User:Moremajorthanmajor/8edIX: Difference between revisions

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This Long Common Practice minor mode is the neutral scale of the Napoli temperament family.
This reformed minor mode is the neutral scale of the Napoli temperament family in Long Common Practice .


==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
|-
! rowspan="3" |Degrees
! rowspan="3" |Degrees
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="5" |Soft Phrygian
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="11" |Phrygian
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! rowspan="2" |Absolute Minimum
!  rowspan="2"|Minimum
! rowspan="2" |Median
!  rowspan="2"|Maximum
!  colspan="3"|Intense Phrygian
! colspan="3" |Intense Phrygian-Soft Aeolian
! colspan="3" |Soft Aeolian
! rowspan="2" |Minimum
! rowspan="2" |Minimum
! rowspan="2" |Min-Med±13¢
! rowspan="2" |Median
! rowspan="2" |Median
! rowspan="2"|Maximum
! rowspan="2" |Min-Max/Med-Max±13¢
! rowspan="2" |Maximum
! colspan="5" |Thirdtone
! colspan="6" |Semitone
|-
|-
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Med-Max±13¢
!Maximum
!Maximum
!Minimum
!Minimum
!Min-Med/Min-Max±13¢
!Median
!Median
!Maximum
!Med-Max±13¢
!Minimum
!15/7±13¢
!Median
!Maximum
!Maximum
|-
|-
| |1
|1
|150
|150
|158.571
!155.007-158.257
|160
!156.818
| colspan="2" |165
!155.314-158.564
|165.7895
! colspan="2" |157.143
| colspan="2" |166.667
!155.93-159.81
|167.647
!158.333-158.571
| colspan="2" |168.75
!157.275-160.621
|170
! colspan="2" |160-160.714
| colspan="2" |171.429
!159.833-163.652
|175
!162-162.5
| |180
!160.97-164.975
|163.305-166.555
|165
|-
|-
| |2
|2
|300
|300
|317.143
!310.014-316.514
|320
!313.636
| colspan="2" |330
!310.627-317.127
|331.579
! colspan="2" |314.286
| colspan="2" |333.333
!311.86-319.62
|335.294
!316.667-317.143
| colspan="2" |337.5
!314.55-321.242
|340
! colspan="2" |320-321.429
| colspan="2" |342.857
!319.668-327.304
|350
!324-325
| |360
!321.939-329.95
|326.611-333.111
|330
|-
|-
| |3
|3
|450
|450
|475.714
!465.021-474.771
|480
!470.4545
| colspan="2" |495
!465.941-475.691
|497.368
! colspan="2" |471.429
| colspan="2" |500
!467.79-497.43
|502.941
!475-475.714
| colspan="2" |506.25
!471.825-481.8635
|510
! colspan="2" |480-482.143
| colspan="2" |514.286
!479.502-490.955
|525
!486-487.5
| |540
!482.909-494.925
|489.916-499.666
|495
|-
|-
| |4
|4
|600
|600
|634.286
|620.0275-633.0275
|640
!627.273
| colspan="2" |660
|621.253-634.253
|663.158
! colspan="2" |628.571
| colspan="2" |666.667
|623.7205-639.24
|670.588
|633.333-634.286
| colspan="2" |675
!629.1-642.485
|680
! colspan="2" |640-642.857
| colspan="2" |685.714
|639.335-654.335
|700
!648-650
| |720
|643.879-659.8995
|653.224-666.221
|660
|-
|-
| |5
|5
|750
|750
|792.857
!775.034-791.284
|800
!784.091
| colspan="2" |825
!778.568-792.818
|828.947
! colspan="2" |785.714
| colspan="2" |833.333
!779.651-799.05
|838.235
!791.667-792.857
| colspan="2" |843.75
!786.375-803.106
|850
! colspan="2" |800-803.571
| colspan="2" |857.143
!799.17-818.259
|875
!810-812.5
| |900
!804.848-8242.874
|816.527-832.777
|825
|-
|-
| |6
|6
|900
|900
|951.429
!930.041-949.541
|960
!940.909
| colspan="2" |990
!931.882-951.382
|994.737
! colspan="2" |942.857
| colspan="2" |1000
!935.581-958.86
|1005.882
!950-951.429
| colspan="2" |1012.5
!943.6495-963.727
|1020
! colspan="2" |960-964.286
| colspan="2" |1028.571
!959.004-981.911
|1050
!972-975
| |1080
!965.818-989.849
|979.832-999.332
|990
|-
|-
| |7
|7
|1050
|1050
|1110
!1085.048-1107.798
|1120
!1097.727
| colspan="2" |1155
!1087.196-1109.946
|1160.526
! colspan="2" |1100
| colspan="2" |1166.667
!1091.511-1118.67
