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This reformed minor mode is the neutral scale of the Napoli and Fujiyama temperament families in Long Common Practice .
This reformed minor mode is the neutral scale of the Napoli and Fujiyama temperament families in Long Common Practice. It also gives the wide values for the period of the Greater [[Ragismic microtemperaments#Octoid|Octoid]] and [[Schismatic family#Octant|octant]] temperaments.


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
|+
! colspan="6" |Nonet
!Period
!Notes
|-
|-
! rowspan="3" |Degrees
|1/1
! colspan="3" |Soft Phrygian
|
! colspan="6" |Phrygian
|
|
|
|
|''150''
|Soft Phrygian mode begins
|-
|-
! rowspan="2" |Minimum-comma
|
! rowspan="2" |Median
|23/22
! rowspan="2" |Maximum+comma
|
! colspan="3" |Thirdtone
|
! colspan="3" |Semitone
|
|
|156.{{Overline|81}}
|
|-
|-
!Minimum-comma
|22\21
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
!Maximum+comma
|
|
|157.143
|Soft Phrygian mode ends, Thirdtone Phrygian mode begins
|-
|-
|1
|21\20
|145-''150''
|
|156.818
|
| colspan="2" |152.143-162.143
|
|158.333-158.571
|
| colspan="2" |155-165.714
|
|162-''162.5''
|157.5
|165-170
|
|-
|-
|2
|20\19
|290-''300''
|
|313.636
|
| colspan="2" |306.286-324.286
|
|316.667-317.143
|
| colspan="2" |310-331.429
|
|324-''325''
|157.895
|330-340
|
|-
|-
|3
|19\18
|435-''450''
|
|470.4545
|
| colspan="2" |458.429-486.429
|
|475-475.714
|
| colspan="2" |465-497.143
|
|486-''487.5''
|158.333
|495-510
|
|-
|-
|4
|
|580-''600''
|37\35
|627.273
|
| colspan="2" |608.571-648.571
|
|633.333-634.286
|
| colspan="2" |620-666.857
|
|648-''650''
|158.571
|660-680
|
|-
|-
|5
|18\17
|725-''750''
|
|784.091
|
| colspan="2" |760.714-810.714
|
|791.667-792.857
|
| colspan="2" |775-827.571
|
|810-''812.5''
|158.8235
|825-850
|
|-
|-
|6
|17\16
|870-''900''
|
|940.909
|
| colspan="2" |912.857-972.857
|
|950-951.429
|
| colspan="2" |930-993.286
|
|972-''975''
|159.375
|990-1020
|
|-
|-
|7
|16\15
|1015-''1050''
|
|1097.727
|
| colspan="2" |1065-1135
|
|1108.333-1110
|
| colspan="2" |1085-1160
|
|1134-''1137.5''
|160
|1155-1190
|Thirdtone Phrygian mode
|}
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
|15\14
! colspan="3" |Intense Phrygian
|
! colspan="3" |Intense Phrygian-Soft Aeolian
|
! colspan="4" |Soft Aeolian
|
|
|
|160.714
|Semitone Phrygian mode begins
|-
|-
!Minimum-comma
|14\13
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!''r¢''
|
!Median
|161.5385
!Maximum+comma
|
|-
|-
|1
|
|160-165
|27\25
|165.7895
|
| colspan="2" |161.667-171.667
|
|167.647
|
| colspan="2" |163.75-173.75
|
|''168.75''
|162
|170
|
|171.429-176.429
|-
|-
|2
|13\12
|320-330
|
|331.579
|
| colspan="2" |323.333-343.333
|
|335.294
|
| colspan="2" |327.5-347.5
|
|''337.5''
|''162.5''
|340
|
|342.857-352.857
|-
|-
|3
|12\11
|480-495
|
|497.368
|
| colspan="2" |485-515
|
|502.941
|
| colspan="2" |491.75-521.75
|
|''506.25''
|163.{{Overline|63}}
|510
|
|514.286-529.286
|-
|-
|4
|
|640-660
|23\21
|663.158
|
| colspan="2" |646.667-686.667
|
|670.588
|
| colspan="2" |655-695
|
|''675''
|164.286
|680
|
|685.714-705.714
|-
|-
|5
|11\10
|800-825
|
|828.947
|
| colspan="2" |808.333-858.333
|
|838.235
|
| colspan="2" |818.75-868.75
|
|''843.75''
|165
|850
|Semitone Phrygian mode ends, Intense Phrygian mode begins
|857.143-882.143
|-
|-
|6
|
|960-990
|21\19
|994.737
|
| colspan="2" |970-1030
|
|1005.882
|
| colspan="2" |982.5-1042.5
|
|''1012.5''
|165.7895
|1020
|
|1028.571-1058.571
|-
|-
|7
|10\9
|1120-1155
|
|1160.526
|
| colspan="2" |1131.667-1201.667
|
|1173.529
|
| colspan="2" |1146.25-1216.25
|
|''1181.25''
|166.{{Overline|6}}
|1190
|Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
|1200-1235
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="6" |Aeolian
! colspan="8" |Intense Aeolian
|-
|-
! colspan="3" |Flattone
|
! colspan="3" |Meantone
|19\17
! colspan="5" |Superpyth
|
! colspan="3" |Ultrapyth
|
|
|
|167.647
|
|-
|-
!Minimum-comma
|9\8
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
!Median
|
! colspan="2" |Maximum+comma~Minimum-comma
|
! colspan="2" |''r¢''
|
!Median
|''168.75''
! colspan="2" |Maximum+comma~Minimum-comma
|Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
!Median
!Maximum+comma
|-
|-
|1
|
|166.429-171.429
|
|173.077
|26\23
| colspan="2" |168.684-178.684
|
|174
|
| colspan="2" |170-180
|
| colspan="2" |''175''
|169.565
|176.471
|
| colspan="2" |172.273-182.273
|178.125
|180-185
|-
|-
|2
|
|332.857-342.857
|17\15
|346.154
|
| colspan="2" |337.368-357.368
|
|348
|
| colspan="2" |340-360
|
| colspan="2" |''350''
|170
|352.941
|
| colspan="2" |344.5455-364.5455
|356.25
|360-370
|-
|-
|3
|8\7
|499.286-514.286
|
|519.231
|
| colspan="2" |506.053-536.053
|
|522
|
| colspan="2" |510-540
|
| colspan="2" |''525''
|171.429
|529.412
|Soft Aeolian mode ends, Flattone Aeolian mode begins
| colspan="2" |516.818-546.818
|534.375
|540-555
|-
|-
|4
|
|665.714-685.714
|
|692.308
|23\20
| colspan="2" |674.737-714.737
|
|696
|
| colspan="2" |680-720
|
| colspan="2" |''700''
|172.5
|705.882
|
| colspan="2" |689.091-729.091
|712.5
|720-740
|-
|-
|5
|
|832.143-857.143
|15\13
|865.385
|
| colspan="2" |843.421-893.421
|
|870
|
| colspan="2" |850-900
|
| colspan="2" |''875''
|173.077
|882.353
|
| colspan="2" |861.364-911.364
|890.625
|900-925
|-
|-
|6
|
|998.571-1028.571
|
|1038.4615
|22\19
| colspan="2" |1012.105-1071.105
|
|1044
|
| colspan="2" |1020-1080
|
| colspan="2" |''1050''
|173.684
|1058.8235
|Flattone Aeolian mode ends, Meantone Aeolian mode begins
| colspan="2" |1033.636-1093.636
|1068.75
|1080-1110
|-
|-
|7
|
|1165-1200
|
|1211.5385
|
| colspan="2" |1180.7895-1250.7895
|29\25
|1218
|
| colspan="2" |1190-1260
|
| colspan="2" |''1225''
|174
|1235.294
|
| colspan="2" |1205.909-1275.909
|1246.875
|1260-1295
|}
Golden/Pyrite Tunings±13¢
 
