User:Moremajorthanmajor/17edIX: Difference between revisions

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==Intervals==
==Intervals==
{| class="wikitable"
{| class="wikitable"
! rowspan="2" |Degrees
! rowspan="2" |Octatonic
! colspan="3" |Phrygian Mode (aka Double) Neapolitan Temperament (natural minor)
! colspan="2" |Phrygian-Aeolian Mode Neapolitan Temperament (intermediate minor)
! colspan="2" |Aeolian Mode Neapolitan Temperament (melodic/harmonic minor)
|-
|-
! | Degrees
!Absolute Minimum
! | Octatonic
!Minimum
! | Minimum
!Maximum
! | Golden
! |Minimum
! | Median
!Maximum
! | Mean
!Minimum
! | ed(9/4)
!Maximum
! | Maximum
|-
|-
| | 1
| |1
| | D
| |Gb
| | 75.294
|70.588
| | 76.902
|73.412
| | 77.647
| colspan="2" |77.647
| | 80
| colspan="2" |80.672
| | 82.583
|84.706
| | 84.706
|-
|-
| | 2
| |2
| | Eb
| |F#v/Gb^
| | 150.588
|141.1765
| | 153.804
|146.8235
| | 155.294
| colspan="2" |155.294
| | 160
| colspan="2" |161.3445
| | 165.166
|169.412
| | 169.412
|-
|-
| | 3
| |3
| | Eb^/D#v
| |F#
| | 225.882
|211.765
| | 230.7055
|220.235
| | 232.941
| colspan="2" |232.941
| | 240
| colspan="2" |242.017
| | 247.749
|254.118
| | 254.118
|-
|-
| | 4
| |4
| | D#
| |G
| | 301.1765
|282.353
| | 307.607
|293.647
| | 310.588
| colspan="2" |310.588
| | 320
| colspan="2" |322.689
| | 330.332
|338.8235
| | 338.8235
|-
|-
| | 5
| |5
| | E
| |A
| | 376.471
|352.941
| | 384.509
|367.059
| | 387.235
| colspan="2" |387.235
| | 400
| colspan="2" |403.361
| | 412.915
|423.529
| | 423.529
|-
|-
| | 6
| |6
| | F
| |B
| | 451.765
|423.529
| | 461.411
|440.471
| | 464.822
| colspan="2" |464.822
| | 480
| colspan="2" |484.034
| | 495.498
|508.235
| | 508.235
|-
|-
| | 7
| |7
| | Gb
| |Hb
| | 527.059
|494.118
| | 538.313
|513.882
| | 542.529
| colspan="2" |542.529
| | 560
|564.706
| | 578.080'5
|
| | 592.941
|592.941
|-
|-
| | 8
| |8
| | Gb^/F#v
| |B#v/Hb^
| | 602.353
|564.706
| | 615.215
|587.294
| | 620.1765
| colspan="2" |620.1765
| | 640
| colspan="2" |645.378
| | 660.663'5
|677.647
| | 677.647
|-
|-
| | 9
| |9
| | F#
| |B#
| | 677.647
|635.294
| | 692.117
|660.706
| | 697.8235
| colspan="2" |697.8235
| | 720
| colspan="2" |726.05
| | 743.246'5
|762.653
| | 762.653
|-
|-
| | 10
| |10
| | G
| |H
| | 752.941
|705.882
| | 769.018
|734.118
| | 777.471
| colspan="2" |777.471
| | 800
| colspan="2" |806.723
| | 825.829
|847.059
| | 847.059
|-
|-
| | 11
| |11
| | H
| |C
| | 828.235
|776.471
| | 845.92
|807.526
| | 855.118
| colspan="2" |855.118
| | 880
| colspan="2" |887.395
| | 908.412
|931.765
| | 931.765
|-
|-
| | 12
| |12
| | A
| |D
| | 903.529
|847.059
| | 922.822
|880.841
| | 932.765
| colspan="2" |932.765
| | 960
| colspan="2" |968.067
| | 990.995
|1016.471
| | 1016.471
|-
|-
| | 13
| |13
| | Bb
| |Eb
| | 978.8235
|917.647
| | 999.724
|954.352
| | 1010.412
| colspan="2" |1010.412
| | 1040
| colspan="2" |1048.7395
| | 1073.578
|1101.1765
| | 1101.1765
|-
|-
| | 14
|14
| | Bb^/A#v
|D#v/Eb^
| | 1055.118
|988.235
| | 1076.626
|1027.765
| | 1088.059
| colspan="2" |1088.059
| | 1120
| colspan="2" |1129.412
| | 1156.161
|1185.882
| | 1185.882
|-
|-
| | 15
|15
| | A#
|D#
| | 1130.412
|1058.8235
| | 1153.528
|1101.1765
| | 1164.706
| colspan="2" |1164.706
| | 1200
| colspan="2" |1210.084
| | 1238.744
|1270.588
| | 1270.588
|-
|-
| | 16
|16
| | B
|E
| | 1204.706
|1129.412
| | 1230.429
|1174.588
| | 1242.353
| colspan="2" |1242.353
| | 1280
| colspan="2" |1290.756
| | 1321.327
|1355.294
| | 1355.294
|-
|-
| | 17
|17
| | C
|F
| | 1280
|1200
| | 1307.331
|1248
| | 1320
| colspan="2" |1320
| | 1360
| colspan="2" |1371.429
| | 1403.91
|1440
| | 1440
|}Golden Tunings
{| class="wikitable"
|-
!Degrees
!Octatonic
!Phrygian Mode (natural minor)
!Phrygian-Aeolian Mode (intermediate minor)
!Aeolian Mode (melodic/harmonic minor)
|-
| |1
| |Gb
|74.251
|78.561
|81.908
|-
| |2
| |F#v/Gb^
|148.5025
|157.121
|163.815
|-
| |3
| |F#
|222.754
|235.982
|245.723
|-
| |4
| |G
|297.005
|314.242
|327.63
|-
| |5
| |A
|371.256
|392.803
|409.538
|-
| |6
| |B
|445.5075
|471.264
|491.4455
|-
| |7
| |Hb
|519.759
|549.924
|573.353
|-
| |8
| |B#v/Hb^
|594.01
|628.485
|655.261
|-
| |9
| |B#
|668.261
|707.0455
|737.168
|-
| |10
| |H
|742.5125
|785.606
|819.076
|-
| |11
| |C
|816.764
|864.168
|900.983
|-
| |12
| |D
|891.015
|942.727
|982.891
|-
| |13
| |Eb
|965.266
|1021.288
|1064.799
|-
|14
|D#v/Eb^
|1039.518
|1099.849
|1146.706
|-
|15
|D#
|1113.769
|1178.409
|1228.614
|-
|16
|E
|1188.02
|1256.97
|1310.521
|-
|17
|F
|1262.271
|1335.53
|1392.429
|}
|}

