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This is the neutral scale of the Middletown temperament family.
This is the neutral scale of the Middletown temperament family.
==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable" style="text-align: center"
! rowspan="5" |Degrees
! rowspan="3" |Degrees
! colspan="8" |Minor mode Middletown temperament
! colspan="3" rowspan="2" |Intense Aeolian-Subpental Dorian
! colspan="2" |Neutral mode Middletown temperament
! colspan="10" |Dorian
! colspan="10" |Major mode Middletown temperament
|-
|-
! colspan="2" rowspan="3" |Intense Aeolian-Dorian
! colspan="4" |Subpental
! colspan="6" |Dorian
! colspan="3" |Pental
! colspan="2" rowspan="3" |Dorian-Mixolydian
! colspan="3" |Superpental
! colspan="8" |Mixolydian
! colspan="2" rowspan="3" |Mixolydian-Ionian
|-
|-
! colspan="2" rowspan="2" |Subpental
!Min
! colspan="2" rowspan="2" |Pental
!Golden±13¢
! colspan="2" rowspan="2" |Superpental
!Max
! colspan="2" rowspan="2" |Subpental
!Min
! colspan="2" rowspan="2" |Pental
!7/3±13¢
! colspan="4" |Superpental
!Golden±13¢
|-
!Max
! colspan="2" |Soft
!Min
! colspan="2" |Intense
!Golden±13¢
|-
!Max
! |Minimum
!Min
! |Maximum
!Golden±13¢
!Minimum
!Max
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
!Minimum
!Maximum
! |Minimum
!Maximum
!Minimum
!Maximum
!Minimum
!Maximum
!Minimum
! |Maximum
|-
|-
| |1
|1
| |160
|160
|160.761-163.65
| colspan="2" |162.963
| colspan="2" |162.963
|161.541-164.43
|162.317-165.2055
| colspan="2" |166.667
| colspan="2" |166.667
|167.6965-170.585
| colspan="2" |169.697
| colspan="2" |169.697
| colspan="2" |171.429
|168.741-171.63
| colspan="2" |173.333
|171.429
| colspan="2" |175
| colspan="2" |177.778
| colspan="2" |179.31
| colspan="2" |183.908
| |186.667
|-
|-
| |2
|2
| |320
|320
|321.522-327.3
| colspan="2" |325.926
| colspan="2" |325.926
|323.082-328.86
|364.633-330.411
| colspan="2" |333.333
| colspan="2" |333.333
|335.393-341.171
| colspan="2" |339.394
| colspan="2" |339.394
| colspan="2" |342.857
|337.483-343.36
| colspan="2" |246.667
|342.857
| colspan="2" |350
| colspan="2" |355.556
| colspan="2" |358.621
| colspan="2" |367.816
| |373.333
|-
|-
| |3
|3
| |480
|480
|482.284-490.95
| colspan="2" |488.889
| colspan="2" |488.889
|484.624-493.29
|486.95-495.617
| colspan="2" |500
| colspan="2" |500
|503.089-511.756
| colspan="2" |509.091
| colspan="2" |509.091
| colspan="2" |514.286
|506.224-514.891
| colspan="2" |520
|514.286
| colspan="2" |525
| colspan="2" |533.333
| colspan="2" |537.931
| colspan="2" |551.724
| |560
|-
|-
| |4
|4
| |640
|640
|643.045-654.6
| colspan="2" |651.852
| colspan="2" |651.852
|646.165-657.72
|649.2665-660.822
| colspan="2" |666.667
| colspan="2" |666.667
|670.786-682.341
| colspan="2" |678.788
| colspan="2" |678.788
| colspan="2" |685.714
|674.965-686.521
| colspan="2" |693.333
|685.714
| colspan="2" |700
| colspan="2" |711.111
| colspan="2" |717.241
| colspan="2" |735.632
| |746.667
|-
|-
| |5
|5
| |800
|800
|803.806-818.25
| colspan="2" |814.815
| colspan="2" |814.815
|807.706-822.1505
|811.583-826.028
| colspan="2" |833.333
| colspan="2" |833.333
|838.482-852.927
| colspan="2" |848.485
| colspan="2" |848.485
| colspan="2" |857.143
|843.707-858.151
| colspan="2" |866.667
|857.143
| colspan="2" |875
| colspan="2" |888.889
| colspan="2" |896.552
| colspan="2" |919.54
| |1033.333
|-
|-
| |6
|6
| |960
|960
|964.567-981.9
| colspan="2" |977.778
