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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" style="text-align: center"
{| class="wikitable"
! rowspan="3" |Degrees
|+
! colspan="4" rowspan="2" |Intense Aeolian-Subpental Dorian
!Decade
! colspan="10" |Dorian
!Period
!Notes
|-
|6\5
|''160.000''
|Intense Aeolian-Subpental Dorian mode begins
|-
|29\24
|''161.111''
|
|-
|23\19
|161.404
|
|-
|17\14
|161.905
|
|-
|-
! colspan="4" |Subpental
|11\9
! colspan="3" |Pental
|162.962
! colspan="3" |Superpental
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
|-
|-
!Min
|27\22
!Golden±13¢
|163.636
!''r¢''
|
!Max
!Min
!7/3±13¢
!Golden±13¢
!Max
!Min
!Golden±13¢
!Max
!Min
!Golden±13¢
!Max
|-
|-
|1
|16\13
|160
|164.103
|160.761-163.65
|
|''161.111''
|-
| colspan="2" |162.963
|21\17
|161.541-164.43
|164.706
|162.317-165.2055
|
| colspan="2" |''166.667''
|-
|167.6965-170.585
|26\21
| colspan="2" |169.697
|165.079
|168.741-171.63
|
|171.429
|-
|-
|2
|5\4
|320
| ''166.667''
|321.522-327.3
|Subpental Dorian mode ends, Pental Dorian mode begins
|''322.222''
| colspan="2" |325.926
|323.082-328.86
|364.633-330.411
| colspan="2" |''333.333''
|335.393-341.171
| colspan="2" |339.394
|337.483-343.36
|342.857
|-
|-
|3
|34\27
|480
|167.901
|482.284-490.95
|
|''483.333''
| colspan="2" |488.889
|484.624-493.29
|486.95-495.617
| colspan="2" |''500''
|503.089-511.756
| colspan="2" |509.091
|506.224-514.891
|514.286
|-
|-
|4
|29\23
|640
|168.116
|643.045-654.6
|
|''644.444''
| colspan="2" |651.852
|646.165-657.72
|649.2665-660.822
| colspan="2" |''666.667''
|670.786-682.341
| colspan="2" |678.788
|674.965-686.521
|685.714
|-
|-
|5
|24\19
|800
|168.421
|803.806-818.25
|
|''805.556''
| colspan="2" |814.815
|807.706-822.1505
|811.583-826.028
| colspan="2" |''833.333''
|838.482-852.927
| colspan="2" |848.485
|843.707-858.151
|857.143
|-
|-
|6
|19\15
|960
|168.889
|964.567-981.9
|
|''966.667''
| colspan="2" |977.778
|969.247-986.581
|973.9-991.233
| colspan="2" |''1000''
|1006.179-1023.512
| colspan="2" |1018.182
|1012.448-1029.781
|1028.571
|-
|-
|7
|14\11
|1120
|169.697
|1125.328-1145.55
|Pental Dorian mode ends, Superpental Dorian mode begins
|''1127.778''
| colspan="2" |1140.741
|1130.7885-1151.011
|1136.216-1156.439
| colspan="2" |''1166.666''
|1173.875-1194.0975
| colspan="2" |1187.879
|1181.189-1201.411
|1200
|-
|-
|8
|23\18
|1280
|170.370
|1286.09-1309.2
|
|''1288.889''
| colspan="2" |1303.704
|1292.33-1315.441
|1278.2435-1321.644
| colspan="2" |''1333.333''
|1341.572-1343.36
| colspan="2" |1357.576
|1349.9305-1373.042
|1371.429
|}
{| class="wikitable" style="text-align: center"
!Degrees
!Min
!22/9±13¢
!Golden±13¢
!''r¢''
!Max
|-
|-
|1
|9\7
|171.429
|171.429
|170.49-173.379
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
|171.314-174.203
|-
|''172.222''
|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
|173.333
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|17\13
|174.358
|
|-
|21\16
|175.000
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|-
|2
|25\19
|342.857
|175.439
|340.9795-346.757
|
|342.617-348.405
|''344.444''
|246.667
|-
|-
|3
|29\22
|514.286
|175.758
|511.469-520.136
|
|513.941-522.608
|''516.667''
|520
|-
|-
|4
|33\25
|685.714
|176.000
|681.959-693.515
|
|685.255-696.81
|''688.889''
|693.333
|-
|-
|5
|4\3
|857.143
|''177.778''
|852.489-866.893
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|856.568-871.012
|''861.111''
