Trackdye: Difference between revisions

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Created page with "'''Trackdye''', short for "tract-aberracted diatonic", is a term for seven aberrismic ternary scales of the form 5L 2m 8s. {| class="wikitable" |+The Seven Forms of Trackdye ! colspan="2" |Diatonic Mode !Tract-Aberrated |- |Lydian |LLLsLLs |sLsLsLsMsLsLsMs |- |Ionian |LLsLLLs |sLsLsMsLsLsLsMs |- |Mixolydian |LLsLLsL |sLsLsMsLsLsMsLs |- |Dorian |LsLLLsL |sLsMsLsLsLsMsLs |- |Aeolian |LsLLsLL |sLsMsLsLsMsLsLs |- |Phrygian |sLLLs..."
 
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'''Trackdye''', short for "[[Stretching and compression|tract-aberracted]] diatonic", is a term for seven [[Aberrisma|aberrismic]] ternary scales of the form 5L 2m 8s.
'''Trackdye''', short for "[[Stretching and compression|tract-aberracted]] diatonic", is a term for seven [[Aberrisma|aberrismic]] ternary scales of the form 5L 2m 8s that may be constructed by compressing a diatonic scale and duplicating it offset by the amount it was compressed by. It is a superset of [[blackdye]] and [[pinedye]], which makes it useful as both a versatile tempered 5-limit scale and a [[straddle-3]] scale depending on the tuning.
{| class="wikitable"
|+Monotone-MOS Analysis
!Condition
!MOS
!Gen Range
!Name
|-
|L=m
|7L 8s
|2\15 - 1\7
|Porcupine
|-
|m=s
|5L 10s
|0\5 - 1\15
|Hard Blackwood
|-
|s=0
|5L 2s
|2\5 - 3\7
|Diatonic
|}
This shows that trackdye tunings tend to have a sharp diatonic fifth.


== Step orders ==
{| class="wikitable"
{| class="wikitable"
|+The Seven Forms of Trackdye
|+The Seven Forms of Trackdye<br>(MOS if L=m and if s=0)
! colspan="2" |Diatonic Mode
! colspan="2" |Diatonic Mode
!Tract-Aberrated
!Tract-Aberrated
Line 34: Line 58:
|sMsLsLsMsLsLsLs
|sMsLsLsMsLsLsLs
|}
|}
Each of these forms has its own set of 15 modes. The modes given in this table are all the only one with ''s'' as the first and last step, which is the standard form for tract-aberrated scales. M is capitalized for visual distinction.
There are also four step orders that are MOS if m=s and if s=0: sL'''sm'''LssLssL'''sm'''Ls, sL'''sm'''LssLssL'''ms'''Ls, sL'''ms'''LssLssL'''sm'''Ls, and sL'''ms'''LssLssL'''ms'''Ls, shown with ssLss in the middle. They are not named nor discussed in this article. There is no step order that satisfies all three monotone-MOS conditions.


