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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="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Decade
! colspan="9" |Dorian
!Period
!Notes
|-
|-
! colspan="3" |Subpental
|6\5
! colspan="3" |Pental
|''160.000''
! colspan="3" |Superpental
|Intense Aeolian-Subpental Dorian mode begins
|-
|-
!Min-comma
|29\24
!Med
|''161.111''
!Max+comma
|
!Min-comma
!Med
!Max+comma
!Min-comma
!Med
!Max+comma
!Min-comma
!Med
!Max+comma
|-
|-
|1
|23\19
|156.667-160
|161.404
|
|-
|17\14
|161.905
|161.905
| colspan="2" |159.63-166.297
|
|164.103
| colspan="2" |163.333-170
|168.889
| colspan="2" |166.364-173.03
|170.37
|168.095-171.429
|-
|-
|2
|11\9
|313.333-320
|162.962
|323.8095
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| colspan="2" |319.26-333.593
|328.205
| colspan="2" |326.667-340
|337.778
| colspan="2" |332.727-346.06
|340.741
|336.19-342.857
|-
|-
|3
|27\22
|470-480
|163.636
|485.714
|
| colspan="2" |478.889-498.889
|492.308
| colspan="2" |490-510
|506.667
| colspan="2" |499.091-519.091
|511.111
|504.286-514.286
|-
|-
|4
|16\13
|626.666-640
|164.103
|647.619
|
| colspan="2" |638.5185-665.185
|656.41
| colspan="2" |653.333-680
|675.556
| colspan="2" |665.4545-682.121
|681.4815
|672.381-685.714
|-
|-
|5
|21\17
|783.333-800
|164.706
|809.524
|
| colspan="2" |798.148-831.4815
|820.512
| colspan="2" |816.667-850
|844.444
| colspan="2" |831.818-851.1515
|851.852
|843.476-857.143
|-
|-
|6
|26\21
|940-960
|165.079
|971.429
|
| colspan="2" |957.778-997.778
|984.615
| colspan="2" |980-1020
|1013.333
| colspan="2" |998.182-1038.182
|1022.222
|1008.571-1028.571
|-
|-
|7
|5\4
|1096.667-1120
| ''166.667''
|1133.333
|Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |1117.407-1164.074
|1148.718
| colspan="2" |1143.333-1190
|1182.222
| colspan="2" |1164.5455-1211.212
|1192.593
|1176.667-1200
|-
|-
|8
|34\27
|1253.333-1280
|167.901
|1295.238
|
| colspan="2" |1277.037-1310.33
|1312.8205
| colspan="2" |1306.667-1360
|1351.111
| colspan="2" |1330.909-1384.242
|1362.963
|1334.762-1371.429
|}
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" |Mohajira
! colspan="3" |Beatles
|-
|-
!Min-comma
|29\23
!''r¢''
|168.116
!Med
|
!Max+comma
!Min-comma
!Med
!Max+comma
|-
|-
|1
|24\19
|171.429-174.762
|168.421
| colspan="2" |''172.222''
|
| colspan="2" |169.216-175.883
|172.8395
|173.333-176.667
|-
|-
|2
|19\15
|342.857-349.524
|168.889
| colspan="2" |''344.444''
|
| colspan="2" |338.431-351.765
|345.679
|346.667-353.333
|-
|-
|3
|14\11
|514.286-524.286
|169.697
| colspan="2" |''516.667''
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |507.647-527.647
|518.5185
|520-530
|-
|-
|4
|23\18
|685.714-699.048
|170.370
| colspan="2" |''688.889''
|
| colspan="2" |676.863-703.529
|691.358
|693.333-706.667
|-
|-
|5
|9\7
|857.143-873.81
|171.429
| colspan="2" |''861.111''
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| colspan="2" |846.078-879.412
|864.1975
|866.667-883.333
|-
|-
|6
|31\24
|1028.571-1048.571
|172.222