|1173.529
!1108.333-1110
| colspan="2" |1081.25
!1100.924-1124.348
|1190
! colspan="2" |1120-1125
| colspan="2" |1200
!1118.838-1145.563
|1225
!1134-1137.5
| |1260
!1126.7875-1154.824
|}
Most harmonic tunings
{| class="wikitable"
|-
! rowspan="2" |Degrees
!Phrygian Mode (natural minor)
!Phrygian-Aeolian Mode (intermediate minor)
!Aeolian Mode (melodic/harmonic minor)
|-
!15/7±13¢
!11/5±13¢
!9/4±13¢
|-
| |1
|163.305-166.555
|169.0005-172.2505
|173.864-177.114
|-
| |2
|326.611-333.111
|338.001-344.501
|347.7275-354.2275
|-
| |3
|489.916-499.666
|507.002-516.752
|521.591-531.341
|-
| |4
|653.221-666.221
|676.002-689.002
|695.455-708.455
|-
| |5
|816.527-832.777
|845.003-861.253
|869.319-885.569
|-
| |6
|979.832-999.332
|1014.003-1033.503
|1043.1825-1062.6825
|-
| |7
|1143.1375-1165.8875
|1143.1375-1165.8875
|1183.004-1205.754
|1155
|1217.046-1239.796
|}Golden Tunings
Phrygian Mode (natural minor)
{| class="wikitable"
|-
!Degrees
! |Min-Med±13¢
!Min-Max±13¢
! |Med-Max±13¢
|-
| |1
|157.246-160.496
|157.911-161.161
|159.834-163.084
|-
| |2
|314.491-320.991
|315.822-322.322
|319.668-326.168
|-
| |3
|471.737-481.487
|473.734-483.484
|479.502-489.252
|-
| |4
|628.982-641.982
|631.645-644.645
|639.335-652.336
|-
| |5
|786.227-802.478
|789.556-805.806
|799.17-815.42
|-
| |6
|943.4735-962.9735
|947.467-966.967
|959.003-978.504
|-
| |7
|1100.719-1123.469
|1105.379-1128.129
|1118.838-1141.588
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! colspan="2"|Intense Phrygian  
! colspan="5" |Intense Phrygian
! colspan="2" |Intense Phrygian-Soft Aeolian
! colspan="5" |Intense Phrygian-Soft Aeolian
! colspan="2" |Soft Aeolian  
! colspan="6" |Soft Aeolian
|-
|-
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!Min-Med/Min-Max±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Med-Max±13¢
!11/5±13¢
!Maximum
|-
|-
| |1
|1
|165
|163.971-167.221
|163.971-167.221
|165.7895
|164.363-167.613
|164.363-167.613
| colspan="2" |166.667
|165.78-169.03
|165.78-169.03
|167.647
|166.271-169.521
|166.271-169.521
| colspan="2" |168.75
|168.065-171.315
|168.065-171.315
|170
|168.695-171.945
|168.695-171.945
|169.0005-172.2505
|171.429
|-
|-
| |2
|2
|330
|327.941-334.441
|327.941-334.441
|331.579
|328.726-335.226
|328.726-335.226
| colspan="2" |333.333
|331.561-338.061
|331.561-338.061
|335.294
|332.541-339.041
|332.541-339.041
| colspan="2" |337.5
|336.13-345.63
|336.13-345.63
|340
|337.39-343.895
|337.39-343.895
|338.001-344.501
|342.857
|-
|-
| |3
|3
|495
|491.912-501.662
|491.912-501.662
|497.368
|493.089-502.839
|493.089-502.839
| colspan="2" |500
|497.341-507.091
|497.341-507.091
|502.941
|498.812-508.562
|498.812-508.562
| colspan="2" |506.25
|504.195-513.945
|504.195-513.945
|510
|506.084-515.834
|506.084-515.834
|507.002-516.752
|514.286
|-
|-
| |4
|4
|660
|655.883-668.883
|655.883-668.883
|663.158
|657.4525-670.4525
|657.4525-670.4525
| colspan="2" |666.667
|663.121-676.121
|663.121-676.121
|670.588
|665.082-678.082
|665.082-678.082
| colspan="2" |675
|672.2605-685.2605
|672.2605-685.2605
|680
|674.779-687.779
|674.779-687.779
|676.002-689.002
|685.714
|-
|-
| |5
|5
|825
|819.8535-836.1035
|819.8535-836.1035
|828.947
|821.816-838.065
|821.816-838.065
| colspan="2" |833.333
|828.902-845.152
|828.902-845.152
|838.235
|831.353-847.603
|831.353-847.603
| colspan="2" |843.75
|840.362-856.567
|840.362-856.567
|850
|843.474-859.724
|843.474-859.724
|845.003-861.253
|857.143
|-
|-
| |6
|6
|990
|983.824-1003.324
|983.824-1003.324
|994.737
|986.178-1005.678
|986.178-1005.678
| colspan="2" |1000
|994.682-1014.182
|994.682-1014.182
|1005.882
|997.623-1017.123
|997.623-1017.123
| colspan="2" |1012.5
|1108.391-1027.891.