== Tuning range ==
{| class="wikitable"
{| class="wikitable"
|+Selected Tunings of Tract-Aberrated Aeolian
|+Selected Tunings of Tract-Aberrated Dorian
!Pental JI
! colspan="2" |2.3.5 JI
!27+34 = 61P (¢)<br>~2.3.5.(7).13
! colspan="3" |~2.3.5.(7).13 (Hemififth)
!61+37 = 98bcc
!Compromise
!37cc (¢)<br>~2.<3.>>3.5.7
! colspan="2" |~2.<<3.>3.5.7.11.13 (Straddle)
|-
!Ratio
!Cents
!27P
!61P
!34P
!39P
!37cc
!67bcccc
|-
|-
|81/80
|81/80
|21.506
|44.444
|39.344
|39.344
|36.735
|35.294
|30.769
|32.432
|32.432
|35.821
|-
|-
|10/9
|10/9
|182.404
|177.778
|177.049
|177.049
|183.673
|176.471
|184.615
|194.595
|194.595
|197.015
|-
|-
|9/8
|9/8
|203.910
|222.222
|216.393
|216.393
|220.408
|211.765
|215.385
|227.027
|227.027
|232.836
|-
|-
|6/5
|6/5
|315.641
|311.111
|314.754
|314.754
|306.122
|317.647
|307.692
|291.892
|291.892
|286.567
|-
|-
|243/200
|243/200
|337.148
|355.556
|354.098
|354.098
|342.857
|352.941
|338.462
|324.324
|324.324
|322.388
|-
|-
|4/3
|4/3
|498.045
|488.889
|491.803
|491.803
|489.796
|494.118
|492.308
|486.486
|486.486
|483.582
|-
|-
|27/20
|27/20
|519.551
|533.333
|531.148
|531.148
|526.531
|529.412
|523.077
|518.919
|518.919
|519.403
|-
|-
|40/27
|40/27
|680.449
|666.667
|668.852
|668.852
|673.469
|670.588
|676.923
|681.081
|681.081
|680.597
|-
|-
|3/2
|3/2
|701.955
|711.111
|708.197
|708.197
|710.204
|705.882
|707.692
|713.514
|713.514
|716.418
|-
|-
|8/5
|400/243
|806.557
|862.852
|795.918
|844.444
|778.378
|845.902
|847.059
|861.538
|875.676
|877.612
|-
|-
|81/50
|5/3
|845.902
|884.359
|832.653
|888.889
|810.811
|885.246
|882.353
|892.308
|908.108
|913.433
|-
|-
|16/9
|16/9
|996.090
|977.778
|983.607
|983.607
|979.592
|988.235
|984.615
|972.973
|972.973
|967.164
|-
|-
|9/5
|9/5
|1017.596
|1022.222
|1022.951
|1022.951
|1016.327
|1023.529
|1015.385
|1005.405
|1005.405
|1002.985
|-
|-
|160/81
|160/81
|1178.494
|1155.556
|1160.656
|1160.656
|1163.265
|1164.706
|1169.231
|1167.568
|1167.568
|1164.179
|-
|-
|2/1
|2/1
Line 116: Line 209:
|1200
|1200
|1200
|1200
|1200.000
|1200.000
|1200.000
|1200.000
|}
|}
== Intervals ==
{| class="wikitable"
{| class="wikitable"
|+Intervals of 98bcc Tract-Aberrated Aeolian
|+Intervals of 39P Tract-Aberrated Dorian
|
|
|0
|0
Line 139: Line 238:
|0
|0
|0
|0
|37
|31
|184
|185
|220
|215
|306
|308
|343
|339
|490
|492
|527
|523
|673
|677
|710
|708
|796
|862
|833
|892
|980
|985
|1016
|1015
|1163
|1169
|1200
|1200
|-
|-
|37
|31
|0
|0
|147
|154
|184
|185
|269
