User:Moremajorthanmajor/8edIX: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
No edit summary
No edit summary
Line 4: Line 4:


{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="3" |Degrees
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="4" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="3" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="9" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
! colspan="3" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
!Absolute Minimum
! rowspan="2" |Absolute Minimum
! |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" |Median
!  rowspan="2"|Maximum
|-
!Minimum
!Median
!Median
! |Maximum
!Maximum
! |Minimum
!Minimum
!Median
!Median
! |Maximum
!Maximum
!Minimum
!Minimum
!Median
!Median
! |Maximum
!Maximum
|-
|-
| |1
| |1
Line 25: Line 35:
|160
|160
| colspan="2" |165
| colspan="2" |165
|165.7895
| colspan="2" |166.667
|167.647
|167.647
| colspan="2" |168.75
|170
| colspan="2" |171.429
| colspan="2" |171.429
|175
|175
Line 35: Line 49:
|320
|320
| colspan="2" |330
| colspan="2" |330
|331.579
| colspan="2" |333.333
|335.294
|335.294
| colspan="2" |337.5
|340
| colspan="2" |342.857
| colspan="2" |342.857
|350
|350
Line 45: Line 63:
|480
|480
| colspan="2" |495
| colspan="2" |495
|497.368
| colspan="2" |500
|502.941
|502.941
| colspan="2" |506.25
|510
| colspan="2" |514.286
| colspan="2" |514.286
|525
|525
Line 55: Line 77:
|640
|640
| colspan="2" |660
| colspan="2" |660
|663.158
| colspan="2" |666.667
|670.588
|670.588
| colspan="2" |675
|680
| colspan="2" |685.714
| colspan="2" |685.714
|700
|700
Line 65: Line 91:
|800
|800
| colspan="2" |825
| colspan="2" |825
|828.947
| colspan="2" |833.333
|838.235
|838.235
| colspan="2" |843.75
|850
| colspan="2" |857.143
| colspan="2" |857.143
|875
|875
Line 75: Line 105:
|960
|960
| colspan="2" |990
| colspan="2" |990
|994.737
| colspan="2" |1000
|1005.882
|1005.882
| colspan="2" |1012.5
|1020
| colspan="2" |1028.571
| colspan="2" |1028.571
|1050
|1050
Line 85: Line 119:
|1120
|1120
| colspan="2" |1155
| colspan="2" |1155
|1160.526
| colspan="2" |1166.667
|1173.529
|1173.529
| colspan="2" |1081.25
|1190
| colspan="2" |1200
| colspan="2" |1200
|1225
|1225
Line 141: Line 179:
|-
|-
!Degrees
!Degrees
!Min-Med-13c
! |Min-Med±13¢
!Min-Max-13c
!Min-Max±13¢
!Min-Med
! |Med-Max±13¢
!Min-Max
!Med-Max-13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
|157.246
|157.246-160.496
|157.911
|157.911-161.161
|158.871
|159.834-163.084
| |159.536
|159.834
|160.496
|161.161
|161.469
|163.084
|-
|-
| |2
| |2
|314.491
|314.491-320.991
|315.822
|315.822-322.322
|317.741
|319.668-326.168
| |319.0725
|319.668
|320.991
|322.322
|322.938
|326.168
|-
|-
| |3
| |3
|471.737
|471.737-481.487
|473.734
|473.734-483.484
|476.612
|479.502-489.252
| |478.609
|479.502
|481.487
|483.484
|484.407
|489.252
|-
|-
| |4
| |4
|628.982
|628.982-641.982
|631.645
|631.645-644.645
|635.482
|639.335-652.336
| |638.145
|639.335
|641.982
|644.645
|645.876
|652.336
|-
|-
| |5
| |5
|786.227
|786.227-802.478
|789.556
|789.556-805.806
|794.353
|799.17-815.42
| |797.681
|799.17
|802.478
|805.806
|807.345
|815.42
|-
|-
| |6
| |6
|943.4735
|943.4735-962.9735
|947.467
|947.467-966.967
|953.2235
|959.003-978.504
| |957.317
|959.003
|962.9735
|966.967
|968.814
|978.504
|-
|-
| |7
| |7
|1100.719
|1100.719-1123.469
|1105.379
|1105.379-1128.129
|1112.094
|1118.838-1141.588
| |1116.754
|1118.838
|1123.469
|1128.129
|1130.263
|1141.588
|}
|}
Phrygian-Aeolian Mode (intermediate minor)
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
! rowspan="2" |Degrees
!Min-Med/Min-Max-13c
!  colspan="2"|Intense Phrygian
!Med-Max-13c
! colspan="2" |Intense Phrygian-Soft Aeolian
!Min-Med/Min-Max
! colspan="2" |Soft Aeolian
!Med-Max
|-
!Min-Med/Min-Max+13c
!Min-Med/Min-Max±13¢
!Med-Max+13c
!Med-Max±13¢
!Min-Med-13c (Aeolian)
!Min-Med/Min-Max±13¢
!Med-Max±13¢
!Min-Med/Min-Max±13¢
!Med-Max±13¢
|-
|-
| |1
| |1
|165.316
|163.971-167.221
|166.789
|164.363-167.613
|166.941
|165.78-169.03
|168.414
|166.271-169.521
|168.566
|168.065-171.315
|170.039
|168.695-171.945
|171.04
|-
|-
| |2
| |2
|330.633
|327.941-334.441
|333.578
|328.726-335.226
|333.883
|331.561-338.061
|336.828
|332.541-339.041
|337.133
|336.13-345.63
|340.078
|337.39-343.895
|342.081
|-
|-
| |3
| |3
|495.949
|491.912-501.662
|500.3675
|493.089-502.839
|500.824
|497.341-507.091
|505.2425
|498.812-508.562
|505.699
|504.195-513.945
|510.1175
|506.084-515.834
|513.121
|-
|-
| |4
| |4
|661.265
|655.883-668.883
|667.157
|657.4525-670.4525
|667.765
|663.121-676.121
|673.658
|665.082-678.082
|674.265
|672.2605-685.2605
|680.157
|674.779-687.779
|684.161
|-
|-
| |5
| |5
|826.5815
|819.8535-836.1035
|833.946
|821.816-838.065
|834.7065
|828.902-845.152
|842.071
|831.353-847.603
|842.8315
|840.362-856.567
|850.196
|843.474-859.724
|855.202
|-
|-
| |6
| |6
|991.898
|983.824-1003.324
|1000.735
|986.178-1005.678
|1000.648
|994.682-1014.182
|1010.485
|997.623-1017.123
|1011.398
|1108.391-1027.891.
|1020.235
|1012.169-1031.669
|1026.242
|-
|-
| |7
| |7
|1157.241
|1147.795-1170.545
|1167.524
|1150.542-1173.292
|1168.589
|1160.4625-1183.2125
|1178.899
|1163.894-1186.644
|1179.964
|1176.456-1199.206
|1190.274
|1180.8635-1203.6135
|1197.282
|}Aeolian Mode (melodic/harmonic minor)
|}Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
{| class="wikitable"
|-
|-
!Degrees
!Degrees
!Min-Med-13c
!Min-Med±13¢
!Min-Med
!Min-Max±13¢
!Min-Max
! |Med-Max±13¢
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
|-
| |1
| |1
|172.429
|171.04-174.29
|172.665
|172.429-175.679
| |174.054
| |175.075-178.325
|174.29
|175.075
|175.679
|176.7
|178.325
|-
|-
| |2
| |2
|344.857
|342.081-348.581
|345.331
|344.857-351.357
| |348.107
| |350.1495-356.3495
|348.581
|350.1495
|351.357
|353.3995
|356.3495
|-
|-
| |3
| |3
|517.286
|513.121-522.871
|517.996
|517.286-527.036
| |522.161
| |525.224-536.974
|522.871
|525.224
|527.036
|530.099
|536.974
|-
|-
| |4
| |4
|689.7145
|684.661-697.161
|690.661
|689.7145-702.7145
| |696.2145
| |700.299-713.299
|697.161
|700.299
|702.7145
|706.799
|713.299
|-
|-
| |5
| |5
|862.143
|855.202-871.452
|863.367
|862.143-878.393
| |870.268
| |875.374-891.624
|871.452
|875.374
|878.393
|883.499
|891.624
|-
|-
| |6
| |6
|1034.572
|1026.242-1045.742
|1035.992
|1028.572-1054.072
| |1044.321
| |1050.448-1069.948
|1045.742
|1050.448
|1054.072
|1060.198
|1069.498
|-
|-
| |7
| |7
|1207
|1197.282-1220.032
|1208.657
|1207-1229.75
| |1218.375
| |1225.523-1248.273
|1220.032
|1225.523
|1229.75
|1236.898
|1248.273
|}
|}
[[Category:8-tone]]
[[Category:8-tone]]
[[Category:ed9/4]]
[[Category:ed9/4]]