|1108.391-1027.891.
|1020
|1012.169-1031.669
|1012.169-1031.669
|1014.003-1033.503
|1028.571
|-
|-
| |7
|7
|1155
|1147.795-1170.545
|1147.795-1170.545
|1160.526
|1150.542-1173.292
|1150.542-1173.292
| colspan="2" |1166.667
|1160.4625-1183.2125
|1160.4625-1183.2125
|1173.529
|1163.894-1186.644
|1163.894-1186.644
| colspan="2" |1081.25
|1176.456-1199.206
|1176.456-1199.206
|1190
|1180.8635-1203.6135
|1180.8635-1203.6135
|}Aeolian Mode (melodic/harmonic minor)
|1183.004-1205.754
|1200
|}
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! colspan="5" |Aeolian
! colspan="6" |Intense Aeolian
|-
|-
!Degrees
!Minimum
!Min-Med±13¢
!Min-Med/Min-Max±13¢
!Min-Max±13¢
!Median
! |Med-Max±13¢
!Med-Max±13¢
!Maximum
!Minimum
!9/4±13¢
!Min-Med/Min-Max±13¢
!Median
!Med-Max±13¢
!Maximum
|-
|-
| |1
|1
|171.429
|171.04-174.29
|171.04-174.29
|172.429-175.679
!173.077
| |175.075-178.325
!171.879-175.129
| colspan="2" |175
|173.864-177.114
|175.075-178.325
!177.273
!176.246-179.496
|180
|-
|-
| |2
|2
|342.857
|342.081-348.581
|342.081-348.581
|344.857-351.357
!346.154
| |350.1495-356.3495
!343.7575-350.2575
| colspan="2" |350
|347.7275-354.2275
|350.1495-356.3495
!354.5455
!352.492-358.992
|360
|-
|-
| |3
|3
|514.286
|513.121-522.871
|513.121-522.871
|517.286-527.036
!519.231
| |525.224-536.974
!515.636-525.386
| colspan="2" |525
|521.591-531.341
|525.224-536.974
!531.818
!528.738-538.488
|540
|-
|-
| |4
|4
|684.661-697.161
|685.714
|689.7145-702.7145
|684.161-697.161
| |700.299-713.299
|692.308
|687.515-700.515
| colspan="2" |700
|695.455-708.455
|700.299-713.299
!709.091
|704.983-717.983
|720
|-
|-
| |5
|5
|857.143
|855.202-871.452
|855.202-871.452
|862.143-878.393
!865.385
| |875.374-891.624
!859.394-875.644
| colspan="2" |875
|869.319-885.569
|875.374-891.624
!886.364
!881.229-897.479
|900
|-
|-
| |6
|6
|1028.571
|1026.242-1045.742
|1026.242-1045.742
|1028.572-1054.072
!1038.4615
| |1050.448-1069.948
!1031.272-1050.772
| colspan="2" |1050
|1043.1825-1062.6825
|1050.448-1069.948
!1063.636
!1057.475-1076.975
|1080
|-
|-
| |7
|7
|1200
|1197.282-1220.032
|1197.282-1220.032
|1207-1229.75
!1211.5385
| |1225.523-1248.273
!1203.151-1225.901
| colspan="2" |1225
|1217.046-1239.796
|1225.523-1248.273
!1240.909
!1233.721-1256.471
|1260
|}
|}
[[Category:8-tone]]
[[Category:8-tone]]

Revision as of 19:40, 22 December 2018

This reformed minor mode is the neutral scale of the Napoli temperament family in Long Common Practice .