|277
|306
|308
|453
|462
|490
|492
|637
|646
|674
|677
|759
|831
|796
|862
|943
|954
|980
|985
|1127
|1139
|1163
|1169
|1200
|1200
|-
|-
|184
|185
|0
|0
|37
|31
|122
|123
|159
|154
|306
|308
|343
|339
|490
|492
|527
|523
|612
|677
|649
|708
|796
|800
|833
|831
|980
|985
|1016
|1015
|1053
|1046
|1200
|1200
|-
|-
|220
|215
|0
|0
|86
|92
|122
|123
|269
|277
|306
|308
|453
|462
|490
|492
|576
|646
|612
|677
|759
|769
|796
|800
|943
|954
|980
|985
|1016
|1015
|1163
|1169
|1200
|1200
|-
|-
|306
|308
|0
|0
|37
|31
|184
|185
|220
|215
|367
|369
|404
|400
|490
|554
|527
|585
|674
|677
|710
|708
|857
|862
|894
|892
|931
|923
|1078
|1077
|1114
|1108
|1200
|1200
|-
|-
|343
|339
|0
|0
|147
|154
|184
|185
|331
|339
|367
|369
|453
|523
|490
|554
|637
|646
|674
|677
|820
|831
|857
|862
|894
|892
|1041
|1046
|1078
|1077
|1163
|1169
|1200
|1200
|-
|-
|490
|492
|0
|0
|37
|31
|184
|185
|220
|215
|306
|369
|343
|400
|490
|492
|527
|523
|674
|677
|710
|708
|747
|739
|894
|892
|931
|923
|1016
|1015
|1053
|1046
|1200
|1200
|-
|-
|527
|523
|0
|0
|147
|154
|184
|185
|269
|339
|306
|369
|453
|462
|490
|492
|637
|646
|674
|677
|710
|708
|857
|862
|894
|892
|980
|985
|1016
|1015
|1163
|1169
|1200
|1200
|-
|-
|673
|677
|0
|0
|37
|31
|122
|185
|159
|215
|306
|308
|343
|339
|490
|492
|527
|523
|563
|554
|710
|708
|747
|739
|833
|831
|869
|862
|1016
|1015
|1053
|1046
|1200
|1200
|-
|-
|710
|708
|0
|0
|86
|154
|122
|185
|269
|277
|306
|308
|453
|462
|490
|492
|527
|523
|674
|677
|710
|708
|796
|800
|833
|831
|980
|985
|1016
|1015
|1163
|1169
|1200
|1200
|-
|-
|796
|862
|0
|0
|37
|31
|184
|123
|220
|154
|367
|308
|404
|339
|441
|369
|588
|523
|625
|554
|710
|646
|747
|677
|894
|831
|931
|862
|1078
|1015
|1114
|1046
|1200
|1200
|-
|-
|833
|892
|0
|0
|147
|92
|184
|123
|331
|277
|367
|308
|404
|339
|551
|492
|588
|523
|674
|615
|710
|646
|857
|800
|894
|831
|1041
|985
|1078
|1015
|1163
|1169
|1200
|1200
|-
|-
|980
|985
|0
|0
|37
|31
|184
|185
|220
|215
|257
|246
|404
|400
|441
|431
|527
|523
|563
|554
|710
|708
|747
|739
|894
|892
|931
|923
|1016
|1077
|1053
|1108
|1200
|1200
|-
|-
|1016
|1015
|0
|0
|147
|154
|184
|185
|220
|215
|367
|369
|404
|400
|490
|492
|527
|523
|674
|677
|710
|708
|857
|862
|894
|892
|980
|1046
|1016
|1077
|1163
|1169
|1200
|1200
|-
|-
|1163
|1169
|0
|0
|37
|31
|74
|62
|220
|215
|257
|246
|343
|339
|380
|369
|527
|523
|563
|554
|710
|708
|747
|739
|833
|892
|869
|923
|1016
|1015
|1053
|1046
|1200
|1200
|}
|}

