User:Moremajorthanmajor/13edIX: Difference between revisions

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Line 162: Line 162:
|1440
|1440
|}
|}
Golden Tunings
Most harmonic tunings
{| class="wikitable"
{| class="wikitable"
|-
|-
! rowspan="2" |Degrees
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! rowspan="2" |Octatonic
! colspan="9" |Phrygian Mode (natural minor)
!Phrygian Mode (natural minor)
! colspan="7" |Phrygian-Aeolian Mode (intermediate minor)
!Phrygian-Aeolian Mode (intermediate minor)
! colspan="8" |Aeolian Mode (melodic/harmonic minor)
!Aeolian Mode (melodic/harmonic minor)
|-
|-
!15/7±13¢
!11/5±13¢
!9/4±13¢
|-
| |1
| |F#/Gb
|100.496-102.496
|104-106
|106.993-108.993
|-
| |2
| |G
|200.991-204.912
|208.001-212.001
|213.986-217.986
|-
| |3
| |G#/Ab
|301.487-307.487
|312.001-318.001
|320.979-326.979
|-
| |4
| |A
|401.982-409.982
|416.001-424.001
|427.972-435.972
|-
| |5
| |B
|502.478-512.478
|520.002-530.002
|534.965-544.965
|-
| |6
| |B#/Hb
|602.974-614.974
|624.002-636.002
|641.9585-653.9585
|-
| |7
| |H
|703.469-717.469
|728.002-742.0022
|748.9515-762.9515
|-
| |8
| |C
|803.965-819.965
|832.003-848.002
|855.945-871.945
|-
| |9
| |C#/Db
|904.46-922.46
|936.003-924.003
|962.938-980.938
|-
| |10
| |D
|1004.956-1024.956
|1040.003-1060.003
|1069.931-1089.931
|-
| |11
| |D#/Eb
|1105.452-1127.452
|1144.004-1166.004
|1177-924-1199.924
|-
| |12
| |E
|1205.947-1299.947
|1248.004-1272.004
|1283.917-1307.917
|-
| |13
| |F
|1306.443-1332.443
|1352.004-1378.004
|1390.91-1416.91
|}
Golden Tunings
Phrygian Mode (natural minor)
{| class="wikitable"
|-
!Degrees
!Octatonic
!Min-Med-13c
!Min-Med-13c
!Min-Max-13c
!Min-Max-13c
Line 177: Line 266:
!Med-Max-13c
!Med-Max-13c
!Min-Med+13c
!Min-Med+13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
!Min-Med/Min-Max-13c
!Med-Max-13c
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
!Min-Max-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Min-Max+13c
!Med-Max
!Med-Max
Line 207: Line 281:
|99.359
|99.359
|100.359
|100.359
|101.733
|102.639
|102.733
|103.639
|103.733
|104.639
|105.256
|106.11
|106.256
|107.11
|107.256
|107.738
|108.11
|108.738
|109.738
|-
|-
| |2
| |2
Line 234: Line 293:
|198.719
|198.719
|200.719
|200.719
|203.466
|205.279
|205.466
|207.279
|207.466
|205.279
|210.511
|212.22
|212.511
|214.22
|214.511
|215.477
|216.22
|217.477
|219.477
|-
|-
| |3
| |3
Line 261: Line 305:
|298.078
|298.078
|301.078
|301.078
|305.199
|311.9185
|308.199
|310.9185
|311.199
|313.9185
|315.767
|318.33
|318.767
|321.33
|321.767
|323.215
|324.33
|326.215
|329.215
|-
|-
| |4
| |4
Line 288: Line 317:
|397.4375
|397.4375
|401.4375
|401.4375
|406.932
|410.558
|410.932
|414.558
|414.932
|418.558
|421.022
|424.44
|425.022
|428.44
|429.022
|430.953
|432.44
|434.953
|438.953
|-
|-
| |5
| |5
Line 315: Line 329:
|496.797
|496.797
|501.797
|501.797
|508.6655
|513.1975
|513.6655
|518.1975
|518.6655
|523.1975
|526.278
|530.55
|531.278
|535.55
|536.278
|538.6915
|540.55
|543.6915
|548.6915
|-
|-
| |6
| |6
Line 342: Line 341:
|596.156
|596.156
|602.156
|602.156
|610.399
|615.837
|616.399
|621.837
|622.399
|627.837
|631.534
|636.6595
|637.534
|642.6595
|643.534
|646.43
|648.6595
|652.43
|658.43
|-
|-
| |7
| |7
Line 369: Line 353:
|695.516
|695.516
|702.516
|702.516
|712.132
|718.4765
|719.132
|725.4765
|726.132
|732.4765
|736.789
|742.769
|743.789
|749.769
|750.789
|754.168
|756.769
|761.168
|768.168
|-
|-
| |8
| |8
Line 396: Line 365:
|794.875
|794.875
|802.875
|802.875
|813.865
|821.116
|821.865
|829.116
|829.865
|837.116
|842.045
|848.879
|850.045
|856.879
|858.045
