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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
|-
|6\5
|''160.000''
|Intense Aeolian-Subpental Dorian mode begins
|-
|29\24
|''161.111''
|
|-
|23\19
|161.404
|
|-
|17\14
|161.905
|
|-
|11\9
|162.962
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|27\22
|163.636
|
|-
|16\13
|164.103
|
|-
|21\17
|164.706
|
|-
|26\21
|165.079
|
|-
|-
! colspan="2" rowspan="3" |Aeolian-Dorian
|5\4
! colspan="6" |Dorian
| ''166.667''
! colspan="2" rowspan="3" |Dorian-Mixolydian
|Subpental Dorian mode ends, Pental Dorian mode begins
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
|34\27
! colspan="2" rowspan="2" |Pental
|167.901
! colspan="2" rowspan="2" |Superpental
|
! colspan="2" rowspan="2" |Subpental
! colspan="2" rowspan="2" |Pental
! colspan="4" |Superpental
|-
|-
! colspan="2" |Soft
|29\23
! colspan="2" |Intense
|168.116
|
|-
|-
! |Minimum
|24\19
! |Maximum
|168.421
!Minimum
|
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|19\15
| |160
|168.889
| 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
|14\11
| |320
|169.697
| colspan="2" |325.926
|Pental Dorian mode ends, Superpental Dorian mode begins
| 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
|23\18
| |480
|170.370
| 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
|9\7
| |640
|171.429
| colspan="2" |651.852
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| 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
|31\24
| |800
|172.222
| 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
|22\17
| |960
|172.549
| colspan="2" |977.778
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian 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
|35\27
| |1120
|172.840
| 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
|13\10
|1280
|173.333
| colspan="2" |1303.704
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
| colspan="2" |1333.333
|-
| colspan="2" |1357.576
|17\13
| colspan="2" |1371.429
|174.358
| colspan="2" |1386.667
|
| colspan="2" |1400
|-
| colspan="2" |1422.222
|21\16
| colspan="2" |1434.483
|175.000
| colspan="2" |1471.264
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|1493.333
|-
|}Golden tunings
|25\19
{| class="wikitable"
|175.439
|+
|
! rowspan="4" |Degrees
|-
! colspan="4" |Minor mode Middletown temperament
|29\22
!Neutral mode Middletown temperament
|175.758
! colspan="5" |Major mode Middletown temperament
|
|-
|33\25
|176.000
|
|-
|4\3
|''177.778''
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|-
|51\38
|178.947
|
|-
|47\35
|179.048
|
|-
|43\32
|179.167
|
|-
|39\29
|179.310
|
|-
|-
! 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
|162.206
|180.392
|163.761
|
|169.141
|170.186
|172.758
|174.536
|175.2885
|179.218
|182.152
|184.174
|-
|-
|2
|19\14
|324.411
|180.952
|327.522
|
|338.282
|340.3715
|345.516
|349.071
|351.577
|358.4365
|364.304
|368.347
|-
|-
|3
|15\11
|486.617
|181.818
|491.283
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|507.423
|510.557
|518.274
|523.607
|525.865
|537.655
|546.456
|552.521
|-
|-
|4
|26\19
|648.823
|182.456
|655.044
|
|676.564
|680.743
|691.0325
|698.142
|701.154
|716.873
|728.6075
|736.695
|-
|-
|5
| 11\8
|811.028
|''183.333''
|818.805
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|845.7045
|850.928
|863.791
|872.678
|876.442
|896.091
|910.759
|920.8685
|-
|-
|6
|18\13
|973.234
|184.615
|982.5665
|
|1014.8455
|1021.115
|1036.549
|1047.214
|1051.731
|1075.3095
|1092.911
|1105.042
|-
|-
|7
|25\18
|1135.4395
|185.185
|1146.3275
|
|1183.986
|1191.3
|1209.307
|1221.749
|1227.019
|1254.528
|1275.063
|1289.215
|-
|-
|8
|7\5
|1297.645
|186.667
|1310.089
|Mixolydian-Ionian mode ends
|1353.127
|}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.
|1361.486
|1382.065
|1396.285
|1402.308
|1433.746
|1457.215
|1473.3895
|}
 
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
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