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This is the neutral scale of the Middletown temperament family. It also gives the period of the 9th-decade White Oak temperament family.
This is the neutral scale of the Middletown temperament family.
==Intervals==
 
{| class="wikitable"
== Intervals ==
|+
{| class="wikitable" style="text-align: center"
!Decade
! rowspan="3" |Degrees
!Period
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Notes
! colspan="9" |Dorian
|-
|6\5
|''160.000''
|Intense Aeolian-Subpental Dorian mode begins
|-
|-
! colspan="3" |Subpental
|29\24
! colspan="3" |Pental
|''161.111''
! colspan="3" |Superpental
|
|-
|-
!Min-comma
|23\19
!Med
|161.404
! colspan="2" |Max+comma~Min-comma
|
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! colspan="2" |Max+comma~Min-comma
!Med
!Max+comma
|-
|-
|1
|17\14
|155.556-160
|161.905
|161.905
| colspan="2" |158.5185-167.407
|
|164.103
| colspan="2" |162.222-171.111
|168.889
| colspan="2" |165.2525-174.141
|170.37
|171.429-175.873
|-
|-
|2
|11\9
|311.111-320
|162.962
|323.8095
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| colspan="2" |317.037-334.814
|328.205
| colspan="2" |324.444-342.222
|337.778
| colspan="2" |330.505-348.283
|340.741
|342.857-351.746
|-
|-
|3
|27\22
|466.667-480
|163.636
|485.714
|
| colspan="2" |475.556-502.222
|492.308
| colspan="2" |486.667-513.333
|506.667
| colspan="2" |495.758-522.424
|511.111
|514.286-527.619
|-
|-
|4
|16\13
|622.222-640
|164.103
|647.619
|
| colspan="2" |634.074-669.63
|656.41
| colspan="2" |648.889-684.444
|675.556
| colspan="2" |661.01-696.566
|681.4815
|685.714-703.492
|-
|-
|5
|21\17
|777.778-800
|164.706
|809.524
|
| colspan="2" |792.593-837.037
|820.512
| colspan="2" |811.111-855.556
|844.444
| colspan="2" |826.263-870.707
|851.852
|857.143-878.365
|-
|-
|6
|26\21
|943.333-960
|165.079
|971.429
|
| colspan="2" |951.111-1004.444
|984.615
| colspan="2" |973.333-1026.667
|1013.333
| colspan="2" |988.515-1044.848
|1022.222
|1028.571-1055.238
|-
|-
|7
|5\4
|1088.889-1120
| ''166.667''
|1133.333
|Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |1109.63-1171.852
|1148.718
| colspan="2" |1135.556-1197.778
|1182.222
| colspan="2" |1156.768-1218.99
|1192.593
|1200-1231.111
|-
|-
|8
|34\27
|1244.444-1280
|167.901
|1295.238
|
| colspan="2" |1238.148-1339.259
|1312.8205
| colspan="2" |1297.778-1368.889
|1351.111
| colspan="2" |1321.02-1392.131
|1362.963
|1371.429-1406.984
|}
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! colspan="4" |Mohajira
! colspan="3" |Beatles
|-
|-
!Min-comma
|29\23
!''r¢''
|168.116
!Med
|
! colspan="2" |Max+comma~Min-comma
!Med
!Max+comma
|-
|-
|1
|24\19
|166.984-171.429
|168.421
| colspan="2" |''172.222''
|
| colspan="2" |168.105-176.9935
|172.8395
|173.333-177.778
|-
|-
|2
|19\15
|333.968-342.857
|168.889
| colspan="2" |''344.444''
|
| colspan="2" |336.209-353.987
|345.679
|346.667-355.556
|-
|-
|3
|14\11
|500.952-514.286
|169.697
| colspan="2" |''516.667''
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |504.314-530.98
|518.5185
|520-533.333
|-
|-
|4
|23\18
|667.9365-685.714
|170.370
| colspan="2" |''688.889''
|
| colspan="2" |672.418-707.974
|691.358
|693.333-711.111
|-
|-
|5
|9\7
|834.921-857.143
|171.429
| colspan="2" |''861.111''
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| colspan="2" |840.523-885.967
|864.1975
|866.667-888.889
|-
|-
|6
|31\24
|1001.904-1028.571
|172.222
| colspan="2" |''1033.333''
|
| colspan="2" |1008.6275-1062.961
|1037.037
|1040-1066.667
|-
|-
|7
|22\17
|1168.889-1200
|172.549
| colspan="2" |''1205.556''
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
| colspan="2" |1176.732-1239.954
|1209.8765
|1213.333-1244.444
|-
|-
|8
|35\27
|1335.873-1371.429
|172.840
| colspan="2" |''1377.778''
|
| colspan="2" |1344.837-1416.948
|1382.716
|1386.667-1422.222
|}
{| 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
! colspan="2" |Max+comma~Min-comma
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! colspan="2" |Max+comma~Min-comma
!Med
! |Max+comma
|-
| |1
|168.889-173.333
|174.359
| colspan="2" |170.556-179.444
|175.439
|175.439
| colspan="2" |173.333-182.222
|
|179.167
| colspan="2" |174.866-183.755
|181.609
| colspan="2" |179.464-188.3525
|184.314
| |186.667-191.111
|-
|-
| |2
|29\22
|337.778-346.667
|175.758
|348.718
|
| colspan="2" |341.111-358.889
|350.877
| colspan="2" |346.667-364.444
|358.333
| colspan="2" |349.732-367.51
|363.218
| colspan="2" |368.927-376.705
|368.6275
| |373.333-382.222
|-
|-
| |3
|33\25
|506.667-520
|176.000
|523.077
|
| colspan="2" |511.667-538.333
|526.316
| colspan="2" |520-546.667
|537.5
| colspan="2" |524.598-551.264
|544.828
| colspan="2" |538.391-565.0575
|552.941
| |560-573.333
|-
|-
| |4
|4\3
|675.556-693.333
|''177.778''
|697.436
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
| colspan="2" |682.222-717.778
|701.754
| colspan="2" |693.333-728.889
|716.667
| colspan="2" |699.464-735.019
|726.437
| colspan="2" |717.854-753.41
|737.255
| |746.667-764.444
|-
|-
| |5
|51\38
|844.444-866.667
|178.947
|871.795
|
| colspan="2" |852.778-897.222
|877.193
| colspan="2" |866.667-911.111
|895.833
| colspan="2" |874.3295-918.774
|908.046
| colspan="2" |897.318-942.7625
|921.569
| |933.333-955.556
|-
|-
| |6
|47\35
|1013.333-1040
|179.048
|1046.154
|
| colspan="2" |1023.333-1076.667
|1052.632
| colspan="2" |1040-1093.333
|1075
| colspan="2" |1049.195-1102.529
|1089.655
| colspan="2" |1076.782-1130.115
|1105.882
| |1120-1146.667
|-
|-
| |7
|43\32
|1182.222-1213.333
|179.167
|1220.513
|
| colspan="2" |1193.889-1256.111
|1228.07
| colspan="2" |1213.333-1275.556
|1254.167
| colspan="2" |1224.061-1286.2835
|1271.264
| colspan="2" |1256.245-1318.457
|1290.196
| |1306.667-1337.778
|-
|8
|1351.111-1386.667
|1394.872
| colspan="2" |1364.444-1435.556
|1403.509
| colspan="2" |1386.667-1457.778
|1433.333
| colspan="2" |1398.927-1470.038
|1452.874
| colspan="2" |1438.709-1506.82
|1474.51
|1493.333-1528.889
|}Relative cents
 
