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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" style="text-align: center"
|+
! rowspan="3" |Degrees
!Decade
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
!Period
! colspan="9" |Dorian
!Notes
|-
|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.{{Overline|5}}-160
|161.905
|161.905
| colspan="2" |158.{{Overline|518}}-167.{{Overline|407}}
|
|164.103
| colspan="2" |162.{{Overline|2}}-171.{{Overline|1}}
|168.889
| colspan="2" |165.2525-174.141
|170.{{Overline|370}}
|171.429-175.873
|-
|-
|2
|11\9
|311.{{Overline|1}}-320
|162.962
|323.8095
|Intense Aeolian-Subpental Dorian mode ends, Subpental Dorian mode begins
| colspan="2" |317.{{Overline|037}}-334.{{Overline|814}}
|328.205
| colspan="2" |324.{{Overline|4}}-342.{{Overline|2}}
|337.{{Overline|7}}
| colspan="2" |330.505-348.283
|340.{{Overline|740}}
|342.857-351.746
|-
|-
|3
|27\22
|466.{{Overline|6}}-480
|163.636
|485.714
|
| colspan="2" |475.{{Overline|5}}-502.{{Overline|2}}
|492.308
| colspan="2" |486.{{Overline|6}}-513.{{Overline|3}}
|506.{{Overline|6}}
| colspan="2" |495.758-522.424
|511.{{Overline|1}}
|514.286-527.619
|-
|-
|4
|16\13
|622.{{Overline|2}}-640
|164.103
|647.619
|
| colspan="2" |634.{{Overline|074}}-669.{{Overline|629}}
|656.41
| colspan="2" |648.{{Overline|8}}-684.{{Overline|4}}
|675.{{Overline|5}}
| colspan="2" |661.01-696.566
|681.{{Overline|481}}
|685.714-703.492
|-
|-
|5
|21\17
|777.{{Overline|7}}-800
|164.706
|809.524
|
| colspan="2" |792.{{Overline|592}}-837.{{Overline|037}}
|820.512
| colspan="2" |811.{{Overline|1}}-855.{{Overline|5}}
|844.{{Overline|4}}
| colspan="2" |826.263-870.707
|851.{{Overline|851}}
|857.143-878.365
|-
|-
|6
|26\21
|943.{{Overline|3}}-960
|165.079
|971.429
|
| colspan="2" |951.{{Overline|1}}-1004.{{Overline|4}}
|984.615
| colspan="2" |973.{{Overline|3}}-1026.{{Overline|6}}
|1013.{{Overline|3}}
| colspan="2" |988.515-1044.848
|1022.{{Overline|2}}
|1028.571-1055.238
|-
|-
|7
|5\4
|1088.{{Overline|8}}-1120
| ''166.667''
|1133.{{Overline|3}}
|Subpental Dorian mode ends, Pental Dorian mode begins
| colspan="2" |1109.{{Overline|629}}-1171.{{Overline|851}}
|1148.718
| colspan="2" |1135.{{Overline|5}}-1197.{{Overline|7}}
|1182.{{Overline|2}}
| colspan="2" |1156.768-1218.99
|1192.{{Overline|592}}
|1200-1231.{{Overline|1}}
|-
|-
|8
|34\27
|1244.{{Overline|4}}-1280
|167.901
|1295.238
|
| colspan="2" |1238.{{Overline|148}}-1339.{{Overline|259}}
|1312.8205
| colspan="2" |1297.{{Overline|7}}-1368.{{Overline|8}}
|1351.{{Overline|1}}
| colspan="2" |1321.02-1392.131
|1362.{{Overline|962}}
|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.{{Overline|2}}''
|
| colspan="2" |168.105-176.9935
|172.8395
|173.{{Overline|3}}-177.{{Overline|7}}
|-
|-
|2
|19\15
|333.968-342.857
|168.889
| colspan="2" |''344.{{Overline|4}}''
|
| colspan="2" |336.209-353.987
|345.679
|346.{{Overline|6}}-355.{{Overline|5}}
|-
|-
|3
|14\11
|500.952-514.286
|169.697
| colspan="2" |''516.{{Overline|6}}''
|Pental Dorian mode ends, Superpental Dorian mode begins
| colspan="2" |504.314-530.98
|518.{{Overline|518}}
|520-533.{{Overline|3}}
|-
|-
|4
|23\18
|667.9365-685.714
|170.370
