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Thesaurus of Diatonic Sets Vic Dillahay vicdillahay.com
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Thesaurus of Diatonic Sets
Vic Dillahay
vicdillahay.com
Copyright © 2013 Victor Carlton Dillahay
All rights reserved.
Contents
About the Sets............................................................................................... 1
Sets of 0 Notes............................................................................................... 3
• Silence ................................................................................................. 5
• On Any Degree: Silence …................................................... 6
Sets of 1 Note ............................................................................................... 9
• Scale Degrees ...................................................................................... 11
• On I: {R} ............................................................................... 12
• On II: {2} .............................................................................. 14
• On III: {3} ............................................................................. 16
• On IV: {4} ............................................................................. 18
• On V: {5} ............................................................................... 20
• On VI: {6} ............................................................................. 22
• On VII: {7} ........................................................................... 24
Sets of 2 Notes:.............................................................................................. 27
• 4ths/5ths ............................................................................................. 29
• On I: {R, 4} ........................................................................... 30
• On II: {2, 5} .......................................................................... 32
• On III: {3, 6} ......................................................................... 34
• On IV: {4, 7} ......................................................................... 36
• On V: {R, 5} .......................................................................... 38
• On VI: {2, 6} ......................................................................... 40
• On VII: {3, 7} ....................................................................... 42
• 3rds/6ths ............................................................................................ 45
• On I: {R, 3} ........................................................................... 46
• On II: {2, 4} .......................................................................... 48
• On III: {3, 5} ......................................................................... 50
• On IV: {4, 6} ......................................................................... 52
• On V: {5, 7} ........................................................................... 54
• On VI: {R, 6} ........................................................................ 56
• On VII: {2, 7} ....................................................................... 58
• 2nds/7ths ............................................................................................ 61
• On I: {R, 2} ........................................................................... 62
• On II: {2, 3} .......................................................................... 64
• On III: {3, 4} ......................................................................... 66
• On IV: {4, 5} ......................................................................... 68
• On V: {5, 6} ........................................................................... 70
• On VI: {6, 7} ......................................................................... 72
• On VII: {R, 7} ....................................................................... 74
Sets of 3 Notes:.............................................................................................. 77
• Triads .................................................................................................. 79
• On I: {R, 3, 5} ....................................................................... 80
• On II: {2, 4, 6} ....................................................................... 82
• On III: {3, 5, 7} ..................................................................... 84
• On IV: {R, 4, 6} ..................................................................... 86
• On V: {2, 5, 7} ....................................................................... 88
• On VI: {R, 3, 6} ..................................................................... 90
• On VII: {2, 4, 7} .................................................................... 92
• Sus2s ................................................................................................... 95
• On I: {R, 2, 5} ........................................................................ 96
• On II: {2, 3, 6} ....................................................................... 98
• On III: {3, 4, 7} .................................................................... 100
• On IV: {R, 4, 5} .................................................................... 102
• On V: {2, 5, 6} ...................................................................... 104
• On VI: {3, 6, 7} .................................................................... 106
• On VII: {R, 4, 7} .................................................................. 108
• 7no5s ................................................................................................. 111
• On I: {R, 3, 7} ...................................................................... 112
• On II: {R, 2, 4} ..................................................................... 114
• On III: {2, 3, 5} .................................................................... 116
• On IV: {3, 4, 6} ..................................................................... 118
• On V: {4, 5, 7} ...................................................................... 120
• On VI: {R, 5, 6} .................................................................... 122
• On VII: {2, 6, 7}..................................................................... 124
• 7no3s .................................................................................................. 127
• On I: {R, 5, 7} ....................................................................... 128
• On II: {R, 2, 6} ...................................................................... 130
• On III: {2, 3, 7} ...................................................................... 132
• On IV: {R, 3, 4} ..................................................................... 134
• On V: {2, 4, 5} ........................................................................ 136
• On VI: {3, 5, 6} ...................................................................... 138
• On VII: {4, 6, 7} ..................................................................... 140
• 3 Note Clusters .................................................................................... 143
• On I: {R, 2, 3} ........................................................................ 144
• On II: {2, 3, 4} ....................................................................... 146
• On III: {3, 4, 5} ...................................................................... 148
• On IV: {4, 5, 6} ....................................................................... 150
• On V: {5, 6, 7} ........................................................................ 152
• On VI: {R, 6, 7} ...................................................................... 154
• On VII: {R, 2, 7} ..................................................................... 156
Sets of 4 Notes:................................................................................................ 159
• 7ths ....................................................................................................... 161
• On I: {R, 3, 5, 7} ..................................................................... 162
• On II: {R, 2, 4, 6} .................................................................... 164
• On III: {2, 3, 5, 7} .................................................................... 166
• On IV: {R, 3, 4, 6} .................................................................... 168
• On V: {2, 4, 5, 7} ...................................................................... 170
• On VI: {R, 3, 5, 6} .................................................................... 172
• On VII: {2, 4, 6, 7} ................................................................... 174
• Add9s .................................................................................................... 177
• On I: {R, 2, 3, 5} ...................................................................... 178
• On II: {2, 3, 4, 6} ..................................................................... 180
• On III: {3, 4, 5, 7} .................................................................... 182
• On IV: {R, 4, 5, 6} .................................................................... 184
• On V: {2, 5, 6, 7} ...................................................................... 186
• On VI: {R, 3, 6, 7} .................................................................... 188
• On VII: {R, 2, 4, 7} ................................................................... 190
• 7sus4s ..................................................................................................... 193
• On I: {R, 4, 5, 7} ....................................................................... 194
• On II: {R, 2, 5, 6} ...................................................................... 196
• On III: {2, 3, 6, 7} ..................................................................... 198
• On IV: {R, 3, 4, 7} ..................................................................... 200
• On V: {R, 2, 4, 5} ....................................................................... 202
• On VI: {2, 3, 5, 6} ..................................................................... 204
• On VII: {3, 4, 6, 7} .................................................................... 206
• Add4s ...................................................................................................... 209
• On I: {R, 3, 4, 5} ....................................................................... 210
• On II: {2, 4, 5, 6} ...................................................................... 212
• On III: {3, 5, 6, 7} ..................................................................... 214
• On IV: {R, 4, 6, 7} .............................................................,....... 216
• On V: {R, 2, 5, 7} ....................................................................... 218
• On VI: {R, 2, 3, 6} ..................................................................... 220
• On VII: {2, 3, 4, 7} .................................................................... 222
• 4 Note Clusters ....................................................................................... 225
• On I: {R, 2, 3, 4} ........................................................................ 226
• On II: {2, 3, 4, 5} ....................................................................... 228
• On III: {3, 4, 5, 6} ...................................................................... 230
• On IV: {4, 5, 6, 7} ...................................................................... 232
• On V: {R, 5, 6, 7} ....................................................................... 234
• On VI: {R, 2, 6, 7} ..................................................................... 236
• On VII: {R, 2, 3, 7} ................................................................... 238
Sets of 5 Notes:.................................................................................................. 241
• 9ths ......................................................................................................... 243
• On I: {R, 2, 3, 5, 7} .................................................................... 244
• On II: {R, 2, 3, 4, 6} ................................................................... 246
• On III: {2, 3, 4, 5, 7} .................................................................. 248
• On IV: {R, 3, 4, 5, 6} .................................................................. 250
• On V: {2, 4, 5, 6, 7} .................................................................... 252
• On VI: {R, 3, 5, 6, 7} ................................................................. 254
• On VII: {R, 2, 4, 6, 7} ................................................................ 256
• 6/9s .......................................................................................................... 259
• On I: {R, 2, 3, 5, 6} .................................................................... 260
• On II: {2, 3, 4, 6, 7} ................................................................... 262
• On III: {R, 3, 4, 5, 7} ................................................................. 264
• On IV: {R, 2, 4, 5, 6} .................................................................. 266
• On V: {2, 3, 5, 6, 7} .................................................................... 268
• On VI: {R, 3, 4, 6, 7} .................................................................. 270
• On VII: {R, 2, 4, 5, 7} ................................................................ 272
• 5 Note Clusters ........................................................................................ 275
• On I: {R, 2, 3, 4, 5} .................................................................... 276
• On II: {2, 3, 4, 5, 6} ................................................................... 278
• On III: {3, 4, 5, 6, 7} ................................................................. 280
• On IV: {R, 4, 5, 6, 7} ................................................................. 282
• On V: {R, 2, 5, 6, 7} ................................................................... 284
• On VI: {R, 2, 3, 6, 7} ................................................................. 286
• On VII: {R, 2, 3, 4, 7} ................................................................ 288
Sets of 6 Notes:................................................................................................... 291
• 11ths ........................................................................................................ 293
• On I: {R, 2, 3, 4, 5, 7} ................................................................. 294
• On II: {R, 2, 3, 4, 5, 6} ............................................................... 296
• On III: {2, 3, 4, 5, 6, 7} .............................................................. 298
• On IV: {R, 3, 4, 5, 6, 7} ............................................................. 300
• On V: {R, 2, 4, 5, 6, 7} .............................................................. 302
• On VI: {R, 2, 3, 5, 6, 7} ............................................................ 304
• On VII: {R, 2, 3, 4, 6, 7} ........................................................... 306
Sets of 7 Notes:................................................................................................... 309
• 13ths ........................................................................................................ 311
• On Any Degree: {R, 2, 3, 4, 5, 6, 7} .......................................... 312
Diatonic Interval Vector for Each Set Type..................................................... 314
Diatonic Steps in Each Set Type....................................................................... 315
A Few Ideas for Using This Book in Jazz......................................................... 316
From VicDillahay.com
About the Sets
The Contents of Each Set Listing:
• Set Name -- The elements of the set in order. A chord with the R, 3rd, 9th, and 11th would be
read as {R, 2, 3, 4}.
