493.29
|176.000
|511.469-520.136
|
|524.438-533.105
|-
|-
| |4
|4\3
|646.165-657.72
|''177.778''
|681.959-693.515
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|699.2505-710.806
|-
|-
| |5
|51\38
|807.706-822.1505
|178.947
|852.489-866.893
|
|874.063-888.508
|-
|-
| |6
|47\35
|969.247-986.581
|179.048
|1022.939-1040.272
|
|1048.876-1066.5425
|-
|-
| |7
|43\32
|1130.7885-1151.011
|179.167
|1193.428-1215.651
|
|1223.688-1244.466
|-
|-
|8
|39\29
|1292.33-1315.441
|179.310
|1363.918-1387.293
|
|1398.4501-1422.391
|}Golden tunings±13¢
 
{| 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
|35\26
! colspan="3" |Dorian
|179.417
! rowspan="3" |Dorian-Mixolydian
|
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
|31\23
! rowspan="2" |Pental
|179.710
! rowspan="2" |Superpental
|
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
|-
!Soft
|27\20
!Intense
|180.000
|
|-
|-
| |1
|23\17
| |160.761-163.65
|180.392
|162.317-165.2055
|
|167.6965-170.585
|168.741-171.63
|171.314-174.203
|173.091-175.98
|173.844-176.733
|177.774-180.663
|180.707-183.596
|182.729-185.618
|-
|-
| |2
|19\14
| |321.522-327.3
|180.952
|364.633-330.411
|
|335.393-341.171
|337.483-343.36
|342.617-348.405
|346.182-351.96
|347.688-353.466
|355.548-361.325
|361.415-367.193
|365.4585-371.236
|-
|-
| |3
|15\11
| |482.284-490.95
|181.818
|486.95-495.617
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|503.089-511.756
|506.224-514.891
|513.941-522.608
|519.2735-527.94
|521.532-530.199
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
|-
| |4
|26\19
| |643.045-654.6
|182.456
|649.2665-660.822
|
|670.786-682.341
|674.965-686.521
|685.255-696.81
|692.365-703.92
|695.376-706.932
|711.095-722.651
|722.83-734.385
|730.917-742.4725
|-
|-
| |5
| 11\8
| |803.806-818.25
|''183.333''
|811.583-826.028
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|838.482-852.927
|843.707-858.151
|856.568-871.012
|865.456-879.9
|869.22-883.6645
|888.896-903.3135
|903.537-917.982
|913.646-928.091
|-
|-
| |6
|18\13
| |964.567-981.9
|184.615
|973.9-991.233
|
|1006.179-1023.512
|1012.448-1029.781
|1027.882-1045.2155
|1038.547-1055.88
|1043.064-1060.3975
|1033.634-1083.976
|1084.245-1101.578
|1096.3755-1113.709
|-
|-
| |7
|25\18
| |1125.328-1145.55
|185.185
|1136.216-1156.439
|
|1173.875-1194.0975
|1181.189-1201.411
|1199.196-1219.418
|1211.638-1231.86
|1216.908-1237.13
|1244.417-1264.639
|1264.952-1285.174
|1279.105-1299.327
|-
|-
|8
|7\5
|1286.09-1309.2
|186.667
|1278.2435-1321.644
|Mixolydian-Ionian mode ends
|1341.572-1343.36
|}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.
|1349.9305-1373.042
 
|1370.5095-1393.621
==See also==
|1384.729-1407.84
*[[9ed5/2]] - equal division of the classic major tenth
|1390.752-1413.863
* [[9ed7/3]] - equal division of the septimal minor tent
|1422.19-1445.3015
|1445.6595-1445.821
|1461.834-1484.945
|}By a surprising coincidence, the 9ed of the Pyrite 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]]
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