Intervals

Degrees Soft Phrygian Phrygian
Minimum Min-Med±13¢ Median Min-Max/Med-Max±13¢ Maximum Thirdtone Semitone
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 15/7±13¢ Maximum
1 150 155.007-158.257 156.818 155.314-158.564 157.143 155.93-159.81 158.333-158.571 157.275-160.621 160-160.714 159.833-163.652 162-162.5 160.97-164.975 163.305-166.555 165
2 300 310.014-316.514 313.636 310.627-317.127 314.286 311.86-319.62 316.667-317.143 314.55-321.242 320-321.429 319.668-327.304 324-325 321.939-329.95 326.611-333.111 330
3 450 465.021-474.771 470.4545 465.941-475.691 471.429 467.79-497.43 475-475.714 471.825-481.8635 480-482.143 479.502-490.955 486-487.5 482.909-494.925 489.916-499.666 495
4 600 620.0275-633.0275 627.273 621.253-634.253 628.571 623.7205-639.24 633.333-634.286 629.1-642.485 640-642.857 639.335-654.335 648-650 643.879-659.8995 653.224-666.221 660
5 750 775.034-791.284 784.091 778.568-792.818 785.714 779.651-799.05 791.667-792.857 786.375-803.106 800-803.571 799.17-818.259 810-812.5 804.848-8242.874 816.527-832.777 825
6 900 930.041-949.541 940.909 931.882-951.382 942.857 935.581-958.86 950-951.429 943.6495-963.727 960-964.286 959.004-981.911 972-975 965.818-989.849 979.832-999.332 990
7 1050 1085.048-1107.798 1097.727 1087.196-1109.946 1100 1091.511-1118.67 1108.333-1110 1100.924-1124.348 1120-1125 1118.838-1145.563 1134-1137.5 1126.7875-1154.824 1143.1375-1165.8875 1155
Degrees Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ 11/5±13¢ Maximum
1 165 163.971-167.221 165.7895 164.363-167.613 166.667 165.78-169.03 167.647 166.271-169.521 168.75 168.065-171.315 170 168.695-171.945 169.0005-172.2505 171.429
2 330 327.941-334.441 331.579 328.726-335.226 333.333 331.561-338.061 335.294 332.541-339.041 337.5 336.13-345.63 340 337.39-343.895 338.001-344.501 342.857
3 495 491.912-501.662 497.368 493.089-502.839 500 497.341-507.091 502.941 498.812-508.562 506.25 504.195-513.945 510 506.084-515.834 507.002-516.752 514.286
4 660 655.883-668.883 663.158 657.4525-670.4525 666.667 663.121-676.121 670.588 665.082-678.082 675 672.2605-685.2605 680 674.779-687.779 676.002-689.002 685.714
5 825 819.8535-836.1035 828.947 821.816-838.065 833.333 828.902-845.152 838.235 831.353-847.603 843.75 840.362-856.567 850 843.474-859.724 845.003-861.253 857.143
6 990 983.824-1003.324 994.737 986.178-1005.678 1000 994.682-1014.182 1005.882 997.623-1017.123 1012.5 1108.391-1027.891. 1020 1012.169-1031.669 1014.003-1033.503 1028.571
7 1155 1147.795-1170.545 1160.526 1150.542-1173.292 1166.667 1160.4625-1183.2125 1173.529 1163.894-1186.644 1081.25 1176.456-1199.206 1190 1180.8635-1203.6135 1183.004-1205.754 1200
Degrees Aeolian Intense Aeolian
Minimum Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum Minimum 9/4±13¢ Min-Med/Min-Max±13¢ Median Med-Max±13¢ Maximum
1 171.429 171.04-174.29 173.077 171.879-175.129 175 173.864-177.114 175.075-178.325 177.273 176.246-179.496 180
2 342.857 342.081-348.581 346.154 343.7575-350.2575 350 347.7275-354.2275 350.1495-356.3495 354.5455 352.492-358.992 360
3 514.286 513.121-522.871 519.231 515.636-525.386 525 521.591-531.341 525.224-536.974 531.818 528.738-538.488 540
4 685.714 684.161-697.161 692.308 687.515-700.515 700 695.455-708.455 700.299-713.299 709.091 704.983-717.983 720
5 857.143 855.202-871.452 865.385 859.394-875.644 875 869.319-885.569 875.374-891.624 886.364 881.229-897.479 900
6 1028.571 1026.242-1045.742 1038.4615 1031.272-1050.772 1050 1043.1825-1062.6825 1050.448-1069.948 1063.636 1057.475-1076.975 1080
7 1200 1197.282-1220.032 1211.5385 1203.151-1225.901 1225 1217.046-1239.796 1225.523-1248.273 1240.909 1233.721-1256.471 1260
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