• Set Description -- The set type and the degree on which it is built.
• Diatonic Interval Vector -- All of the intervals that may be formed by this set, read in order as
2nds/7ths, 3rds/6ths, and 4ths/5ths. 213 means two 2nds, one 3rd, and three 4ths.
• Subsets -- Sets which are wholly contained within the original set. {2, 4, 5} is a subset of {R, 2,
3, 4} while {R, 2, 3, 5} is not.
• Supersets -- Sets that contain the entire original set. {R, 2, 3, 4, 5} is a superset of {R, 2, 3, 4}
but {R, 3, 4, 5, 6} is not.
• Sets with No Common Tones -- Sets that do not contain any element of the original set. {5, 6,
7} has no tones in common with {R, 2, 3, 4}.
Order of Sets:
• The sets are ordered first by their number of notes, from 0 to 7.
• Sets of the same number of notes are grouped by intervallic content. Each group is named for a
chord which may be built from its intervals.
• The chords are ordered from the most evenly distributed intervals to the least.
• The sets in each group are listed by the root of the chord in order of scale degree, from I
through VII.
1
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2
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Sets of 0 Notes • Silence
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4
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Silence on Each Degree
• On I: Silence
• On II: Silence
• On III: Silence
• On IV: Silence
• On V: Silence
• On VI: Silence
• On VII: Silence
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{}
Silence.
Diatonic Interval Vector:
000
Subsets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {3, 6}, {4, 7}, {R, 5}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {4, 6}, {5, 7}, {1, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {2, 4, 6}, {3, 5, 7}, {R, 4, 6}, {2, 5, 7}, {R, 3, 6}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {3, 4, 7}, {R, 4, 5}, {2, 5, 6}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {2, 3, 5}, {3, 4, 6}, {4, 5, 7}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 3, 7}, {R, 3, 4}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
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• 7s: {R, 3, 5, 7}, {R, 2, 4, 6}, {2, 3, 5, 7}, {R, 3, 4, 6}, {2, 4, 5, 7}, {R, 3, 5, 6}, {2, 4, 6, 7}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {R, 4, 5, 6}, {2, 5, 6, 7}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {2, 3, 6, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {3, 5, 6, 7}, {R, 4, 6, 7}, {R, 2, 5, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7},
{R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 3, 5, 6,
7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7},
{R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7},
{R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7},
{R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
7
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8
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Sets of 1 Note • Scale Degrees
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Each Degree of the Scale
• On I: {R}
• On II: {2}
• On III: {3}
• On IV: {4}
• On V: {5}
• On VI: {6}
• On VII: {7}
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{R}
Single note on I.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {R}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {R}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: {R, 3, 5}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {R, 6, 7}, {R, 2, 7}
12
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• 7s: {R, 3, 5, 7}, {R, 2, 4, 6}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {R, 4, 5, 6}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {R, 3, 4, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {R, 4, 6, 7}, {R, 2, 5, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 5, 6, 7}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 4}, {3, 5}, {4, 6}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}
• Triads: {2, 4, 6}, {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {2, 3, 5}, {3, 4, 6}, {4, 5, 7}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}, {4, 5, 6}, {5, 6, 7}
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {3, 4, 5, 7}, {2, 5, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {2, 4, 5, 6}, {3, 5, 6, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}
• 13ths: None
13
From VicDillahay.com
{2}
Single note on II.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {2}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {2}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: {2, 4, 6}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {2, 5, 6}
• 7no5s: {R, 2, 4}, {2, 3, 5}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {2, 3, 7}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {R, 2, 7}
14
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {2, 5, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 6, 7}, {R, 2, 4, 5}, {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}, {R, 2, 5, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {4, 6}, {5, 7}, {R, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {3, 4, 7}, {R, 4, 5}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {3, 4, 6}, {4, 5, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {R, 3, 4}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}, {5, 6, 7}, {R, 6, 7}
• 7s: {R, 3, 5, 7}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {3, 4, 5, 7}, {R, 4, 5, 6}, {R, 3, 6, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {3, 5, 6, 7}, {R, 4, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}
• 13ths: None
15
From VicDillahay.com
{3}
Single note on III.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {3}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {3}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: {R, 3, 5}, {3, 5, 7}, {R, 3, 6}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {3, 6, 7}
• 7no5s: {R, 3, 7}, {2, 3, 5}, {3, 4, 6}
• 7no3s: {2, 3, 7}, {R, 3, 4}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}
16
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {R, 3, 4, 7}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {3, 5, 6, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {2, 5, 6}, {R, 4, 7}
• 7no5s: {R, 2, 4}, {4, 5, 7}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 4, 5}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {R, 4, 5, 6}, {2, 5, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}, {R, 4, 6, 7}, {R, 2, 5, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 4, 5, 6, 7}
• 13ths: None
17
From VicDillahay.com
{4}
Single note on IV.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {4}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {4}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: {2, 4, 6}, {R, 4, 6}, {2, 4, 7}
• Sus2s: {3, 4, 7}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 2, 4}, {3, 4, 6}, {4, 5, 7}
• 7no3s: {R, 3, 4}, {2, 4, 5}, {4, 6, 7}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}, {4, 5, 6}
18
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {3, 4, 5, 7}, {R, 4, 5, 6}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {R, 4, 6, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {R, 5}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {R, 3, 7}, {2, 3, 5}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 3, 7}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {2, 5, 6, 7}, {R, 3, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {3, 5, 6, 7}, {R, 2, 5, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 5, 6, 7}
• 13ths: None
19
From VicDillahay.com
{5}
Single note on V.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {5}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {5}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {2, 5, 6}
• 7no5s: {2, 3, 5}, {4, 5, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {2, 4, 5}, {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}, {5, 6, 7}
20
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {2, 4, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {3, 4, 5, 7}, {R, 4, 5, 6}, {2, 5, 6, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {R, 2, 4, 5}, {2, 3, 5, 6}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {3, 5, 6, 7}, {R, 2, 5, 7}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7},
{R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {4, 6}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {R, 3, 6}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {3, 4, 6}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {2, 3, 7}, {R, 3, 4}, {4, 6, 7}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {2, 3, 6, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 6, 7}
• 13ths: None
21
From VicDillahay.com
{6}
Single note on VI.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {6}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {2, 3, 6}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {3, 4, 6}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}, {R, 6, 7}
22
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {R, 3, 5, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {R, 4, 5, 6}, {2, 5, 6, 7}, {R, 3, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 6, 7}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {2, 4, 5, 6}, {3, 5, 6, 7}, {R, 4, 6, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {3, 4, 7}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {2, 3, 5}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {2, 3, 7}, {R, 3, 4}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {R, 2, 3, 5}, {3, 4, 5, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {R, 2, 5, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}
• 13ths: None
23
From VicDillahay.com
{7}
Single note on VII.