Revision as of 16:09, 8 November 2026

Trackdye, short for "tract-aberracted diatonic", is a term for seven aberrismic ternary scales of the form 5L 2m 8s that may be constructed by compressing a diatonic scale and duplicating it offset by the amount it was compressed by. It is a superset of blackdye and pinedye, which makes it useful as both a versatile tempered 5-limit scale and a straddle-3 scale depending on the tuning.

Monotone-MOS Analysis
Condition MOS Gen Range Name
L=m 7L 8s 2\15 - 1\7 Porcupine
m=s 5L 10s 0\5 - 1\15 Hard Blackwood
s=0 5L 2s 2\5 - 3\7 Diatonic

This shows that trackdye tunings tend to have a sharp diatonic fifth.

Step orders

The Seven Forms of Trackdye
(MOS if L=m and if s=0)
Diatonic Mode Tract-Aberrated
Lydian LLLsLLs sLsLsLsMsLsLsMs
Ionian LLsLLLs sLsLsMsLsLsLsMs
Mixolydian LLsLLsL sLsLsMsLsLsMsLs
Dorian LsLLLsL sLsMsLsLsLsMsLs
Aeolian LsLLsLL sLsMsLsLsMsLsLs
Phrygian sLLLsLL sMsLsLsLsMsLsLs
Locrian sLLsLLL sMsLsLsMsLsLsLs

Each of these forms has its own set of 15 modes. The modes given in this table are all the only one with s as the first and last step, which is the standard form for tract-aberrated scales. M is capitalized for visual distinction.

There are also four step orders that are MOS if m=s and if s=0: sLsmLssLssLsmLs, sLsmLssLssLmsLs, sLmsLssLssLsmLs, and sLmsLssLssLmsLs, shown with ssLss in the middle. They are not named nor discussed in this article. There is no step order that satisfies all three monotone-MOS conditions.

Tuning range

Selected Tunings of Tract-Aberrated Dorian
2.3.5 JI ~2.3.5.(7).13 (Hemififth) Compromise ~2.<<3.>3.5.7.11.13 (Straddle)
Ratio Cents 27P 61P 34P 39P 37cc 67bcccc
81/80 21.506 44.444 39.344 35.294 30.769 32.432 35.821
10/9 182.404 177.778 177.049 176.471 184.615 194.595 197.015
9/8 203.910 222.222 216.393 211.765 215.385 227.027 232.836
6/5 315.641 311.111 314.754 317.647 307.692 291.892 286.567
243/200 337.148 355.556 354.098 352.941 338.462 324.324 322.388
4/3 498.045 488.889 491.803 494.118 492.308 486.486 483.582
27/20 519.551 533.333 531.148 529.412 523.077 518.919 519.403
40/27 680.449 666.667 668.852 670.588 676.923 681.081 680.597
3/2 701.955 711.111 708.197 705.882 707.692 713.514 716.418
400/243 862.852 844.444 845.902 847.059 861.538 875.676 877.612
5/3 884.359 888.889 885.246 882.353 892.308 908.108 913.433
16/9 996.090 977.778 983.607 988.235 984.615 972.973 967.164
9/5 1017.596 1022.222 1022.951 1023.529 1015.385 1005.405 1002.985
160/81 1178.494 1155.556 1160.656 1164.706 1169.231 1167.568 1164.179
2/1 1200 1200 1200 1200.000 1200.000 1200.000 1200.000

Intervals

Intervals of 39P Tract-Aberrated Dorian
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
0 0 31 185 215 308 339 492 523 677 708 862 892 985 1015 1169 1200
31 0 154 185 277 308 462 492 646 677 831 862 954 985 1139 1169 1200
185 0 31 123 154 308 339 492 523 677 708 800 831 985 1015 1046 1200
215 0 92 123 277 308 462 492 646 677 769 800 954 985 1015 1169 1200
308 0 31 185 215 369 400 554 585 677 708 862 892 923 1077 1108 1200
339 0 154 185 339 369 523 554 646 677 831 862 892 1046 1077 1169 1200
492 0 31 185 215 369 400 492 523 677 708 739 892 923 1015 1046 1200
523 0 154 185 339 369 462 492 646 677 708 862 892 985 1015 1169 1200
677 0 31 185 215 308 339 492 523 554 708 739 831 862 1015 1046 1200
708 0 154 185 277 308 462 492 523 677 708 800 831 985 1015 1169 1200
862 0 31 123 154 308 339 369 523 554 646 677 831 862 1015 1046 1200
892 0 92 123 277 308 339 492 523 615 646 800 831 985 1015 1169 1200
985 0 31 185 215 246 400 431 523 554 708 739 892 923 1077 1108 1200
1015 0 154 185 215 369 400 492 523 677 708 862 892 1046 1077 1169 1200
1169 0 31 62 215 246 339 369 523 554 708 739 892 923 1015 1046 1200
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