{| class="wikitable"
|-
|-
! rowspan="3" |Degrees
|7\6
! colspan="2" |Soft Phrygian
|
! colspan="4" |Phrygian
|
|
|
|
|''175''
|Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
|-
|-
! rowspan="2" |Min-Med
|
! rowspan="2" |Min-Max/Med-Max
|
! colspan="2" |Thirdtone
|20\17
! colspan="2" |Semitone
|
|
|
|176.471
|
|-
|-
!Min-Med/Min-Max
|
!Med-Max
|14\11
!Min-Med/Min-Max
|
!Med-Max
|
|
|
|177.{{Overline|27}}
|Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
|-
|-
|1
|
|155.007-158.257
|
|155.314-158.564
|19\16
|155.93-159.81
|
|157.275-160.621
|
|159.833-163.652
|
|160.97-164.975
|178.125
|-
|
|2
|310.014-316.514
|310.627-317.127
|311.86-319.62
|314.55-321.242
|319.668-327.304
|321.939-329.95
|-
|3
|465.021-474.771
|465.941-475.691
|467.79-497.43
|471.825-481.8635
|479.502-490.955
|482.909-494.925
|-
|4
|620.0275-633.0275
|621.253-634.253
|623.7205-639.24
|629.1-642.485
|639.335-654.335
|643.879-659.8995
|-
|5
|775.034-791.284
|778.568-792.818
|779.651-799.05
|786.375-803.106
|799.17-818.259
|804.848-824.874
|-
|6
|930.041-949.541
|931.882-951.382
|935.581-958.86
|943.6495-963.727
|959.004-981.911
|965.818-989.849
|-
|7
|1085.048-1107.798
|1087.196-1109.946
|1091.511-1118.67
|1100.924-1124.348
|1118.838-1145.563
|1126.7875-1154.824
|}
{| class="wikitable"
|-
! rowspan="2" |Degrees
! colspan="2" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian
|-
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|163.971-167.221
|164.363-167.613
|165.78-169.03
|166.271-169.521
|168.065-171.315
|168.695-171.945
|-
|2
|327.941-334.441
|328.726-335.226
|331.561-338.061
|332.541-339.041
|336.13-345.63
|337.39-343.895
|-
|3
|491.912-501.662
|493.089-502.839
|497.341-507.091
|498.812-508.562
|504.195-513.945
|506.084-515.834
|-
|4
|655.883-668.883
|657.4525-670.4525
|663.121-676.121
|665.082-678.082
|672.2605-685.2605
|674.779-687.779
|-
|5
|819.8535-836.1035
|821.816-838.065
|828.902-845.152
|831.353-847.603
|840.362-856.567
|843.474-859.724
|-
|6
|983.824-1003.324
|986.178-1005.678
|994.682-1014.182
|997.623-1017.123
|1108.391-1027.891.
|1012.169-1031.669
|-
|7
|1147.795-1170.545
|1150.542-1173.292
|1160.4625-1183.2125
|1163.894-1186.644
|1176.456-1199.206
|1180.8635-1203.6135
|}
{| class="wikitable"
! rowspan="3" |Degrees
! colspan="4" |Aeolian
! colspan="4" |Intense Aeolian
|-
! colspan="2" |Flattone
! colspan="2" |Meantone
! colspan="2" |Superpyth
! colspan="2" |Ultrapyth
|-
!Min-Med
!Med-Max~Min-Max
!Min-Med/Min-Max
!Med-Max
!Min-Med
!Min-Max/Med-Max
!Min-Med/Min-Max
!Med-Max
|-
|1
|171.04-174.29
| colspan="2" |171.641-175.524
|172.504-175.754
|174.582-177.832
|175.074-178.324
|176.246-179.495
|176.8035-180.0535
|-
|2
|342.081-348.581
| colspan="2" |343.282-351.048
|345.008-351.508
|349.1645-355.6645
|350.149-356.649
|352.492-358.992
|353.607-360.107
|-
|3
|513.121-522.871
| colspan="2" |514.923-526.572
|517.5125-527.2625
|523.747-533.497
|525.224-534.974
|528.738-538.488
|530.4105-540.1605
|-
|-
|4
|
|684.161-697.161
|
| colspan="2" |686.5635-702.096
|
|690.017-703.017
|25\21
|698.329-711.329
|
|700.299-713.299
|
|704.983-717.983
|178.571
|707.214-720.214
|
|-
|-
|5
|
|855.202-871.472
|
| colspan="2" |858.204-877.62
|
|862.521-878.771
|
|872.911-889.161
|31\26
|875.373-890.623
|
|881.229-897.479
|178.846
|884.018-900.268
|
|-
|-
|6
|
|1026.242-1045.742
|
| colspan="2" |1029.845-1053.1445
|
|1035.025-1054.525
|
|1047.4935-1066.9935
|
|1050.448-1069.998
|37\31
|1057.475-1076.975
|179.032
|1060.821-1080.321
|
|-
|-
|7
|6\5
|1197.282-1220.032
|
| colspan="2" |1201.486-1228.6685
|
|1207.529-1230.279
|
|1222.076-1244.826
|
|1225.523-1248.273
|
|1233.721-1256.471
|180
|1237.625-1260.375
|Ultrapyth Intense Aeolian mode ends
|}
|}
[[Category:8-tone scales]]
[[Category:8-tone scales]]