Diatonic Interval Vector:
000
Subsets:
• Silence: {}
• Scale Degrees: {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {3, 4, 7}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {4, 5, 7}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {2, 3, 7}, {4, 6, 7}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
24
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {3, 4, 5, 7}, {2, 5, 6, 7}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {2, 3, 6, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}, {R, 4, 6, 7}, {R, 2, 5, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7},
{R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {2, 5}, {3, 6}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}
• Triads: {R, 3, 5}, {2, 4, 6}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {R, 4, 5}, {2, 5, 6}
• 7no5s: {R, 2, 4}, {2, 3, 5}, {3, 4, 6}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {R, 3, 4}, {2, 4, 5}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {R, 4, 5, 6}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}, {2, 3, 5, 6}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}
• 13ths: None
25
From VicDillahay.com
26
From VicDillahay.com
Sets of 2 Notes • 4ths/5ths
• 3rds/6ths
• 2nds/7ths
27
From VicDillahay.com
28
From VicDillahay.com
4ths on Each Degree
• On I: {R, 4}
• On II: {2, 5}
• On III: {3, 6}
• On IV: {4, 7}
• On V: {R, 5}
• On VI: {2, 6}
• On VII: {3, 7}
29
From VicDillahay.com
{R, 4}
Fourth built on I.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {R, 4}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 2, 4}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
30
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}
• Add9s: {R, 4, 5, 6}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {R, 4, 6, 7}
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {5, 6}, {6, 7}
• Triads: {3, 5, 7}, {2, 5, 7}
• Sus2s: {2, 3, 6}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {2, 3, 5}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}
• 7s: {2, 3, 5, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
31
From VicDillahay.com
{2, 5}
Fourth built on II.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {2}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {2, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 5, 7}
• Sus2s: {R, 2, 5}, {2, 5, 6}
• 7no5s: {2, 3, 5}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
32
From VicDillahay.com
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {R, 2, 3, 5}, {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}, {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}, {R, 2, 5, 7}
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}, {6, 7}, {R, 7}
• Triads: {R, 4, 6}, {R, 3, 6}
• Sus2s: {3, 4, 7}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {3, 4, 6}
• 7no3s: {R, 3, 4}, {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}
• 7s: {R, 3, 4, 6}
• Add9s: {R, 3, 6, 7}
• 7sus4s: {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
33
From VicDillahay.com
{3, 6}
Fourth built on III.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {3}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {3, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 3, 6}
• Sus2s: {2, 3, 6}, {3, 6, 7}
• 7no5s: {3, 4, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
34
From VicDillahay.com
• 7s: {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {2, 3, 4, 6}, {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}
• 3rds/6ths: {2, 4}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {4, 5}, {R, 7}
• Triads: {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 2, 4}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 7}
• 7s: {2, 4, 5, 7}
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 4, 5}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
35
From VicDillahay.com
{4, 7}
Fourth built on IV.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {4}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {4, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 4, 7}
• Sus2s: {3, 4, 7}, {R, 4, 7}
• 7no5s: {4, 5, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
36
From VicDillahay.com
• 7s: {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {3, 4, 5, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 3}, {3, 5}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {5, 6}
• Triads: {R, 3, 5}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}
• 7s: {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 5, 6}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
37
From VicDillahay.com
{R, 5}
Fourth built on V.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {R}, {5}
• 4ths/5ths: {R, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {R, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 3, 5}
• Sus2s: {R, 2, 5}, {R, 4, 5}
• 7no5s: {R, 5, 6}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
38
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {R, 4, 5, 6}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {R, 2, 5, 7}
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 4}, {4, 6}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {6, 7}
• Triads: {2, 4, 6}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {4, 6, 7}
• 3 Note Clusters: {2, 3, 4}
• 7s: {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}
• 7sus4s: {2, 3, 6, 7}, {3, 4, 6, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
39
From VicDillahay.com
{2, 6}
Fourth built on VI.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {2}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {2, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 4, 6}
• Sus2s: {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 6, 7}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
40
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}
• Sus2s: {3, 4, 7}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {R, 3, 4}
• 3 Note Clusters: {3, 4, 5}
• 7s: {R, 3, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
41
From VicDillahay.com
{3, 7}
Fourth built on VII.
Diatonic Interval Vector:
001
Subsets:
• Silence: {}
• Scale Degrees: {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: {3, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {3, 5, 7}
• Sus2s: {3, 4, 7}, {3, 6, 7}
• 7no5s: {R, 3, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
42
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}
• Add9s: {3, 4, 5, 7}, {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {4, 5}, {5, 6}
• Triads: {2, 4, 6}, {R, 4, 6}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {2, 5, 6}
• 7no5s: {R, 2, 4}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {2, 4, 5}
• 3 Note Clusters: {4, 5, 6}
• 7s: {R, 2, 4, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
43
From VicDillahay.com
44
From VicDillahay.com
3rds on Each Degree
• On I: {R, 3}
• On II: {2, 4}
• On III: {3, 5}
• On IV: {4, 6}
• On V: {5, 7}
• On VI: {R, 6}
• On VII: {2, 7}
45
From VicDillahay.com
{R, 3}
Third built on I.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}
• 4ths/5ths: None
• 3rds/6ths: {R, 3}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {R, 3}
• 2nds/7ths: None
• Triads: {R, 3, 5}, {R, 3, 6}
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}
46
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {R, 3, 6, 7}
• 7sus4s: {R, 3, 4, 7}
• Add4s: {R, 3, 4, 5}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {5, 7}, {2, 7}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}
• Triads: {2, 4, 6}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {2, 5, 6}
• 7no5s: {4, 5, 7}, {2, 6, 7}
• 7no3s: {2, 4, 5}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}
• 7s: {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
47
From VicDillahay.com
{2, 4}
Third built on II.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}
• 4ths/5ths: None
• 3rds/6ths: {2, 4}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {2, 4}
• 2nds/7ths: None
• Triads: {2, 4, 6}, {2, 4, 7}
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {2, 3, 4}
48
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {R, 2, 4, 7}
• 7sus4s: {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}
• 9ths: {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {R, 6}
• 2nds/7ths: {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {R, 3, 6}
• Sus2s: {3, 6, 7}
• 7no5s: {R, 3, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}
• 7s: {R, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
49
From VicDillahay.com
{3, 5}
Third built on III.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {3}, {5}
• 4ths/5ths: None
• 3rds/6ths: {3, 5}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {3, 5}
• 2nds/7ths: None
• Triads: {R, 3, 5}, {3, 5, 7}
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}
50
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {3, 4, 5, 7}
• 7sus4s: {2, 3, 5, 6}
• Add4s: {R, 3, 4, 5}, {3, 5, 6, 7}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {2, 4, 7}
• Sus2s: {R, 4, 7}
• 7no5s: {R, 2, 4}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {2, 4, 6, 7}
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
51
From VicDillahay.com
{4, 6}
Third built on IV.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {4}, {6}
• 4ths/5ths: None
• 3rds/6ths: {4, 6}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {4, 6}
• 2nds/7ths: None
• Triads: {2, 4, 6}, {R, 4, 6}
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}
52
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {R, 4, 5, 6}
• 7sus4s: {3, 4, 6, 7}
• Add4s: {2, 4, 5, 6}, {R, 4, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {5}, {7}
• 4ths/5ths: {2, 5}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}
• Sus2s: {R, 2, 5}
• 7no5s: {R, 3, 7}, {2, 3, 5}
• 7no3s: {R, 5, 7}, {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
53
From VicDillahay.com
{5, 7}
Third built on V.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {5}, {7}
• 4ths/5ths: None
• 3rds/6ths: {5, 7}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {5, 7}
• 2nds/7ths: None
• Triads: {3, 5, 7}, {2, 5, 7}
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {5, 6, 7}
54
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {3, 4, 5, 7}, {2, 5, 6, 7}
• 7sus4s: {R, 4, 5, 7}
• Add4s: {3, 5, 6, 7}, {R, 2, 5, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {6}
• 4ths/5ths: {R, 4}, {3, 6}, {2, 6}
• 3rds/6ths: {R, 3}, {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}
• Triads: {2, 4, 6}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {2, 3, 6}
• 7no5s: {R, 2, 4}, {3, 4, 6}
• 7no3s: {R, 2, 6}, {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
55
From VicDillahay.com
{R, 6}
Third built on VI.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {R}, {6}
• 4ths/5ths: None
• 3rds/6ths: {R, 6}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {R, 6}
• 2nds/7ths: None
• Triads: {R, 4, 6}, {R, 3, 6}
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 6, 7}
56
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 4, 5, 6}, {R, 3, 6, 7}
• 7sus4s: {R, 2, 5, 6}
• Add4s: {R, 4, 6, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {5}, {7}
• 4ths/5ths: {2, 5}, {4, 7}, {3, 7}
• 3rds/6ths: {2, 4}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}
• Triads: {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {3, 4, 7}
• 7no5s: {2, 3, 5}, {4, 5, 7}
• 7no3s: {2, 3, 7}, {2, 4, 5}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
57
From VicDillahay.com
{2, 7}
Third built on VII.