|861.906
|864.879
|869.906
|877.906
|-
|-
| |9
| |9
Line 423: Line 377:
|894.234
|894.234
|903.234
|903.234
|915.598
|923.755
|924.598
|932.755
|933.598
|941.755
|947.3
|954.989
|956.3
|963.989
|965.3
|969.645
|972.989
|978.645
|986.645
|-
|-
| |10
| |10
Line 450: Line 389:
|993.594
|993.594
|1003.594
|1003.594
|1017.331
|1026.395
|1027.331
|1036.395
|1037.331
|1046.395
|1052.556
|1061.099
|1062.556
|1071.099
|1072.556
|1077.383
|1081.099
|1087.383
|1077.383
|-
|-
| |11
| |11
Line 477: Line 401:
|1092.953
|1092.953
|1103.953
|1103.953
|1119.064
|1129.034
|1130.064
|1140.034
|1141.064
|1151.034
|1157.8115
|1167.209
|1168.8115
|1178.209
|1179.8115
|1185.121
|1189.209
|1196.121
|1207.121
|-
|-
| |12
| |12
Line 504: Line 413:
|1192.312
|1192.312
|1204.312
|1204.312
|1220.797
|1231.674
|1232.797
|1243.674
|1244.797
|1255.674
|1264.067
|1273.319
|1275.067
|1285.319
|1287.067
|1392.86
|1297.319
|1304.86
|1317.86
|-
|-
| |13
| |13
Line 531: Line 425:
|1291.672
|1291.672
|1304.672
|1304.672
|}
Phrygian-Aeolian Mode (intermediate minor)
{| class="wikitable"
|-
!Degrees
!Octatonic
!Min-Med/Min-Max-13c
!Med-Max-13c
!Min-Med/Min-Max
!Med-Max
!Min-Med/Min-Max+13c
!Med-Max+13c
!Min-Med-13c (Aeolian)
|-
| |1
| |F#/Gb
|101.733
|102.639
|102.733
|103.639
|103.733
|104.639
|105.256
|-
| |2
| |G
|203.466
|205.279
|205.466
|207.279
|207.466
|205.279
|210.511
|-
| |3
| |G#/Ab
|305.199
|311.9185
|308.199
|310.9185
|311.199
|313.9185
|315.767
|-
| |4
| |A
|406.932
|410.558
|410.932
|414.558
|414.932
|418.558
|421.022
|-
| |5
| |B
|508.6655
|513.1975
|513.6655
|518.1975
|518.6655
|523.1975
|526.278
|-
| |6
| |B#/Hb
|610.399
|615.837
|616.399
|621.837
|622.399
|627.837
|631.534
|-
| |7
| |H
|712.132
|718.4765
|719.132
|725.4765
|726.132
|732.4765
|736.789
|-
| |8
| |C
|813.865
|821.116
|821.865
|829.116
|829.865
|837.116
|842.045
|-
| |9
| |C#/Db
|915.598
|923.755
|924.598
|932.755
|933.598
|941.755
|947.3
|-
| |10
| |D
|1017.331
|1026.395
|1027.331
|1036.395
|1037.331
|1046.395
|1052.556
|-
| |11
| |D#/Eb
|1119.064
|1129.034
|1130.064
|1140.034
|1141.064
|1151.034
|1157.8115
|-
| |12
| |E
|1220.797
|1231.674
|1232.797
|1243.674
|1244.797
|1255.674
|1264.067
|-
| |13
| |F
|1322.53
|1322.53
|1334.313
|1334.313
Line 538: Line 568:
|1360.313
|1360.313
|1368.322
|1368.322
|}
Aeolian Mode (melodic/harmonic minor)
{| class="wikitable"
|-
!Degrees
!Octatonic
!Min-Max-13c
!Min-Med
!Min-Max
!Min-Med+13c
!Med-Max-13c
!Min-Max+13c
!Med-Max
!Med-Max+13c
|-
| |1
| |F#/Gb
|106.11
|106.256
|107.11
|107.256
|107.738
|108.11
|108.738
|109.738
|-
| |2
| |G
|212.22
|212.511
|214.22
|214.511
|215.477
|216.22
|217.477
|219.477
|-
| |3
| |G#/Ab
|318.33
|318.767
|321.33
|321.767
|323.215
|324.33
|326.215
|329.215
|-
| |4
| |A
|424.44
|425.022
|428.44
|429.022
|430.953
|432.44
|434.953
|438.953
|-
| |5
| |B
|530.55
|531.278
|535.55
|536.278
|538.6915
|540.55
|543.6915
|548.6915
|-
| |6
| |B#/Hb
|636.6595
|637.534
|642.6595
|643.534
|646.43
|648.6595
|652.43
|658.43
|-
| |7
| |H
|742.769
|743.789
|749.769
|750.789
|754.168
|756.769
|761.168
|768.168
|-
| |8
| |C
|848.879
|850.045
|856.879
|858.045
|861.906
|864.879
|869.906
|877.906
|-
| |9
| |C#/Db
|954.989
|956.3
|963.989
|965.3
|969.645
|972.989
|978.645
|986.645
|-
| |10
| |D
|1061.099
|1062.556
|1071.099
|1072.556
|1077.383
|1081.099
|1087.383
|1077.383
|-
| |11
| |D#/Eb
|1167.209
|1168.8115
|1178.209
|1179.8115
|1185.121
|1189.209
|1196.121
|1207.121
|-
| |12
| |E
|1273.319
|1275.067
|1285.319
|1287.067
|1392.86
|1297.319
|1304.86
|1317.86
|-
| |13
| |F
|1379.429
|1379.429
|1381.322
|1381.322