| colspan="2" |''688.{{Overline|8}}''
|
| colspan="2" |672.418-707.974
|691.358
|693.{{Overline|3}}-711.{{Overline|1}}
|-
|-
|5
|9\7
|834.921-857.143
|171.429
| colspan="2" |''861.{{Overline|1}}''
|Superpental Dorian mode ends, Mohajira Dorian-Mixolydian mode begins
| colspan="2" |840.523-885.967
|864.1975
|866.{{Overline|6}}-888.{{Overline|8}}
|-
|-
|6
|31\24
|1001.904-1028.571
|172.222
| colspan="2" |''1033.{{Overline|3}}''
|
| colspan="2" |1008.6275-1062.961
|1037.{{Overline|037}}
|1040-1066.{{Overline|6}}
|-
|-
|7
|22\17
|1168.{{Overline|8}}-1200
|172.549
| colspan="2" |''1205.{{Overline|5}}''
|Mohajira Dorian-Mixolydian mode ends, Beatles Dorian-Mixolydian mode begins
| colspan="2" |1176.732-1239.954
|1209.8765
|1213.{{Overline|3}}-1244.{{Overline|4}}
|-
|-
|8
|35\27
|1335.873-1371.429
|172.840
| colspan="2" |''1377.{{Overline|7}}''
|
| colspan="2" |1344.837-1416.948
|1382.716
|1386.{{Overline|6}}-1422.{{Overline|2}}
|}
{| 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.{{Overline|8}}-173.{{Overline|3}}
|174.359
| colspan="2" |170.{{Overline|5}}-179.{{Overline|4}}
|175.439
|175.439
| colspan="2" |173.{{Overline|3}}-182.{{Overline|2}}
|
|179.1{{Overline|6}}
| colspan="2" |174.866-183.755
|181.609
| colspan="2" |179.464-188.3525
|184.314
| |186.{{Overline|6}}-191.{{Overline|1}}
|-
| |2
|337.{{Overline|7}}-346.{{Overline|6}}
|348.718
| colspan="2" |341.{{Overline|1}}-358.{{Overline|8}}
|350.877
| colspan="2" |346.{{Overline|6}}-364.{{Overline|4}}
|358.{{Overline|3}}
| colspan="2" |349.732-367.51
|363.218
| colspan="2" |368.927-376.705
|368.6275
| |373.{{Overline|3}}-382.{{Overline|2}}
|-
| |3
|506.{{Overline|6}}-520
|523.077
| colspan="2" |511.{{Overline|6}}-538.{{Overline|3}}
|526.316
| colspan="2" |520-546.{{Overline|6}}
|537.5
| colspan="2" |524.598-551.264
|544.828
| colspan="2" |538.391-565.0575
|552.941
| |560-573.{{Overline|3}}
|-
| |4
|675.{{Overline|5}}-693.{{Overline|3}}
|697.436
| colspan="2" |682.{{Overline|2}}-717.{{Overline|7}}
|701.754
| colspan="2" |693.{{Overline|3}}-728.{{Overline|8}}
|716.{{Overline|6}}
| colspan="2" |699.464-735.019
|726.437
| colspan="2" |717.854-753.41
|737.255
| |746.{{Overline|6}}-764.{{Overline|4}}
|-
| |5
|844.{{Overline|4}}-866.{{Overline|6}}
|871.795
| colspan="2" |852.{{Overline|7}}-897.{{Overline|2}}
|877.193
| colspan="2" |866.{{Overline|6}}-911.{{Overline|1}}
|895.8{{Overline|3}}
| colspan="2" |874.3295-918.774
|908.046
| colspan="2" |897.318-942.7625
|921.569
| |933.{{Overline|3}}-955.{{Overline|5}}
|-
| |6
|1013.{{Overline|3}}-1040
|1046.154
| colspan="2" |1023.{{Overline|3}}-1076.{{Overline|6}}
|1052.632
| colspan="2" |1040-1093.{{Overline|3}}
|1075
| colspan="2" |1049.195-1102.529
|1089.655
| colspan="2" |1076.782-1130.115
|1105.882
| |1120-1146.{{Overline|6}}
|-
| |7
|1182.{{Overline|2}}-1213.{{Overline|3}}
|1220.513
| colspan="2" |1193.{{Overline|8}}-1256.{{Overline|1}}
|1228.07
| colspan="2" |1213.{{Overline|3}}-1275.{{Overline|5}}
|1254.1{{Overline|6}}
| colspan="2" |1224.061-1286.2835
|1271.264
| colspan="2" |1256.245-1318.457
|1290.196
| |1306.{{Overline|6}}-1337.{{Overline|7}}
|-
|8
|1351.{{Overline|1}}-1386.{{Overline|6}}
|1394.872