Diatonic Interval Vector:
010
Subsets:
• Silence: {}
• Scale Degrees: {2}, {7}
• 4ths/5ths: None
• 3rds/6ths: {2, 7}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: {2, 7}
• 2nds/7ths: None
• Triads: {2, 5, 7}, {2, 4, 7}
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {R, 2, 7}
58
From VicDillahay.com
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 5, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {2, 3, 6, 7}
• Add4s: {R, 2, 5, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {3, 6}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}
• Triads: {R, 3, 5}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {R, 4, 5}
• 7no5s: {3, 4, 6}, {R, 5, 6}
• 7no3s: {R, 3, 4}, {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}
• 7s: {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
59
From VicDillahay.com
2nds on Each Degree
• On I: {R, 2}
• On II: {2, 3}
• On III: {3, 4}
• On IV: {4, 5}
• On V: {5, 6}
• On VI: {6, 7}
• On VII: {R, 7}
60
From VicDillahay.com
61
From VicDillahay.com
{R, 2}
Second built on I.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: {R, 2, 5}
• 7no5s: {R, 2, 4}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 2, 3}, {R, 2, 7}
62
From VicDillahay.com
• 7s: {R, 2, 4, 6}
• Add9s: {R, 2, 3, 5}, {R, 2, 4, 7}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {R, 2, 5, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {3, 5}, {4, 6}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}, {6, 7}
• Triads: {3, 5, 7}
• Sus2s: {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}, {4, 5, 7}
• 7no3s: {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}, {5, 6, 7}
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: None
• 13ths: None
63
From VicDillahay.com
{2, 3}
Second built on II.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: {2, 3, 6}
• 7no5s: {2, 3, 5}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}
64
From VicDillahay.com
• 7s: {2, 3, 5, 7}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}
• 3rds/6ths: {4, 6}, {5, 7}, {R, 6}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 5}, {R, 4, 7}
• 7no5s: {4, 5, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}, {R, 6, 7}
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 4, 5, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: None
• 13ths: None
65
From VicDillahay.com
{3, 4}
Second built on III.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: {3, 4, 7}
• 7no5s: {3, 4, 6}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}
66
From VicDillahay.com
• 7s: {R, 3, 4, 6}
• Add9s: {2, 3, 4, 6}, {3, 4, 5, 7}
• 7sus4s: {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {5, 6}, {6, 7}, {R, 7}
• Triads: {2, 5, 7}
• Sus2s: {R, 2, 5}, {2, 5, 6}
• 7no5s: {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: None
• 13ths: None
67
From VicDillahay.com
{4, 5}
Second built on IV.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {4}, {5}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: {R, 4, 5}
• 7no5s: {4, 5, 7}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}
68
From VicDillahay.com
• 7s: {2, 4, 5, 7}
• Add9s: {3, 4, 5, 7}, {R, 4, 5, 6}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {6, 7}, {R, 7}
• Triads: {R, 3, 6}
• Sus2s: {2, 3, 6}, {3, 6, 7}
• 7no5s: {R, 3, 7}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: None
• 13ths: None
69
From VicDillahay.com
{5, 6}
Second built on V.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {5}, {6}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: {2, 5, 6}
• 7no5s: {R, 5, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}
70
From VicDillahay.com
• 7s: {R, 3, 5, 6}
• Add9s: {R, 4, 5, 6}, {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}, {3, 5, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {R, 7}
• Triads: {2, 4, 7}
• Sus2s: {3, 4, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}
• 7no3s: {2, 3, 7}, {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {R, 2, 7}
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 3, 4, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: None
• 13ths: None
71
From VicDillahay.com
{6, 7}
Second built on VI.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: {3, 6, 7}
• 7no5s: {2, 6, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}
72
From VicDillahay.com
• 7s: {2, 4, 6, 7}
• Add9s: {2, 5, 6, 7}, {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}, {R, 4, 6, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}, {5}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}
• Triads: {R, 3, 5}
• Sus2s: {R, 2, 5}, {R, 4, 5}
• 7no5s: {R, 2, 4}, {2, 3, 5}
• 7no3s: {R, 3, 4}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: None
• 13ths: None
73
From VicDillahay.com
{R, 7}
Second built on VII.
Diatonic Interval Vector:
100
Subsets:
• Silence: {}
• Scale Degrees: {R}, {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: {R, 4, 7}
• 7no5s: {R, 3, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {R, 6, 7}, {R, 2, 7}
74
From VicDillahay.com
• 7s: {R, 3, 5, 7}
• Add9s: {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}
• Add4s: {R, 4, 6, 7}, {R, 2, 5, 7}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}
• 3rds/6ths: {2, 4}, {3, 5}, {4, 6}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}, {5, 6}
• Triads: {2, 4, 6}
• Sus2s: {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}, {3, 4, 6}
• 7no3s: {2, 4, 5}, {3, 5, 6}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}, {4, 5, 6}
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: None
• 13ths: None
75
From VicDillahay.com
76
From VicDillahay.com
Sets of 3 Notes • Triads
• Sus2s
• 7no5s
• 7no3s
• 3 Note Clusters
77
From VicDillahay.com
78
From VicDillahay.com
Triads on Each Degree
• On I: {R, 3, 5}
• On II: {2, 4, 6}
• On III: {3, 5, 7}
• On IV: {R, 4, 6}
• On V: {2, 5, 7}
• On VI: {R, 3, 6}
• On VII: {2, 4, 7}
79
From VicDillahay.com
{R, 3, 5}
Triad built on I.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {5}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: None
• Triads: {R, 3, 5}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 3, 5}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
80
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {6}, {7}
• 4ths/5ths: {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {2, 7}
• 2nds/7ths: {6, 7}
• Triads: {2, 4, 6}, {2, 4, 7}
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: {2, 4, 6, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
81
From VicDillahay.com
{2, 4, 6}
Triad built on II.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: None
• Triads: {2, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
82
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {5}, {7}
• 4ths/5ths: {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}
• 2nds/7ths: {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: {R, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
83
From VicDillahay.com
{3, 5, 7}
Triad built on III.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {3}, {5}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: None
• Triads: {3, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {3, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
84
From VicDillahay.com
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {6}
• 4ths/5ths: {R, 4}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}
• Triads: {2, 4, 6}, {R, 4, 6}
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: {R, 2, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
85
From VicDillahay.com
{R, 4, 6}
Triad built on IV.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {6}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: None
• Triads: {R, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
86
From VicDillahay.com
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {5}, {7}
• 4ths/5ths: {2, 5}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}
• Triads: {3, 5, 7}, {2, 5, 7}
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: {2, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
87
From VicDillahay.com
{2, 5, 7}
Triad built on V.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {2}, {5}, {7}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: None
• Triads: {2, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
88
From VicDillahay.com
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {2, 3, 5, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {6}
• 4ths/5ths: {R, 4}, {3, 6}
• 3rds/6ths: {R, 3}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}
• Triads: {R, 4, 6}, {R, 3, 6}
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: {R, 3, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
89
From VicDillahay.com
{R, 3, 6}
Triad built on VI.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: None
• Triads: {R, 3, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {R, 3, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
90
From VicDillahay.com
• 7s: {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {5}, {7}
• 4ths/5ths: {2, 5}, {4, 7}
• 3rds/6ths: {2, 4}, {5, 7}, {2, 7}
• 2nds/7ths: {4, 5}
• Triads: {2, 5, 7}, {2, 4, 7}
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: {2, 4, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
91
From VicDillahay.com
{2, 4, 7}
Triad built on VII.
Diatonic Interval Vector:
021
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: None
• Triads: {2, 4, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: {2, 4, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
92
From VicDillahay.com
• 7s: {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {5}, {6}
• 4ths/5ths: {3, 6}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}, {R, 6}
• 2nds/7ths: {5, 6}
• Triads: {R, 3, 5}, {R, 3, 6}
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: {R, 3, 5, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
93
From VicDillahay.com
94
From VicDillahay.com
Sus2s on Each Degree
• On I: {R, 2, 5}
• On II: {2, 3, 6}
• On III: {3, 4, 7}
• On IV: {R, 4, 5}
• On V: {2, 5, 6}
• On VI: {3, 6, 7}
• On VII: {R, 4, 7}
95
From VicDillahay.com
{R, 2, 5}
Sus2 built on I.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {5}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: None
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: {R, 2, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {R, 2, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
96
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {3, 4}, {6, 7}
• Triads: None
• Sus2s: {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {3, 4, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
97
From VicDillahay.com
{2, 3, 6}
Sus2 built on II.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: None
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: {2, 3, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {2, 3, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
98
From VicDillahay.com
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {4, 5}, {R, 7}
• Triads: None
• Sus2s: {R, 4, 5}, {R, 4, 7}
• 7no5s: {4, 5, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 4, 5, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
99
From VicDillahay.com
{3, 4, 7}
Sus2 built on III.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: None
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: {3, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {3, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
100
From VicDillahay.com
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {5}, {6}
• 4ths/5ths: {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {R, 2}, {5, 6}
• Triads: None
• Sus2s: {R, 2, 5}, {2, 5, 6}
• 7no5s: {R, 5, 6}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
101
From VicDillahay.com
{R, 4, 5}
Sus2 built on IV.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {5}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: None
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: {R, 4, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {R, 4, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
102
From VicDillahay.com
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {2, 3}, {6, 7}
• Triads: None
• Sus2s: {2, 3, 6}, {3, 6, 7}
• 7no5s: {2, 6, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
103
From VicDillahay.com
{2, 5, 6}
Sus2 built on V.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {2}, {5}, {6}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: None
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: {2, 5, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {2, 5, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
104
From VicDillahay.com
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {3, 4}, {R, 7}
• Triads: None
• Sus2s: {3, 4, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 3, 4, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
105
From VicDillahay.com
{3, 6, 7}
Sus2 built on VI.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: None
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: {3, 6, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {3, 6, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
106
From VicDillahay.com
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {5}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {R, 2}, {4, 5}
• Triads: None
• Sus2s: {R, 2, 5}, {R, 4, 5}
• 7no5s: {R, 2, 4}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 4, 5}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
107
From VicDillahay.com
{R, 4, 7}
Sus2 built on VII.