| colspan="2" |977.778
|969.247-986.581
|973.9-991.233
| colspan="2" |1000
| colspan="2" |1000
|1006.179-1023.512
| colspan="2" |1018.182
| colspan="2" |1018.182
| colspan="2" |1028.571
|1012.448-1029.781
| colspan="2" |1040
|1028.571
| colspan="2" |1050
| colspan="2" |1066.667
| colspan="2" |1075.862
| colspan="2" |1103.448
| |1120
|-
|-
| |7
|7
| |1120
|1120
|1125.328-1145.55
| colspan="2" |1140.741
| colspan="2" |1140.741
|1130.7885-1151.011
|1136.216-1156.439
| colspan="2" |1166.666
| colspan="2" |1166.666
|1173.875-1194.0975
| colspan="2" |1187.879
| colspan="2" |1187.879
| colspan="2" |1200
|1181.189-1201.411
| colspan="2" |1213.333
|1200
| colspan="2" |1225
| colspan="2" |1244.444
| colspan="2" |1255.172
| colspan="2" |1287.356
| |1306.667
|-
|-
|8
|8
|1280
|1280
|1286.09-1309.2
| colspan="2" |1303.704
| colspan="2" |1303.704
|1292.33-1315.441
|1278.2435-1321.644
| colspan="2" |1333.333
| colspan="2" |1333.333
|1341.572-1343.36
| colspan="2" |1357.576
| colspan="2" |1357.576
| colspan="2" |1371.429
|1349.9305-1373.042
| colspan="2" |1386.667
|1371.429
| colspan="2" |1400
|}
| colspan="2" |1422.222
{| class="wikitable" style="text-align: center"
| colspan="2" |1434.483
!Degrees
| colspan="2" |1471.264
!Min
|1493.333
|}Most harmonic tunings
{| class="wikitable"
|-
! rowspan="2" |Degrees
!Minor mode Middletown temperament
!Neutral mode Middletown temperament
!Major mode Middletown temperament
|-
!7/3±13¢
!22/9±13¢
!22/9±13¢
!5/2±13¢
!Golden±13¢
!Max
|-
|-
| |1
|1
|161.541-164.43
|171.429
|170.49-173.379
|170.49-173.379
|174.813-177.7015
|171.314-174.203
|173.333
|-
|-
| |2
|2
|323.082-328.86
|342.857
|340.9795-346.757
|340.9795-346.757
|349.625-355.403
|342.617-348.405
|246.667
|-
|-
| |3
|3
|484.624-493.29
|514.286
|511.469-520.136
|511.469-520.136
|524.438-533.105
|513.941-522.608
|520
|-
|-
| |4
|4
|646.165-657.72
|685.714
|681.959-693.515
|681.959-693.515
|699.2505-710.806
|685.255-696.81
|693.333
|-
|-
| |5
|5
|807.706-822.1505
|857.143
|852.489-866.893
|852.489-866.893
|874.063-888.508
|856.568-871.012
|866.667
|-
|-
| |6
|6
|969.247-986.581
|1028.571
|1022.939-1040.272
|1022.939-1040.272
|1048.876-1066.5425
|1027.882-1045.2155
|1040
|-
|-
| |7
|7
|1130.7885-1151.011
|1200
|1193.428-1215.651
|1193.428-1215.651
|1223.688-1244.466
|1199.196-1219.418
|1213.333
|-
|-
|8
|8
|1292.33-1315.441
|1371.429
|1363.918-1387.293
|1363.918-1387.293
|1398.4501-1422.391
|1370.5095-1393.621
|}Golden tunings±13¢
|1386.667
 
|}
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="4" |Degrees
! rowspan="4" |Degrees
! colspan="4" |Minor mode Middletown temperament
! colspan="13" |Mixolydian
!Neutral mode Middletown temperament
! colspan="3" rowspan="3" |Mixolydian-Ionian
! colspan="5" |Major mode Middletown temperament
|-
|-
! rowspan="3" |Intense Aeolian-Dorian
! colspan="3" rowspan="2" |Subpental
! colspan="3" |Dorian
! colspan="4" rowspan="2" |Pental
! rowspan="3" |Dorian-Mixolydian
! colspan="6" |Superpental
! colspan="4" |Mixolydian
! rowspan="3" |Mixolydian-Ionian
|-
|-
! rowspan="2" |Subpental
! colspan="3" |Soft
! rowspan="2" |Pental
! colspan="3" |Intense
! rowspan="2" |Superpental
! rowspan="2" |Subpental
! rowspan="2" |Pental
! colspan="2" |Superpental
|-
|-
!Soft
!Minimum
!Intense
!Golden±13¢
!Maximum
! |Minimum
!Golden±13¢
!5/2±13¢
!Maximum
!Minimum
!Golden±13¢
!Maximum
!Minimum
!Golden±13¢
!Maximum
!Minimum
!Golden±13¢
! |Maximum
|-