| colspan="2" |''1033.333''
|
| colspan="2" |1015.294-1055.294
|1037.037
|1040-1060
|-
|-
|7
|22\17
|1200-1223.333
|172.549
| colspan="2" |''1205.556''
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
| colspan="2" |1184.51-1231.1765
|1209.8765
|1213.333-1236.667
|-
|-
|8
|35\27
|1371.429-1398.095
|172.840
| colspan="2" |''1377.778''
|
| colspan="2" |1353.7255-1407.059
|1382.716
|1386.667-1413.333
|}
{| class="wikitable"
|-
|-
! rowspan="4" |Degrees
|13\10
! colspan="12" |Mixolydian
|173.333
! colspan="3" rowspan="3" |Mixolydian-Ionian
|Beatles Dorian-Mixolydian mode ends, Subpental Mixolydian mode begins
|-
|-
! colspan="3" rowspan="2" |Subpental
|17\13
! colspan="3" rowspan="2" |Pental
|174.358
! colspan="6" |Superpental
|
|-
|-
! colspan="3" |Soft
|21\16
! colspan="3" |Intense
|175.000
|Subpental Mixolydian mode ends, Pental Mixolydian mode begins
|-
|-
!Min-comma
|25\19
!Med
!Max+comma
! |Min-comma
!Med
!Max+comma
!Min-comma
!Med
!Max+comma
!Min-comma
!Med
!Max+comma
!Min-comma
!Med
! |Max+comma
|-
| |1
|170-173.333
|174.359
| colspan="2" |171.667-178.333
|175.439
|175.439
| colspan="2" |174.444-181.111
|
|179.167
| colspan="2" |157.977-182.644
|181.609
| colspan="2" |180.575-187.241
|184.314
| |186.667-190
|-
|-
| |2
|29\22
|340-346.667
|175.758
|348.718
|
| colspan="2" |343.333-356.667
|350.877
| colspan="2" |348.889-362.222
|358.333
| colspan="2" |355.954-365.287
|363.218
| colspan="2" |361.149-374.483
|368.6275
| |373.333-380
|-
|-
| |3
|33\25
|510-520
|176.000
|523.077
|
| colspan="2" |515-535
|526.316
| colspan="2" |523.333-543.333
|537.5
| colspan="2" |527.931-547.931
|544.828
| colspan="2" |541.724-561.724
|552.941
| |560-570
|-
|-
| |4
|4\3
|680-693.333
|''177.778''
|697.436
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| colspan="2" |686.667-713.333
|701.754
| colspan="2" |697.778-724.444
|716.667
| colspan="2" |703.908-730.576
|726.437
| colspan="2" |722.299-748.9655
|737.255
| |746.667-760
|-
|-
| |5
|51\38
|850-866.667
|178.947
|871.795
|
| colspan="2" |858.333-891.667
|877.193
| colspan="2" |872.222-905.556
|895.833
| colspan="2" |879.885-912.218
|908.046
| colspan="2" |903.207-936.8735
|921.569
| |933.333-950
|-
|-
| |6
|47\35
|1020-1040
|179.048
|1046.154
|
| colspan="2" |1030-1070
|1052.632
| colspan="2" |1046.667-1086.667
|1075
| colspan="2" |1055.862-1095.862
|1089.655
| colspan="2" |1083.448-1123.448
|1105.882
| |1120-1140
|-
|-
| |7
|43\32
|1190-1213.333
|179.167
|1220.513
|
| colspan="2" |1201.667-1248.333
|1228.07
| colspan="2" |1221.111-1267.778
|1254.167
| colspan="2" |1221.839-1268.506
|1271.264
| colspan="2" |1264.023-1330.69
|1290.196
| |1306.667-1330
|-
|-
|8
|39\29
|1360-1386.667
|179.310
|1394.872
|
| colspan="2" |1373.333-1426.667
|1403.509
| colspan="2" |1395.556-1448.889
|1433.333
| colspan="2" |1407.816-1462.419
|1452.874
| colspan="2" |1444.598-1496.931
|1474.51
|1493.333-1520
|}Relative cents
 
{| class="wikitable" style="text-align: center"
!Degrees
!Intense Aeolian-Subpental Dorian
!Dorian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|-