Diatonic Interval Vector:
102
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: None
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: {R, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: {R, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
108
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {2, 3}, {5, 6}
• Triads: None
• Sus2s: {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
109
From VicDillahay.com
•
110
From VicDillahay.com
7no5s on Each Degree
• On I: {R, 3, 7}
• On II: {R, 2, 4}
• On III: {2, 3, 5}
• On IV: {3, 4, 6}
• On V: {4, 5, 7}
• On VI: {R, 5, 6}
• On VII: {2, 6, 7}
111
From VicDillahay.com
{R, 3, 7}
7no5 built on I.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: None
• 3 Note Clusters: None
112
From VicDillahay.com
• 7s: {R, 3, 5, 7}
• Add9s: {R, 3, 6, 7}
• 7sus4s: {R, 3, 4, 7}
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {5}, {6}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: {2, 4, 6}
• Sus2s: {2, 5, 6}
• 7no5s: None
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
113
From VicDillahay.com
{R, 2, 4}
7no5 built on II.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: None
• 3 Note Clusters: None
114
From VicDillahay.com
• 7s: {R, 2, 4, 6}
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 2, 4, 5}
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: {3, 5, 7}
• Sus2s: {3, 6, 7}
• 7no5s: None
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
115
From VicDillahay.com
{2, 3, 5}
7no5 built on III.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: None
• 3 Note Clusters: None
116
From VicDillahay.com
• 7s: {2, 3, 5, 7}
• Add9s: {R, 2, 3, 5}
• 7sus4s: {2, 3, 5, 6}
• Add4s: None
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 7}
• 7no5s: None
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
117
From VicDillahay.com
{3, 4, 6}
7no5 built on IV.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: None
• 3 Note Clusters: None
118
From VicDillahay.com
• 7s: {R, 3, 4, 6}
• Add9s: {2, 3, 4, 6}
• 7sus4s: {3, 4, 6, 7}
• Add4s: None
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {5}, {7}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: {2, 5, 7}
• Sus2s: {R, 2, 5}
• 7no5s: None
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
119
From VicDillahay.com
{4, 5, 7}
7no5 built on V.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {4}, {5}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: None
• 3 Note Clusters: None
120
From VicDillahay.com
• 7s: {2, 4, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: {R, 4, 5, 7}
• Add4s: None
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: {R, 3, 6}
• Sus2s: {2, 3, 6}
• 7no5s: None
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
121
From VicDillahay.com
{R, 5, 6}
7no5 built on VI.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {5}, {6}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: None
• 3 Note Clusters: None
122
From VicDillahay.com
• 7s: {R, 3, 5, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 2, 5, 6}
• Add4s: None
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: {2, 4, 7}
• Sus2s: {3, 4, 7}
• 7no5s: None
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
123
From VicDillahay.com
{2, 6, 7}
7no5 built on VII.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {2}, {6}, {7}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: None
• 3 Note Clusters: None
124
From VicDillahay.com
• 7s: {2, 4, 6, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: {2, 3, 6, 7}
• Add4s: None
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}, {5}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: {R, 3, 5}
• Sus2s: {R, 4, 5}
• 7no5s: None
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
125
From VicDillahay.com
126
From VicDillahay.com
7no3s on Each Degree
• On I: {R, 5, 7}
• On II: {R, 2, 6}
• On III: {2, 3, 7}
• On IV: {R, 3, 4}
• On V: {2, 4, 5}
• On VI: {3, 5, 6}
• On VII: {4, 6, 7}
127
From VicDillahay.com
{R, 5, 7}
7no3 built on I.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {5}, {7}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
128
From VicDillahay.com
• 7s: {R, 3, 5, 7}
• Add9s: None
• 7sus4s: {R, 4, 5, 7}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: {2, 4, 6}
• Sus2s: {2, 3, 6}
• 7no5s: {3, 4, 6}
• 7no3s: None
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
129
From VicDillahay.com
{R, 2, 6}
7no3 built on II.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
130
From VicDillahay.com
• 7s: {R, 2, 4, 6}
• Add9s: None
• 7sus4s: {R, 2, 5, 6}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {5}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: {3, 5, 7}
• Sus2s: {3, 4, 7}
• 7no5s: {4, 5, 7}
• 7no3s: None
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
131
From VicDillahay.com
{2, 3, 7}
7no3 built on III.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
132
From VicDillahay.com
• 7s: {2, 3, 5, 7}
• Add9s: None
• 7sus4s: {2, 3, 6, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 5}
• 7no5s: {R, 5, 6}
• 7no3s: None
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
133
From VicDillahay.com
{R, 3, 4}
7no3 built on IV.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
134
From VicDillahay.com
• 7s: {R, 3, 4, 6}
• Add9s: None
• 7sus4s: {R, 3, 4, 7}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: {2, 5, 7}
• Sus2s: {2, 5, 6}
• 7no5s: {2, 6, 7}
• 7no3s: None
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
135
From VicDillahay.com
{2, 4, 5}
7no3 built on V.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
136
From VicDillahay.com
• 7s: {2, 4, 5, 7}
• Add9s: None
• 7sus4s: {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: {R, 3, 6}
• Sus2s: {3, 6, 7}
• 7no5s: {R, 3, 7}
• 7no3s: None
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
137
From VicDillahay.com
{3, 5, 6}
7no3 built on VI.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {3}, {5}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
138
From VicDillahay.com
• 7s: {R, 3, 5, 6}
• Add9s: None
• 7sus4s: {2, 3, 5, 6}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: {2, 4, 7}
• Sus2s: {R, 4, 7}
• 7no5s: {R, 2, 4}
• 7no3s: None
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
139
From VicDillahay.com
{4, 6, 7}
7no3 built on VII.
Diatonic Interval Vector:
111
Subsets:
• Silence: {}
• Scale Degrees: {4}, {6}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
140
From VicDillahay.com
• 7s: {2, 4, 6, 7}
• Add9s: None
• 7sus4s: {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {5}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: {R, 3, 5}
• Sus2s: {R, 2, 5}
• 7no5s: {2, 3, 5}
• 7no3s: None
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
141
From VicDillahay.com
142
From VicDillahay.com
3 Note Clusters on Each Degree
• On I: {R, 2, 3}
• On II: {2, 3, 4}
• On III: {3, 4, 5}
• On IV: {4, 5, 6}
• On V: {5, 6, 7}
• On VI: {R, 6, 7}
• On VII: {R, 2, 7}
143
From VicDillahay.com
{R, 2, 3}
3 note cluster built on I.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}
• 4ths/5ths: None
• 3rds/6ths: {R, 3}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 3}
144
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {5}, {6}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {4, 6}, {5, 7}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
145
From VicDillahay.com
{2, 3, 4}
3 note cluster built on II.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}
• 4ths/5ths: None
• 3rds/6ths: {2, 4}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {2, 3, 4}
146
From VicDillahay.com
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}
• 9ths: {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {5}, {6}, {7}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {5, 7}, {R, 6}
• 2nds/7ths: {5, 6}, {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
147
From VicDillahay.com
{3, 4, 5}
3 note cluster built on III.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {5}
• 4ths/5ths: None
• 3rds/6ths: {3, 5}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {3, 4, 5}
148
From VicDillahay.com
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {6}, {7}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
149
From VicDillahay.com
{4, 5, 6}
3 note cluster built on IV.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {4}, {5}, {6}
• 4ths/5ths: None
• 3rds/6ths: {4, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {4, 5, 6}
150
From VicDillahay.com
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {R, 3}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
151
From VicDillahay.com
{5, 6, 7}
3 note cluster built on V.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {5}, {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: {5, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {5, 6, 7}
152
From VicDillahay.com
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 3, 5, 6, 7}
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {R, 3}, {2, 4}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
153
From VicDillahay.com
{R, 6, 7}
3 note cluster built on VI.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {R}, {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 6, 7}
154
From VicDillahay.com
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {R, 3, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {2, 4}, {3, 5}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
155
From VicDillahay.com
{R, 2, 7}
3 note cluster built on VII.