{| class="wikitable" style="text-align: center"
!Degrees
!Intense Aeolian-Subpental Dorian
!Dorian
!Subpental-Soft Superpental Mixolydian
!Intense Superpental Mixolydian ~ Mixolydian-Ionian
|-
|1
|161.111
|166.667
|177.778
|183.333
|-
|2
|322.222
|333.333
|355.556
|366.667
|-
|3
|483.333
|500
|533.333
|550
|-
|4
|644.444
|666.667
|711.111
|733.333
|-
|5
|805.556
|833.333
|888.889
|916.667
|-
|6
|966.667
|1000
|1066.667
|1100
|-
|7
|1127.778
|1166.666
|1244.444
|1283.333
|-
|8
|1288.889
|1333.333
|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
!Pental
!Superpental
|-
|1
|160.761-163.65
|162.317-165.2055
|167.6965-170.585
|168.741-171.63
|-
|2
|321.522-327.3
|364.633-330.411
|335.393-341.171
|337.483-343.36
|-
|3
|482.284-490.95
|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
|39\29
|1025.264-1042.597
|179.310
|1027.882-1045.215
|
|-
|-
|7
|35\26
|1196.141-1216.363
|179.417
|1199.196-1219.418
|
|-
|-
|8
|31\23
|1367.018-1389.119
|179.710
|1370.5095-1393.621
|
|}
{| class="wikitable" style="text-align: center"
|-
|-
! rowspan="3" |Degrees
|27\20
! colspan="4" |Mixolydian
|180.000
! rowspan="3" |Mixolydian-Ionian
|
|-
|-
! rowspan="2" |Subpental
|23\17
! rowspan="2" |Pental
|180.392
! colspan="2" |Superpental
|
|-
|-
!Soft
|19\14
!Intense
|180.952
|
|-
|-
|1
|15\11
|173.091-175.98
|181.818
|173.844-176.733
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|177.774-180.663
|180.707-183.596
|182.729-185.618
|-
|-
|2
|26\19
|346.182-351.96
|182.456
|347.688-353.466
|
|355.548-361.325
|361.415-367.193
|365.4585-371.236
|-
|-
|3
| 11\8
|519.2735-527.94
|''183.333''
|521.532-530.199
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|533.321-541.988
|542.122-550.789
|548.188-556.854
|-
|-
|4
|18\13
|692.365-703.92
|184.615
|695.376-706.932
|
|711.095-722.651
|722.83-734.385
|730.917-742.4725
|-
|-
|5
|25\18
|865.456-879.9
|185.185
|869.22-883.6645
|
|888.896-903.3135
|903.537-917.982
|913.646-928.091
|-
|-
|6
|7\5
|1038.547-1055.88
|186.667
|1043.064-1060.3975
|Mixolydian-Ionian mode ends
|1033.634-1083.976
|}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.
|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.
 
== See also ==
* [[9ed5/2]] - equal division of the classic major tenth
* [[9ed7/3]] - equal division of the septimal minor tenth


[[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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