|-
| |1
| |1
| |160.761-163.65
|173.333
|162.317-165.2055
|167.6965-170.585
|168.741-171.63
|171.314-174.203
|173.091-175.98
|173.091-175.98
| colspan="2" |175
|173.844-176.733
|173.844-176.733
|174.813-177.7015
| colspan="2" |177.778
|177.774-180.663
|177.774-180.663
| colspan="2" |179.31
|180.707-183.596
|180.707-183.596
| colspan="2" |183.908
|182.729-185.618
|182.729-185.618
| |186.667
|-
|-
| |2
| |2
| |321.522-327.3
|246.667
|364.633-330.411
|335.393-341.171
|337.483-343.36
|342.617-348.405
|346.182-351.96
|346.182-351.96
| colspan="2" |350
|347.688-353.466
|347.688-353.466
|349.625-355.403
| colspan="2" |355.556
|355.548-361.325
|355.548-361.325
| colspan="2" |358.621
|361.415-367.193
|361.415-367.193
| colspan="2" |367.816
|365.4585-371.236
|365.4585-371.236
| |373.333
|-
|-
| |3
| |3
| |482.284-490.95
|520
|486.95-495.617
|503.089-511.756
|506.224-514.891
|513.941-522.608
|519.2735-527.94
|519.2735-527.94
| colspan="2" |525
|521.532-530.199
|521.532-530.199
|524.438-533.105
| colspan="2" |533.333
|533.321-541.988
|533.321-541.988
| colspan="2" |537.931
|542.122-550.789
|542.122-550.789
| colspan="2" |551.724
|548.188-556.854
|548.188-556.854
| |560
|-
|-
| |4
| |4
| |643.045-654.6
|693.333
|649.2665-660.822
|670.786-682.341
|674.965-686.521
|685.255-696.81
|692.365-703.92
|692.365-703.92
| colspan="2" |700
|695.376-706.932
|695.376-706.932
|699.2505-710.806
| colspan="2" |711.111
|711.095-722.651
|711.095-722.651
| colspan="2" |717.241
|722.83-734.385
|722.83-734.385
| colspan="2" |735.632
|730.917-742.4725
|730.917-742.4725
| |746.667
|-
|-
| |5
| |5
| |803.806-818.25
|866.667
|811.583-826.028
|838.482-852.927
|843.707-858.151
|856.568-871.012
|865.456-879.9
|865.456-879.9
| colspan="2" |875
|869.22-883.6645
|869.22-883.6645
|874.063-888.508
| colspan="2" |888.889
|888.896-903.3135
|888.896-903.3135
| colspan="2" |896.552
|903.537-917.982
|903.537-917.982
| colspan="2" |919.54
|913.646-928.091
|913.646-928.091
| |1033.333
|-
|-
| |6
| |6
| |964.567-981.9
|1040
|973.9-991.233
|1006.179-1023.512
|1012.448-1029.781
|1027.882-1045.2155
|1038.547-1055.88
|1038.547-1055.88
| colspan="2" |1050
|1043.064-1060.3975
|1043.064-1060.3975
|1048.876-1066.5425
| colspan="2" |1066.667
|1033.634-1083.976
|1033.634-1083.976
| colspan="2" |1075.862
|1084.245-1101.578
|1084.245-1101.578
| colspan="2" |1103.448
|1096.3755-1113.709
|1096.3755-1113.709
| |1120
|-
|-
| |7
| |7
| |1125.328-1145.55
|1213.333
|1136.216-1156.439
|1173.875-1194.0975
|1181.189-1201.411
|1199.196-1219.418
|1211.638-1231.86
|1211.638-1231.86
| colspan="2" |1225
|1216.908-1237.13
|1216.908-1237.13
|1223.688-1244.466
| colspan="2" |1244.444
|1244.417-1264.639
|1244.417-1264.639
| colspan="2" |1255.172
|1264.952-1285.174
|1264.952-1285.174
| colspan="2" |1287.356
|1279.105-1299.327
|1279.105-1299.327
| |1306.667
|-
|-
|8
|8
|1286.09-1309.2
|1386.667
|1278.2435-1321.644
|1341.572-1343.36
|1349.9305-1373.042
|1370.5095-1393.621
|1384.729-1407.84
|1384.729-1407.84
| colspan="2" |1400
|1390.752-1413.863
|1390.752-1413.863
|1398.4501-1422.391
| colspan="2" |1422.222
|1422.19-1445.3015
|1422.19-1445.3015
| colspan="2" |1434.483
|1445.6595-1445.821
|1445.6595-1445.821
| colspan="2" |1471.264
|1461.834-1484.945
|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.
|}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]]
[[Category:EdX]]
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