Diatonic Interval Vector:
210
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {7}
• 4ths/5ths: None
• 3rds/6ths: {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 7}
156
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {5}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {3, 5}, {4, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
157
From VicDillahay.com
158
From VicDillahay.com
Sets of 4 Notes • 7ths
• Add9s
• 7sus4s
• Add4s
• 4 Note Clusters
159
From VicDillahay.com
160
From VicDillahay.com
7ths on Each Degree
• On I: {R, 3, 5, 7}
• On II: {R, 2, 4, 6}
• On III: {2, 3, 5, 7}
• On IV: {R, 3, 4, 6}
• On V: {2, 4, 5, 7}
• On VI: {R, 3, 5, 6}
• On VII: {2, 4, 6, 7}
161
From VicDillahay.com
{R, 3, 5, 7}
7th built on I.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {5}, {7}
• 4ths/5ths: {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}
• 2nds/7ths: {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: {R, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
162
From VicDillahay.com
• 7s: {R, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: None
• Triads: {2, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
163
From VicDillahay.com
{R, 2, 4, 6}
7th built on II.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {6}
• 4ths/5ths: {R, 4}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}
• Triads: {2, 4, 6}, {R, 4, 6}
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: {R, 2, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
164
From VicDillahay.com
• 7s: {R, 2, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {5}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: None
• Triads: {3, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
165
From VicDillahay.com
{2, 3, 5, 7}
7th built on III.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {5}, {7}
• 4ths/5ths: {2, 5}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}
• Triads: {3, 5, 7}, {2, 5, 7}
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: {2, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
166
From VicDillahay.com
• 7s: {2, 3, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {6}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: None
• Triads: {R, 4, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
167
From VicDillahay.com
{R, 3, 4, 6}
7th built on IV.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {6}
• 4ths/5ths: {R, 4}, {3, 6}
• 3rds/6ths: {R, 3}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}
• Triads: {R, 4, 6}, {R, 3, 6}
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: {R, 3, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
168
From VicDillahay.com
• 7s: {R, 3, 4, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {5}, {7}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: None
• Triads: {2, 5, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
169
From VicDillahay.com
{2, 4, 5, 7}
7th built on V.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {5}, {7}
• 4ths/5ths: {2, 5}, {4, 7}
• 3rds/6ths: {2, 4}, {5, 7}, {2, 7}
• 2nds/7ths: {4, 5}
• Triads: {2, 5, 7}, {2, 4, 7}
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: {2, 4, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
170
From VicDillahay.com
• 7s: {2, 4, 5, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: None
• Triads: {R, 3, 6}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
171
From VicDillahay.com
{R, 3, 5, 6}
7th built on VI.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {5}, {6}
• 4ths/5ths: {3, 6}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}, {R, 6}
• 2nds/7ths: {5, 6}
• Triads: {R, 3, 5}, {R, 3, 6}
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: {R, 3, 5, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
172
From VicDillahay.com
• 7s: {R, 3, 5, 6}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: None
• Triads: {2, 4, 7}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
173
From VicDillahay.com
{2, 4, 6, 7}
7th built on VII.
Diatonic Interval Vector:
132
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {6}, {7}
• 4ths/5ths: {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {2, 7}
• 2nds/7ths: {6, 7}
• Triads: {2, 4, 6}, {2, 4, 7}
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: {2, 4, 6, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
174
From VicDillahay.com
• 7s: {2, 4, 6, 7}
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {5}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: None
• Triads: {R, 3, 5}
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
175
From VicDillahay.com
176
From VicDillahay.com
Add9s on Each Degree
• On I: {R, 2, 3, 5}
• On II: {2, 3, 4, 6}
• On III: {3, 4, 5, 7}
• On IV: {R, 4, 5, 6}
• On V: {2, 5, 6, 7}
• On VI: {R, 3, 6, 7}
• On VII: {R, 2, 4, 7}
177
From VicDillahay.com
{R, 2, 3, 5}
Add9 built on I.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {5}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: {R, 3, 5}
• Sus2s: {R, 2, 5}
• 7no5s: {2, 3, 5}
• 7no3s: None
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
178
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {6}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
179
From VicDillahay.com
{2, 3, 4, 6}
Add9 built on II.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: {2, 4, 6}
• Sus2s: {2, 3, 6}
• 7no5s: {3, 4, 6}
• 7no3s: None
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
180
From VicDillahay.com
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {5}, {7}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
181
From VicDillahay.com
{3, 4, 5, 7}
Add9 built on III.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {5}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: {3, 5, 7}
• Sus2s: {3, 4, 7}
• 7no5s: {4, 5, 7}
• 7no3s: None
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
182
From VicDillahay.com
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
183
From VicDillahay.com
{R, 4, 5, 6}
Add9 built on IV.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 5}
• 7no5s: {R, 5, 6}
• 7no3s: None
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
184
From VicDillahay.com
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
185
From VicDillahay.com
{2, 5, 6, 7}
Add9 built on V.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {2}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: {2, 5, 7}
• Sus2s: {2, 5, 6}
• 7no5s: {2, 6, 7}
• 7no3s: None
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
186
From VicDillahay.com
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
187
From VicDillahay.com
{R, 3, 6, 7}
Add9 built on VI.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: {R, 3, 6}
• Sus2s: {3, 6, 7}
• 7no5s: {R, 3, 7}
• 7no3s: None
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
188
From VicDillahay.com
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
189
From VicDillahay.com
{R, 2, 4, 7}
Add9 built on VII.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: {2, 4, 7}
• Sus2s: {R, 4, 7}
• 7no5s: {R, 2, 4}
• 7no3s: None
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
190
From VicDillahay.com
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {5}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
191
From VicDillahay.com
192
From VicDillahay.com
7sus4s on Each Degree
• On I: {R, 4, 5, 7}
• On II: {R, 2, 5, 6}
• On III: {2, 3, 6, 7}
• On IV: {R, 3, 4, 7}
• On V: {R, 2, 4, 5}
• On VI: {2, 3, 5, 6}
• On VII: {3, 4, 6, 7}
193
From VicDillahay.com
{R, 4, 5, 7}
7sus4 built on I.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {4, 5}, {R, 7}
• Triads: None
• Sus2s: {R, 4, 5}, {R, 4, 7}
• 7no5s: {4, 5, 7}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 4, 5, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
194
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {R, 4, 5, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: None
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: {2, 3, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
195
From VicDillahay.com
{R, 2, 5, 6}
7sus4 built on II.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {5}, {6}
• 4ths/5ths: {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {R, 2}, {5, 6}
• Triads: None
• Sus2s: {R, 2, 5}, {2, 5, 6}
• 7no5s: {R, 5, 6}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
196
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: None
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: {3, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
197
From VicDillahay.com
{2, 3, 6, 7}
7sus4 built on III.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {2, 3}, {6, 7}
• Triads: None
• Sus2s: {2, 3, 6}, {3, 6, 7}
• 7no5s: {2, 6, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
198
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {5}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: None
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: {R, 4, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
199
From VicDillahay.com
{R, 3, 4, 7}
7sus4 built on IV.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {3, 4}, {R, 7}
• Triads: None
• Sus2s: {3, 4, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 3, 4, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
200
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {R, 3, 4, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {5}, {6}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: None
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: {2, 5, 6}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
201
From VicDillahay.com
{R, 2, 4, 5}
7sus4 built on V.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {5}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {R, 2}, {4, 5}
• Triads: None
• Sus2s: {R, 2, 5}, {R, 4, 5}
• 7no5s: {R, 2, 4}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 4, 5}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
202
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {R, 2, 4, 5}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: None
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: {3, 6, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
203
From VicDillahay.com
{2, 3, 5, 6}
7sus4 built on VI.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {2, 3}, {5, 6}
• Triads: None
• Sus2s: {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
204
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {2, 3, 5, 6}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: None
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: {R, 4, 7}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
205
From VicDillahay.com
{3, 4, 6, 7}
7sus4 built on VII.
Diatonic Interval Vector:
213
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {3, 4}, {6, 7}
• Triads: None
• Sus2s: {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: {3, 4, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
206
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: {3, 4, 6, 7}
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {5}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: None
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: {R, 2, 5}
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
207
From VicDillahay.com
208
From VicDillahay.com
Add4s on Each Degree
• On I: {R, 3, 4, 5}
• On II: {2, 4, 5, 6}
• On III: {3, 5, 6, 7}
• On IV: {R, 4, 6, 7}
• On V: {R, 2, 5, 7}
• On VI: {R, 2, 3, 6}
• On VII: {2, 3, 4, 7}
209
From VicDillahay.com
{R, 3, 4, 5}
Add4 built on I.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {5}
• 4ths/5ths: {R, 4}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: {R, 3, 5}
• Sus2s: {R, 4, 5}
• 7no5s: None
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
210
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {6}, {7}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {2, 7}
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
211
From VicDillahay.com
{2, 4, 5, 6}
Add4 built on II.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {5}, {6}
• 4ths/5ths: {2, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: {2, 4, 6}
• Sus2s: {2, 5, 6}
• 7no5s: None
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
212
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {R, 3}
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
213
From VicDillahay.com
{3, 5, 6, 7}
Add4 built on III.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {3}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: {3, 5, 7}
• Sus2s: {3, 6, 7}
• 7no5s: None
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
214
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {2, 4}
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
215
From VicDillahay.com
{R, 4, 6, 7}
Add4 built on IV.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}
• 3rds/6ths: {4, 6}, {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 7}
• 7no5s: None
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
216
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {3, 5}
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
217
From VicDillahay.com
{R, 2, 5, 7}
Add4 built on V.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {5}, {7}
• 4ths/5ths: {2, 5}, {R, 5}
• 3rds/6ths: {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: {2, 5, 7}
• Sus2s: {R, 2, 5}
• 7no5s: None
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
218
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {4, 6}
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
219
From VicDillahay.com
{R, 2, 3, 6}
Add4 built on VI.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {6}
• 4ths/5ths: {3, 6}, {2, 6}
• 3rds/6ths: {R, 3}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: {R, 3, 6}
• Sus2s: {2, 3, 6}
• 7no5s: None
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
220
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {5}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {5, 7}
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
221
From VicDillahay.com
{2, 3, 4, 7}
Add4 built on VII.
