This is the neutral scale of the Middletown temperament family.
Intervals
| Degrees
|
Intense Aeolian-Subpental Dorian
|
Dorian
|
| Subpental
|
Pental
|
Superpental
|
| Min
|
Golden±13¢
|
r¢
|
Max
|
Min
|
Golden±13¢
|
Max
|
Min
|
Golden±13¢
|
Max
|
Min
|
Golden±13¢
|
Max
|
| 1
|
160
|
160.761-163.65
|
161.111
|
162.963
|
162.317-165.2055
|
166.667
|
167.6965-170.585
|
169.697
|
168.741-171.63
|
171.429
|
| 2
|
320
|
321.522-327.3
|
322.222
|
325.926
|
364.633-330.411
|
333.333
|
335.393-341.171
|
339.394
|
337.483-343.36
|
342.857
|
| 3
|
480
|
482.284-490.95
|
483.333
|
488.889
|
486.95-495.617
|
500
|
503.089-511.756
|
509.091
|
506.224-514.891
|
514.286
|
| 4
|
640
|
643.045-654.6
|
644.444
|
651.852
|
649.2665-660.822
|
666.667
|
670.786-682.341
|
678.788
|
674.965-686.521
|
685.714
|
| 5
|
800
|
803.806-818.25
|
805.556
|
814.815
|
811.583-826.028
|
833.333
|
838.482-852.927
|
848.485
|
843.707-858.151
|
857.143
|
| 6
|
960
|
964.567-981.9
|
966.667
|
977.778
|
973.9-991.233
|
1000
|
1006.179-1023.512
|
1018.182
|
1012.448-1029.781
|
1028.571
|
| 7
|
1120
|
1125.328-1145.55
|
1127.778
|
1140.741
|
1136.216-1156.439
|
1166.666
|
1173.875-1194.0975
|
1187.879
|
1181.189-1201.411
|
1200
|
| 8
|
1280
|
1286.09-1309.2
|
1288.889
|
1303.704
|
1278.2435-1321.644
|
1333.333
|
1341.572-1343.36
|
1357.576
|
1349.9305-1373.042
|
1371.429
|
| Degrees
|
Min
|
Golden±13¢
|
r¢
|
Max
|
| 1
|
171.429
|
171.314-174.203
|
172.222
|
173.333
|
| 2
|
342.857
|
342.617-348.405
|
344.444
|
246.667
|
| 3
|
514.286
|
513.941-522.608
|
516.667
|
520
|
| 4
|
685.714
|
685.255-696.81
|
688.889
|
693.333
|
| 5
|
857.143
|
856.568-871.012
|
861.111
|
866.667
|
| 6
|
1028.571
|
1027.882-1045.2155
|
1033.333
|
1040
|
| 7
|
1200
|
1199.196-1219.418
|
1205.556
|
1213.333
|
| 8
|
1371.429
|
1370.5095-1393.621
|
1377.778
|
1386.667
|
| Degrees
|
Mixolydian
|
Mixolydian-Ionian
|
| Subpental
|
Pental
|
Superpental
|
| Soft
|
Intense
|
| Minimum
|
Golden±13¢
|
Maximum
|
Minimum
|
Golden±13¢
|
Maximum
|
Minimum
|
Golden±13¢
|
Maximum
|
Minimum
|
Golden±13¢
|
r¢
|
Maximum
|
Minimum
|
Golden±13¢
|
Maximum
|
| 1
|
173.333
|
173.091-175.98
|
175
|
173.844-176.733
|
177.778
|
177.774-180.663
|
179.31
|
180.707-183.596
|
183.333
|
183.908
|
182.729-185.618
|
186.667
|
| 2
|
246.667
|
346.182-351.96
|
350
|
347.688-353.466
|
355.556
|
355.548-361.325
|
358.621
|
361.415-367.193
|
366.667
|
367.816
|
365.4585-371.236
|
373.333
|
| 3
|
520
|
519.2735-527.94
|
525
|
521.532-530.199
|
533.333
|
533.321-541.988
|
537.931
|
542.122-550.789
|
550
|
551.724
|
548.188-556.854
|
560
|
| 4
|
693.333
|
692.365-703.92
|
700
|
695.376-706.932
|
711.111
|
711.095-722.651
|
717.241
|
722.83-734.385
|
733.333
|
735.632
|
730.917-742.4725
|
746.667
|
| 5
|
866.667
|
865.456-879.9
|
875
|
869.22-883.6645
|
888.889
|
888.896-903.3135
|
896.552
|
903.537-917.982
|
916.667
|
919.54
|
913.646-928.091
|
1033.333
|
| 6
|
1040
|
1038.547-1055.88
|
1050
|
1043.064-1060.3975
|
1066.667
|
1033.634-1083.976
|
1075.862
|
1084.245-1101.578
|
1100
|
1103.448
|
1096.3755-1113.709
|
1120
|
| 7
|
1213.333
|
1211.638-1231.86
|
1225
|
1216.908-1237.13
|
1244.444
|
1244.417-1264.639
|
1255.172
|
1264.952-1285.174
|
1283.333
|
1287.356
|
1279.105-1299.327
|
1306.667
|
| 8
|
1386.667
|
1384.729-1407.84
|
1400
|
1390.752-1413.863
|
1422.222
|
1422.19-1445.3015
|
1434.483
|
1445.6595-1445.821
|
1466.667
|
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. 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.