|1
|35\26
|161.111
|179.417
|166.667
|
|177.778
|183.333
|-
|-
|2
|31\23
|322.222
|179.710
|333.333
|
|355.556
|366.667
|-
|-
|3
|27\20
|483.333
|180.000
|500
|
|533.333
|550
|-
|-
|4
|23\17
|644.444
|180.392
|666.667
|
|711.111
|733.333
|-
|-
|5
|19\14
|805.556
|180.952
|833.333
|
|888.889
|916.667
|-
|-
|6
|15\11
|966.667
|181.818
|1000
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|1066.667
|1100
|-
|-
|7
|26\19
|1127.778
|182.456
|1166.666
|
|1244.444
|1283.333
|-
|-
|8
| 11\8
|1288.889
|''183.333''
|1333.333
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|1422.222
|1466.667
|}Golden/Pyrite Tunings±13¢
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
|-
!Subpental
|18\13
!Pental
|184.615
!Superpental
|
|-
|-
|1
|25\18
|160.761-163.65
|185.185
|162.317-165.2055
|
|167.6965-170.585
|168.741-171.63
|-
|-
|2
|7\5
|321.522-327.3
|186.667
|364.633-330.411
|Mixolydian-Ionian mode ends
|335.393-341.171
|}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.
|337.483-343.36
 
|-
==See also==
|3
*[[9ed5/2]] - equal division of the classic major tenth
|482.284-490.95
* [[9ed7/3]] - equal division of the septimal minor tent
|486.95-495.617
|503.089-511.756
|506.224-514.891
|-
|4
|643.045-654.6
|649.2665-660.822
|670.786-682.341
|674.965-686.521
|-
|5
|803.806-818.25
|811.583-826.028
|838.482-852.927
|843.707-858.151
|-
|6
|964.567-981.9
|973.9-991.233
|1006.179-1023.512
|1012.448-1029.781
|-
|7
|1125.328-1145.55
|1136.216-1156.439
|1173.875-1194.0975
|1181.189-1201.411
|-
|8
|1286.09-1309.2
|1278.2435-1321.644
|1341.572-1343.36
|1349.9305-1373.042
|}
{| class="wikitable" style="text-align: center"
!Degrees
!Mohajira
!Beatles
|-
|1
|170.877-173.776
|171.314-174.203
|-
|2
|341.755-347.513
|342.627-348.405
|-
|3
|512.632-521.2985
|513.941-522.607
|-
|4
|683.509-695.065
|685.255-696.81
|-
|5
|854.386-868.831
|856.568-870.112
|-
|6
|1025.264-1042.997
|1027.882-1045.215
|-
|7
|1196.141-1216.363
|1199.196-1219.418
|-
|8
|1367.018-1389.119
|1370.5095-1393.621
|}
{| class="wikitable" style="text-align: center"
|-
! rowspan="3" |Degrees
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
!Soft
!Intense
|-
|1
|173.091-175.98
|173.844-176.733
|177.774-180.663
|180.707-183.596
|182.729-185.618
|-
|2
|346.182-351.96
|347.688-353.466
|355.548-361.325
|361.415-367.193
|365.4585-371.236
|-
|3
|519.2735-527.94
|521.532-530.199
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
|4
|692.365-703.92
|695.376-706.932
|711.095-722.651
|722.83-734.385
|730.917-742.4725
|-
|5
|865.456-879.9
|869.22-883.6645
|888.896-903.3135
|903.537-917.982
|913.646-928.091
|-
|6
|1038.547-1055.88
|1043.064-1060.3975
|1033.634-1083.976
|1084.245-1101.578
|1096.3755-1113.709
|-
|7
|1211.638-1231.86
|1216.908-1237.13
|1244.417-1264.639
|1264.952-1285.174
|1279.105-1299.327
|-
|8
|1384.729-1407.84
|1390.752-1413.863
|1422.19-1445.3015
|1445.6595-1445.821
|1461.834-1484.945
|}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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