Diatonic Interval Vector:
222
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {7}
• 4ths/5ths: {4, 7}, {3, 7}
• 3rds/6ths: {2, 4}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: {2, 4, 7}
• Sus2s: {3, 4, 7}
• 7no5s: None
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
222
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {5}, {6}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {R, 6}
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
223
From VicDillahay.com
224
From VicDillahay.com
4 Note Clusters on Each Degree
• On I: {R, 2, 3, 4}
• On II: {2, 3, 4, 5}
• On III: {3, 4, 5, 6}
• On IV: {4, 5, 6, 7}
• On V: {R, 5, 6, 7}
• On VI: {R, 2, 6, 7}
• On VII: {R, 2, 3, 7}
225
From VicDillahay.com
{R, 2, 3, 4}
4 note cluster built on I.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: {R, 3}, {2, 4}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: {R, 2, 4}
• 7no3s: {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
226
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {5}, {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: {5, 7}
• 2nds/7ths: {5, 6}, {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
227
From VicDillahay.com
{2, 3, 4, 5}
4 note cluster built on II.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: {2, 4}, {3, 5}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: {2, 3, 5}
• 7no3s: {2, 4, 5}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
228
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: {R, 6}
• 2nds/7ths: {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
229
From VicDillahay.com
{3, 4, 5, 6}
4 note cluster built on III.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {5}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: {3, 5}, {4, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: {3, 4, 6}
• 7no3s: {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
230
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: None
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {7}
• 4ths/5ths: None
• 3rds/6ths: {2, 7}
• 2nds/7ths: {R, 2}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
231
From VicDillahay.com
{4, 5, 6, 7}
4 note cluster built on IV.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {4}, {5}, {6}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: {4, 6}, {5, 7}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: {4, 5, 7}
• 7no3s: {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
232
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}, {3}
• 4ths/5ths: None
• 3rds/6ths: {R, 3}
• 2nds/7ths: {R, 2}, {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {R, 2, 3}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
233
From VicDillahay.com
{R, 5, 6, 7}
4 note cluster built on V.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {R}, {5}, {6}, {7}
• 4ths/5ths: {R, 5}
• 3rds/6ths: {5, 7}, {R, 6}
• 2nds/7ths: {5, 6}, {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 5, 6}
• 7no3s: {R, 5, 7}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
234
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}, {4}
• 4ths/5ths: None
• 3rds/6ths: {2, 4}
• 2nds/7ths: {2, 3}, {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {2, 3, 4}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
235
From VicDillahay.com
{R, 2, 6, 7}
4 note cluster built on VI.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {6}, {7}
• 4ths/5ths: {2, 6}
• 3rds/6ths: {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {6, 7}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {2, 6, 7}
• 7no3s: {R, 2, 6}
• 3 Note Clusters: {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
236
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: None
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}, {5}
• 4ths/5ths: None
• 3rds/6ths: {3, 5}
• 2nds/7ths: {3, 4}, {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {3, 4, 5}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
237
From VicDillahay.com
{R, 2, 3, 7}
4 note cluster built on VII.
Diatonic Interval Vector:
321
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: {R, 3}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: {R, 3, 7}
• 7no3s: {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 2, 7}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
238
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {5}, {6}
• 4ths/5ths: None
• 3rds/6ths: {4, 6}
• 2nds/7ths: {4, 5}, {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: {4, 5, 6}
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
239
From VicDillahay.com
240
From VicDillahay.com
Sets of 5 Notes • 9ths
• 6/9s
• 5 Note Clusters
241
From VicDillahay.com
242
From VicDillahay.com
9ths on Each Degree
• On I: {R, 2, 3, 5, 7}
• On II: {R, 2, 3, 4, 6}
• On III: {2, 3, 4, 5, 7}
• On IV: {R, 3, 4, 5, 6}
• On V: {2, 4, 5, 6, 7}
• On VI: {R, 3, 5, 6, 7}
• On VII: {R, 2, 4, 6, 7}
243
From VicDillahay.com
{R, 2, 3, 5, 7}
9th built on I.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {5}, {7}
• 4ths/5ths: {2, 5}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}
• Sus2s: {R, 2, 5}
• 7no5s: {R, 3, 7}, {2, 3, 5}
• 7no3s: {R, 5, 7}, {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}
• Add9s: {R, 2, 3, 5}
• 7sus4s: None
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
244
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {6}
• 4ths/5ths: None
• 3rds/6ths: {4, 6}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
245
From VicDillahay.com
{R, 2, 3, 4, 6}
9th built on II.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {6}
• 4ths/5ths: {R, 4}, {3, 6}, {2, 6}
• 3rds/6ths: {R, 3}, {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}
• Triads: {2, 4, 6}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {2, 3, 6}
• 7no5s: {R, 2, 4}, {3, 4, 6}
• 7no3s: {R, 2, 6}, {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}
• Add9s: {2, 3, 4, 6}
• 7sus4s: None
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
246
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 3, 4, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {5}, {7}
• 4ths/5ths: None
• 3rds/6ths: {5, 7}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
247
From VicDillahay.com
{2, 3, 4, 5, 7}
9th built on III.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {5}, {7}
• 4ths/5ths: {2, 5}, {4, 7}, {3, 7}
• 3rds/6ths: {2, 4}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}
• Triads: {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {3, 4, 7}
• 7no5s: {2, 3, 5}, {4, 5, 7}
• 7no3s: {2, 3, 7}, {2, 4, 5}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: None
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {2, 3, 4, 5}
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
248
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 3, 4, 5, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {2, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {6}
• 4ths/5ths: None
• 3rds/6ths: {R, 6}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
249
From VicDillahay.com
{R, 3, 4, 5, 6}
9th built on IV.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {3, 6}, {R, 5}
• 3rds/6ths: {R, 3}, {3, 5}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}
• Triads: {R, 3, 5}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {R, 4, 5}
• 7no5s: {3, 4, 6}, {R, 5, 6}
• 7no3s: {R, 3, 4}, {3, 5, 6}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}
• 7s: {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: None
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {3, 4, 5, 6}
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
250
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 3, 4, 5, 6}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {7}
• 4ths/5ths: None
• 3rds/6ths: {2, 7}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
251
From VicDillahay.com
{2, 4, 5, 6, 7}
9th built on V.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {2}, {4}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {5, 7}, {2, 7}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}
• Triads: {2, 4, 6}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {2, 5, 6}
• 7no5s: {4, 5, 7}, {2, 6, 7}
• 7no3s: {2, 4, 5}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}
• 7s: {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: None
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {4, 5, 6, 7}
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
252
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {2, 4, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {3}
• 4ths/5ths: None
• 3rds/6ths: {R, 3}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
253
From VicDillahay.com
{R, 3, 5, 6, 7}
9th built on VI.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {R, 6}
• 2nds/7ths: {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {R, 3, 6}
• Sus2s: {3, 6, 7}
• 7no5s: {R, 3, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}
• 7s: {R, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 3, 6, 7}
• 7sus4s: None
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {R, 5, 6, 7}
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
254
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 3, 5, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {4}
• 4ths/5ths: None
• 3rds/6ths: {2, 4}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
255
From VicDillahay.com
{R, 2, 4, 6, 7}
9th built on VII.