Revision as of 15:27, 5 November 2018

This scale, a Long Common Practice minor mode, occurs in 12edo; where it is the equal division of the minor ninth. It has the Grandfather 5L 3s MOS with a 2:1 ratio of large against small.

Intervals

Degrees Octatonic 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 Minimum Median Maximum Minimum Median Maximum
1 F#/Gb 92.308 97.582 98.4615 101.5385 103.167 105.4945 107.692 110.769
2 G 184.615 195.165 196.923 203.077 206.335 210.989 215.385 221.5385
3 G#/Ab 276.923 292.747 295.385 304.615 309.502 316.4835 323.077 332.308
4 A 369.231 390.33 393.846 406.154 412.67 421.978 430.769 443.076
5 B 461.5385 487.912 491.308 507.692 515.837 527.4725 538.4615 553.846
6 B#/Hb 553.846 585.4945 589.769 609.231 619.0045 632.967 646.154 664.615
7 H 646.154 683.077 690.231 710.769 722.172 738.4615 754.846 775.385
8 C 738.4615 780.66 788.692 812.308 825.339 843.856 861.5385 886.154
9 C#/Db 830.769 878.242 896.154 913.846 929.507 949.4505 969.231 996.923
10 D 923.077 975.824 984.615 1015.385 1031.674 1054.945 1076.923 1107.692
11 D#/Eb 1015.385 1073.407 1083.077 1116.923 1134.842 1160.44 1184.615 1218.4615
12 E 1107.692 1170.99 1181.5385 1218.4615 1238.009 1265.9348 1292.308 1329.231
13 F 1200 1268.571 1280 1320 1341.1765 1371.429 1400 1440

Most harmonic tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
15/7±13¢ 11/5±13¢ 9/4±13¢
1 F#/Gb 100.496-102.496 104-106 106.993-108.993
2 G 200.991-204.912 208.001-212.001 213.986-217.986
3 G#/Ab 301.487-307.487 312.001-318.001 320.979-326.979
4 A 401.982-409.982 416.001-424.001 427.972-435.972
5 B 502.478-512.478 520.002-530.002 534.965-544.965
6 B#/Hb 602.974-614.974 624.002-636.002 641.9585-653.9585
7 H 703.469-717.469 728.002-742.0022 748.9515-762.9515
8 C 803.965-819.965 832.003-848.002 855.945-871.945
9 C#/Db 904.46-922.46 936.003-924.003 962.938-980.938
10 D 1004.956-1024.956 1040.003-1060.003 1069.931-1089.931
11 D#/Eb 1105.452-1127.452 1144.004-1166.004 1177-924-1199.924
12 E 1205.947-1299.947 1248.004-1272.004 1283.917-1307.917
13 F 1306.443-1332.443 1352.004-1378.004 1390.91-1416.91

Golden Tunings

Phrygian Mode (natural minor)