Revision as of 05:15, 17 May 2023

This reformed minor mode is the neutral scale of the Napoli and Fujiyama temperament families in Long Common Practice. It also gives the wide values for the period of the Greater Octoid and octant temperaments.

Intervals

Nonet Period Notes
1/1 150 Soft Phrygian mode begins
23/22 156.81
22\21 157.143 Soft Phrygian mode ends, Thirdtone Phrygian mode begins
21\20 157.5
20\19 157.895
19\18 158.333
37\35 158.571
18\17 158.8235
17\16 159.375
16\15 160 Thirdtone Phrygian mode
15\14 160.714 Semitone Phrygian mode begins
14\13 161.5385
27\25 162
13\12 162.5
12\11 163.63
23\21 164.286
11\10 165 Semitone Phrygian mode ends, Intense Phrygian mode begins
21\19 165.7895
10\9 166.6 Intense Phrygian mode ends, Intense Phrygian-Soft Aeolian mode begins
19\17 167.647
9\8 168.75 Intense Phrygian-Soft Aeolian mode ends, Soft Aeolian mode begins
26\23 169.565
17\15 170
8\7 171.429 Soft Aeolian mode ends, Flattone Aeolian mode begins
23\20 172.5
15\13 173.077
22\19 173.684 Flattone Aeolian mode ends, Meantone Aeolian mode begins
29\25 174
7\6 175 Meantone Aeolian mode ends, Superpyth Intense Aeolian mode begins
20\17 176.471
14\11 177.27 Superpyth Intense Aeolian mode ends, Ultrapyth Intense Aeolian mode begins
19\16 178.125
25\21 178.571
31\26 178.846
37\31 179.032
6\5 180 Ultrapyth Intense Aeolian mode ends
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