|866.667
|-
|-
|6
|51\38
|1028.571
|178.947
|1022.939-1040.272
|
|1027.882-1045.2155
|''1033.333''
|1040
|-
|-
|7
|47\35
|1200
|179.048
|1193.428-1215.651
|
|1199.196-1219.418
|''1205.556''
|1213.333
|-
|-
|8
|43\32
|1371.429
|179.167
|1363.918-1387.293
|
|1370.5095-1393.621
|''1377.778''
|1386.667
|}
{| class="wikitable"
|-
|-
! rowspan="4" |Degrees
|39\29
! colspan="14" |Mixolydian
|179.310
! colspan="3" rowspan="3" |Mixolydian-Ionian
|
|-
|-
! colspan="3" rowspan="2" |Subpental
|35\26
! colspan="4" rowspan="2" |Pental
|179.417
! colspan="7" |Superpental
|
|-
|-
! colspan="3" |Soft
|31\23
! colspan="4" |Intense
|179.710
|
|-
|-
!Minimum
|27\20
!Golden±13¢
|180.000
!Maximum
|
! |Minimum
!Golden±13¢
!5/2±13¢
!Maximum
!Minimum
!Golden±13¢
!Maximum
!Minimum
!Golden±13¢
!''r¢''
!Maximum
!Minimum
!Golden±13¢
! |Maximum
|-
|-
| |1
|23\17
|173.333
|180.392
|173.091-175.98
|
| colspan="2" |175
|173.844-176.733
|174.813-177.7015
| colspan="2" |''177.778''
|177.774-180.663
| colspan="2" |179.31
|180.707-183.596
|''183.333''
| colspan="2" |183.908
|182.729-185.618
| |186.667
|-
|-
| |2
|19\14
|246.667
|180.952
|346.182-351.96
|
| colspan="2" |350
|347.688-353.466
|349.625-355.403
| colspan="2" |''355.556''
|355.548-361.325
| colspan="2" |358.621
|361.415-367.193
|''366.667''
| colspan="2" |367.816
|365.4585-371.236
| |373.333
|-
|-
| |3
|15\11
|520
|181.818
|519.2735-527.94
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
| colspan="2" |525
|521.532-530.199
|524.438-533.105
| colspan="2" |''533.333''
|533.321-541.988
| colspan="2" |537.931
|542.122-550.789
|''550''
| colspan="2" |551.724
|548.188-556.854
| |560
|-
|-
| |4
|26\19
|693.333
|182.456
|692.365-703.92
|
| colspan="2" |700
|695.376-706.932
|699.2505-710.806
| colspan="2" |''711.111''
|711.095-722.651
| colspan="2" |717.241
|722.83-734.385
|''733.333''
| colspan="2" |735.632
|730.917-742.4725
| |746.667
|-
|-
| |5
| 11\8
|866.667
|''183.333''
|865.456-879.9
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
| colspan="2" |875
|869.22-883.6645
|874.063-888.508
| colspan="2" |''888.889''
|888.896-903.3135
| colspan="2" |896.552
|903.537-917.982
|''916.667''
| colspan="2" |919.54
|913.646-928.091
| |1033.333
|-
|-
| |6
|18\13
|1040
|184.615
|1038.547-1055.88
|
| colspan="2" |1050
|1043.064-1060.3975
|1048.876-1066.5425
| colspan="2" |''1066.667''
|1033.634-1083.976
| colspan="2" |1075.862
|1084.245-1101.578
|''1100''
| colspan="2" |1103.448
|1096.3755-1113.709
| |1120
|-
|-
| |7
|25\18
|1213.333
|185.185
|1211.638-1231.86
|
| colspan="2" |1225
|1216.908-1237.13
|1223.688-1244.466
| colspan="2" |''1244.444''
|1244.417-1264.639
| colspan="2" |1255.172
|1264.952-1285.174
|''1283.333''
| colspan="2" |1287.356
|1279.105-1299.327
| |1306.667
|-
|-
|8
|7\5
|1386.667
|186.667
|1384.729-1407.84
|Mixolydian-Ionian mode ends
| colspan="2" |1400
|}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.
|1390.752-1413.863
 
|1398.4501-1422.391
==See also==
| colspan="2" |''1422.222''
*[[9ed5/2]] - equal division of the classic major tenth
|1422.19-1445.3015
* [[9ed7/3]] - equal division of the septimal minor tent
| colspan="2" |1434.483
|1445.6595-1445.821
|''1466.667''
| colspan="2" |1471.264
|1461.834-1484.945
|1493.333
|}By a surprising coincidence, the 9ed of the Pyrite tenth (7φ+6)\(5φ^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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