| colspan="2" |1364.{{Overline|4}}-1435.{{Overline|5}}
|1403.509
| colspan="2" |1386.{{Overline|6}}-1457.{{Overline|7}}
|1433.{{Overline|3}}
| colspan="2" |1398.927-1470.038
|1452.874
| colspan="2" |1438.709-1506.82
|1474.51
|1493.{{Overline|3}}-1528.{{Overline|8}}
|}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.{{Overline|1}}
|166.{{Overline|6}}
|177.{{Overline|7}}
|183.{{Overline|3}}
|-
|2
|322.{{Overline|2}}
|333.{{Overline|3}}
|355.{{Overline|5}}
|366.{{Overline|6}}
|-
|3
|483.{{Overline|3}}
|500
|533.{{Overline|3}}
|550
|-
|4
|644.{{Overline|4}}
|666.{{Overline|6}}
|711.{{Overline|1}}
|733.{{Overline|3}}
|-
|5
|805.{{Overline|5}}
|833.{{Overline|3}}
|888.{{Overline|8}}
|916.{{Overline|6}}
|-
|6
|966.{{Overline|6}}
|1000
|1066.{{Overline|6}}
|1100
|-
|7
|1127.{{Overline|7}}
|1166.{{Overline|6}}
|1244.{{Overline|4}}
|1283.{{Overline|3}}
|-
|8
|1288.{{Overline|8}}
|1333.{{Overline|3}}
|1422.{{Overline|2}}
|1466.{{Overline|6}}
|}Golden/Pyrite Tunings±13¢
 
{| class="wikitable" style="text-align: center"
! rowspan="2" |Degrees
! rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="3" |Dorian
|-
|-
!Subpental
|29\22
!Pental
|175.758
!Superpental
|
|-
|-
|1
|33\25
|160.761-163.65
|176.000
|162.317-165.2055
|
|167.6965-170.585
|168.741-171.63
|-
|-
|2
|4\3
|321.522-327.3
|''177.778''
|364.633-330.411
|Pental Mixolydian mode ends, Soft Superpental Mixolydian mode begins
|335.393-341.171
|337.483-343.36
|-
|-
|3
|51\38
|482.284-490.95
|178.947
|486.95-495.617
|
|503.089-511.756
|506.224-514.891
|-
|-
|4
|47\35
|643.045-654.6
|179.048
|649.2665-660.822
|
|670.786-682.341
|674.965-686.521
|-
|-
|5
|43\32
|803.806-818.25
|179.167
|811.583-826.028
|
|838.482-852.927
|843.707-858.151
|-
|-
|6
|39\29
|964.567-981.9
|179.310
|973.9-991.233
|
|1006.179-1023.512
|1012.448-1029.781
|-
|-
|7
|35\26
|1125.328-1145.55
|179.417
|1136.216-1156.439
|
|1173.875-1194.0975
|1181.189-1201.411
|-
|-
|8
|31\23
|1286.09-1309.2
|179.710
|1278.2435-1321.644
|
|1341.572-1343.36
|1349.9305-1373.042
|}
{| class="wikitable" style="text-align: center"
!Degrees
!Mohajira
!Beatles
|-
|-
|1
|27\20
|170.877-173.776
|180.000
|171.314-174.203
|
|-
|-
|2
|23\17
|341.755-347.513
|180.392
|342.627-348.405
|
|-
|-
|3
|19\14
|512.632-521.2985
|180.952
|513.941-522.607
|
|-
|-
|4
|15\11
|683.509-695.065
|181.818
|685.255-696.81
|Soft Superpental Mixolydian mode ends, Intense Superpental Mixolydian mode begins
|-
|-
|5
|26\19
|854.386-868.831
|182.456
|856.568-870.112
|
|-
|-
|6
| 11\8
|1025.264-1042.597
|''183.333''
|1027.882-1045.215
|Intense Superpental Mixolydian mode ends, Mixolydian-Ionian mode begins
|-
|-
|7
|18\13
|1196.141-1216.363
|184.615
|1199.196-1219.418
|
|-
|-
|8
|25\18
|1367.018-1389.119
|185.185
|1370.5095-1393.621
|
|}
{| class="wikitable" style="text-align: center"
|-
|-
! rowspan="3" |Degrees
|7\5
! colspan="4" |Mixolydian
|186.667
! rowspan="3" |Mixolydian-Ionian
|Mixolydian-Ionian mode ends
|-
|}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.
! 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.
 
== 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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