Degrees Octatonic Min-Med-13c Min-Max-13c Min-Med Min-Max Med-Max-13c Min-Med+13c Min-Max+13c Med-Max Med-Max+13c
1 F#/Gb 96.7665 97.176 97.7665 98.176 98.359 98.7665 99.176 99.359 100.359
2 G 193.533 194.352 195.533 196.352 196.719 197.533 198.352 198.719 200.719
3 G#/Ab 291.2995 291.528 293.2995 294.528 295.078 296.2995 297.528 298.078 301.078
4 A 388.063 389.705 391.063 392.705 393.4375 394.063 396.705 397.4375 401.4375
5 B 484.833 486.881 488.833 490.881 492.797 492.833 495.881 496.797 501.797
6 B#/Hb 581.299 583.057 586.299 589.057 591.156 591.299 595.057 596.156 602.156
7 H 678.366 681.233 684.366 687.233 689.516 690.366 694.233 695.516 702.516
8 C 775.132 778.409 782.132 785.409 787.875 789.132 793.409 794.875 802.875
9 C#/Db 871.899 874.585 879.899 883.585 886.234 888.899 891.585 894.234 903.234
10 D 967.665 971.761 977.665 981.761 984.594 987.665 991.761 993.594 1003.594
11 D#/Eb 1067.432 1068.9375 1075.432 1079.9375 1082.953 1086.432 1091.9375 1092.953 1103.953
12 E 1162.198 1166.114 1173.198 1178.114 1181.312 1185.198 1190.114 1192.312 1204.312
13 F 1257.965 1263.29 1270.965 1276.29 1278.672 1283.965 1289.29 1291.672 1304.672

Phrygian-Aeolian Mode (intermediate minor)

Degrees Octatonic Min-Med/Min-Max-13c Med-Max-13c Min-Med/Min-Max Med-Max Min-Med/Min-Max+13c Med-Max+13c Min-Med-13c (Aeolian)
1 F#/Gb 101.733 102.639 102.733 103.639 103.733 104.639 105.256
2 G 203.466 205.279 205.466 207.279 207.466 205.279 210.511
3 G#/Ab 305.199 311.9185 308.199 310.9185 311.199 313.9185 315.767
4 A 406.932 410.558 410.932 414.558 414.932 418.558 421.022
5 B 508.6655 513.1975 513.6655 518.1975 518.6655 523.1975 526.278
6 B#/Hb 610.399 615.837 616.399 621.837 622.399 627.837 631.534
7 H 712.132 718.4765 719.132 725.4765 726.132 732.4765 736.789
8 C 813.865 821.116 821.865 829.116 829.865 837.116 842.045
9 C#/Db 915.598 923.755 924.598 932.755 933.598 941.755 947.3
10 D 1017.331 1026.395 1027.331 1036.395 1037.331 1046.395 1052.556
11 D#/Eb 1119.064 1129.034 1130.064 1140.034 1141.064 1151.034 1157.8115
12 E 1220.797 1231.674 1232.797 1243.674 1244.797 1255.674 1264.067
13 F 1322.53 1334.313 1335.53 1347.313 1348.53 1360.313 1368.322

Aeolian Mode (melodic/harmonic minor)

Degrees Octatonic Min-Max-13c Min-Med Min-Max Min-Med+13c Med-Max-13c Min-Max+13c Med-Max Med-Max+13c
1 F#/Gb 106.11 106.256 107.11 107.256 107.738 108.11 108.738 109.738
2 G 212.22 212.511 214.22 214.511 215.477 216.22 217.477 219.477
3 G#/Ab 318.33 318.767 321.33 321.767 323.215 324.33 326.215 329.215
4 A 424.44 425.022 428.44 429.022 430.953 432.44 434.953 438.953
5 B 530.55 531.278 535.55 536.278 538.6915 540.55 543.6915 548.6915
6 B#/Hb 636.6595 637.534 642.6595 643.534 646.43 648.6595 652.43 658.43
7 H 742.769 743.789 749.769 750.789 754.168 756.769 761.168 768.168
8 C 848.879 850.045 856.879 858.045 861.906 864.879 869.906 877.906
9 C#/Db 954.989 956.3 963.989 965.3 969.645 972.989 978.645 986.645
10 D 1061.099 1062.556 1071.099 1072.556 1077.383 1081.099 1087.383 1077.383
11 D#/Eb 1167.209 1168.8115 1178.209 1179.8115 1185.121 1189.209 1196.121 1207.121
12 E 1273.319 1275.067 1285.319 1287.067 1392.86 1297.319 1304.86 1317.86
13 F 1379.429 1381.322 1392.429 1394.322 1400.598 1405.429 1413.598 1426.598
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