Revision as of 21:08, 23 November 2018

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

Intervals

Degrees Phrygian Mode (aka Double) Neapolitan Temperament (natural minor) Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor) Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
Absolute Minimum Minimum Median Maximum Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian Minimum Median Maximum
Minimum Median Maximum Minimum Median Maximum Minimum Median Maximum
1 150 158.571 160 165 165.7895 166.667 167.647 168.75 170 171.429 175 180
2 300 317.143 320 330 331.579 333.333 335.294 337.5 340 342.857 350 360
3 450 475.714 480 495 497.368 500 502.941 506.25 510 514.286 525 540
4 600 634.286 640 660 663.158 666.667 670.588 675 680 685.714 700 720
5 750 792.857 800 825 828.947 833.333 838.235 843.75 850 857.143 875 900
6 900 951.429 960 990 994.737 1000 1005.882 1012.5 1020 1028.571 1050 1080
7 1050 1110 1120 1155 1160.526 1166.667 1173.529 1081.25 1190 1200 1225 1260

Most harmonic tunings

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 1183.004-1205.754 1217.046-1239.796

Golden Tunings

Phrygian Mode (natural minor)

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)

Degrees Intense Phrygian Intense Phrygian-Soft Aeolian Soft Aeolian
Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢ Min-Med/Min-Max±13¢ Med-Max±13¢
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

Aeolian Mode (melodic/harmonic minor)

Degrees Min-Med±13¢ Min-Max±13¢ Med-Max±13¢
1 171.04-174.29 172.429-175.679 175.075-178.325
2 342.081-348.581 344.857-351.357 350.1495-356.3495
3 513.121-522.871 517.286-527.036 525.224-536.974
4 684.661-697.161 689.7145-702.7145 700.299-713.299
5 855.202-871.452 862.143-878.393 875.374-891.624
6 1026.242-1045.742 1028.572-1054.072 1050.448-1069.948
7 1197.282-1220.032 1207-1229.75 1225.523-1248.273
Retrieved from "https://en.xen.wiki/index.php?title=User:Moremajorthanmajor/8edIX&oldid=38578"