Revision as of 23:11, 21 October 2018

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 Maximum Minimum Maximum Minimum Maximum
1 Gb 70.588 73.412 77.647 80.672 84.706
2 F#v/Gb^ 141.1765 146.8235 155.294 161.3445 169.412
3 F# 211.765 220.235 232.941 242.017 254.118
4 G 282.353 293.647 310.588 322.689 338.8235
5 A 352.941 367.059 387.235 403.361 423.529
6 B 423.529 440.471 464.822 484.034 508.235
7 Hb 494.118 513.882 542.529 564.706 592.941
8 B#v/Hb^ 564.706 587.294 620.1765 645.378 677.647
9 B# 635.294 660.706 697.8235 726.05 762.653
10 H 705.882 734.118 777.471 806.723 847.059
11 C 776.471 807.526 855.118 887.395 931.765
12 D 847.059 880.841 932.765 968.067 1016.471
13 Eb 917.647 954.352 1010.412 1048.7395 1101.1765
14 D#v/Eb^ 988.235 1027.765 1088.059 1129.412 1185.882
15 D# 1058.8235 1101.1765 1164.706 1210.084 1270.588
16 E 1129.412 1174.588 1242.353 1290.756 1355.294
17 F 1200 1248 1320 1371.429 1440

Golden Tunings

Degrees Octatonic Phrygian Mode (natural minor) Phrygian-Aeolian Mode (intermediate minor) Aeolian Mode (melodic/harmonic minor)
1 Gb 74.251 78.561 81.908
2 F#v/Gb^ 148.5025 157.121 163.815
3 F# 222.754 235.982 245.723
4 G 297.005 314.242 327.63
5 A 371.256 392.803 409.538
6 B 445.5075 471.264 491.4455
7 Hb 519.759 549.924 573.353
8 B#v/Hb^ 594.01 628.485 655.261
9 B# 668.261 707.0455 737.168
10 H 742.5125 785.606 819.076
11 C 816.764 864.168 900.983
12 D 891.015 942.727 982.891
13 Eb 965.266 1021.288 1064.799
14 D#v/Eb^ 1039.518 1099.849 1146.706
15 D# 1113.769 1178.409 1228.614
16 E 1188.02 1256.97 1310.521
17 F 1262.271 1335.53 1392.429
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