Diatonic Interval Vector:
343
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {2, 4, 7}
• Sus2s: {R, 4, 7}
• 7no5s: {R, 2, 4}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {2, 4, 6, 7}
• Add9s: {R, 2, 4, 7}
• 7sus4s: None
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {R, 2, 6, 7}
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
256
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: {R, 2, 4, 6, 7}
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {5}
• 4ths/5ths: None
• 3rds/6ths: {3, 5}
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
257
From VicDillahay.com
258
From VicDillahay.com
6/9s on Each Degree
• On I: {R, 2, 3, 5, 6}
• On II: {2, 3, 4, 6, 7}
• On III: {R, 3, 4, 5, 7}
• On IV: {R, 2, 4, 5, 6}
• On V: {2, 3, 5, 6, 7}
• On VI: {R, 3, 4, 6, 7}
• On VII: {R, 2, 4, 5, 7}
259
From VicDillahay.com
{R, 2, 3, 5, 6}
6/9 built on I.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 3}, {3, 5}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {5, 6}
• Triads: {R, 3, 5}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}
• 7s: {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 5, 6}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
260
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 3, 5, 6}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {7}
• 4ths/5ths: {4, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
261
From VicDillahay.com
{2, 3, 4, 6, 7}
6/9 built on II.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 4}, {4, 6}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {6, 7}
• Triads: {2, 4, 6}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {4, 6, 7}
• 3 Note Clusters: {2, 3, 4}
• 7s: {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}
• 7sus4s: {2, 3, 6, 7}, {3, 4, 6, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
262
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {5}
• 4ths/5ths: {R, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
263
From VicDillahay.com
{R, 3, 4, 5, 7}
6/9 built on III.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}
• Sus2s: {3, 4, 7}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {R, 3, 4}
• 3 Note Clusters: {3, 4, 5}
• 7s: {R, 3, 5, 7}
• Add9s: {3, 4, 5, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
264
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {6}
• 4ths/5ths: {2, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
265
From VicDillahay.com
{R, 2, 4, 5, 6}
6/9 built on IV.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {4, 5}, {5, 6}
• Triads: {2, 4, 6}, {R, 4, 6}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {2, 5, 6}
• 7no5s: {R, 2, 4}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {2, 4, 5}
• 3 Note Clusters: {4, 5, 6}
• 7s: {R, 2, 4, 6}
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
266
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 6}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {7}
• 4ths/5ths: {3, 7}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
267
From VicDillahay.com
{2, 3, 5, 6, 7}
6/9 built on V.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {5, 6}, {6, 7}
• Triads: {3, 5, 7}, {2, 5, 7}
• Sus2s: {2, 3, 6}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {2, 3, 5}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {3, 5, 6}
• 3 Note Clusters: {5, 6, 7}
• 7s: {2, 3, 5, 7}
• Add9s: {2, 5, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
268
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {2, 3, 5, 6, 7}
• 5 Note Clusters: None
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {4}
• 4ths/5ths: {R, 4}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
269
From VicDillahay.com
{R, 3, 4, 6, 7}
6/9 built on VI.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}, {4, 6}, {R, 6}
• 2nds/7ths: {3, 4}, {6, 7}, {R, 7}
• Triads: {R, 4, 6}, {R, 3, 6}
• Sus2s: {3, 4, 7}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {3, 4, 6}
• 7no3s: {R, 3, 4}, {4, 6, 7}
• 3 Note Clusters: {R, 6, 7}
• 7s: {R, 3, 4, 6}
• Add9s: {R, 3, 6, 7}
• 7sus4s: {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
270
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 3, 4, 6, 7}
• 5 Note Clusters: None
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {5}
• 4ths/5ths: {2, 5}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
271
From VicDillahay.com
{R, 2, 4, 5, 7}
6/9 built on VII.
Diatonic Interval Vector:
334
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}
• 3rds/6ths: {2, 4}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {4, 5}, {R, 7}
• Triads: {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 2, 4}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 7}
• 7s: {2, 4, 5, 7}
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 4, 5}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
272
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: {R, 2, 4, 5, 7}
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {6}
• 4ths/5ths: {3, 6}
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
273
From VicDillahay.com
274
From VicDillahay.com
5 Note Clusters on Each Degree
• On I: {R, 2, 3, 4, 5}
• On II: {2, 3, 4, 5, 6}
• On III: {3, 4, 5, 6, 7}
• On IV: {R, 4, 5, 6, 7}
• On V: {R, 2, 5, 6, 7}
• On VI: {R, 2, 3, 6, 7}
• On VII: {R, 2, 3, 4, 7}
275
From VicDillahay.com
{R, 2, 3, 4, 5}
5 note cluster built on I.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {5}
• 4ths/5ths: {R, 4}, {2, 5}, {R, 5}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}
• Triads: {R, 3, 5}
• Sus2s: {R, 2, 5}, {R, 4, 5}
• 7no5s: {R, 2, 4}, {2, 3, 5}
• 7no3s: {R, 3, 4}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}
• 7s: None
• Add9s: {R, 2, 3, 5}
• 7sus4s: {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
276
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 5}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {6}, {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {6, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
277
From VicDillahay.com
{2, 3, 4, 5, 6}
5 note cluster built on II.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {5}, {6}
• 4ths/5ths: {2, 5}, {3, 6}, {2, 6}
• 3rds/6ths: {2, 4}, {3, 5}, {4, 6}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}, {5, 6}
• Triads: {2, 4, 6}
• Sus2s: {2, 3, 6}, {2, 5, 6}
• 7no5s: {2, 3, 5}, {3, 4, 6}
• 7no3s: {2, 4, 5}, {3, 5, 6}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}, {4, 5, 6}
• 7s: None
• Add9s: {2, 3, 4, 6}
• 7sus4s: {2, 3, 5, 6}
• Add4s: {2, 4, 5, 6}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
278
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 7}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
279
From VicDillahay.com
{3, 4, 5, 6, 7}
5 note cluster built on III.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {3, 6}, {4, 7}, {3, 7}
• 3rds/6ths: {3, 5}, {4, 6}, {5, 7}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}, {6, 7}
• Triads: {3, 5, 7}
• Sus2s: {3, 4, 7}, {3, 6, 7}
• 7no5s: {3, 4, 6}, {4, 5, 7}
• 7no3s: {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}, {5, 6, 7}
• 7s: None
• Add9s: {3, 4, 5, 7}
• 7sus4s: {3, 4, 6, 7}
• Add4s: {3, 5, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
280
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {3, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}, {2}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {R, 2}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
281
From VicDillahay.com
{R, 4, 5, 6, 7}
5 note cluster built on IV.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {R}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {R, 5}
• 3rds/6ths: {4, 6}, {5, 7}, {R, 6}
• 2nds/7ths: {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 4, 6}
• Sus2s: {R, 4, 5}, {R, 4, 7}
• 7no5s: {4, 5, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}, {R, 6, 7}
• 7s: None
• Add9s: {R, 4, 5, 6}
• 7sus4s: {R, 4, 5, 7}
• Add4s: {R, 4, 6, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
282
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 4, 5, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}, {3}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {2, 3}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
283
From VicDillahay.com
{R, 2, 5, 6, 7}
5 note cluster built on V.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {R, 5}, {2, 6}
• 3rds/6ths: {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {5, 6}, {6, 7}, {R, 7}
• Triads: {2, 5, 7}
• Sus2s: {R, 2, 5}, {2, 5, 6}
• 7no5s: {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}
• 3 Note Clusters: {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: {2, 5, 6, 7}
• 7sus4s: {R, 2, 5, 6}
• Add4s: {R, 2, 5, 7}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
284
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 5, 6, 7}
• 11ths: {R, 2, 4, 5, 6, 7}, {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}, {4}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {3, 4}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
285
From VicDillahay.com
{R, 2, 3, 6, 7}
5 note cluster built on VI.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {6}, {7}
• 4ths/5ths: {3, 6}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {6, 7}, {R, 7}
• Triads: {R, 3, 6}
• Sus2s: {2, 3, 6}, {3, 6, 7}
• 7no5s: {R, 3, 7}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {2, 3, 7}
• 3 Note Clusters: {R, 2, 3}, {R, 6, 7}, {R, 2, 7}
• 7s: None
• Add9s: {R, 3, 6, 7}
• 7sus4s: {2, 3, 6, 7}
• Add4s: {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
286
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}, {5}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {4, 5}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
287
From VicDillahay.com
{R, 2, 3, 4, 7}
5 note cluster built on VII.
Diatonic Interval Vector:
433
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {7}
• 4ths/5ths: {R, 4}, {4, 7}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {R, 7}
• Triads: {2, 4, 7}
• Sus2s: {3, 4, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}
• 7no3s: {2, 3, 7}, {R, 3, 4}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {R, 2, 7}
• 7s: None
• Add9s: {R, 2, 4, 7}
• 7sus4s: {R, 3, 4, 7}
• Add4s: {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 3, 7}
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: None
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
288
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {5}, {6}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: {5, 6}
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
289
From VicDillahay.com
290
From VicDillahay.com
Sets of 6 Notes • 11ths
291
From VicDillahay.com
292
From VicDillahay.com
11ths on Each Degree
• On I: {R, 2, 3, 4, 5, 7}
• On II: {R, 2, 3, 4, 5, 6}
• On III: {2, 3, 4, 5, 6, 7}
• On IV: {R, 3, 4, 5, 6, 7}
• On V: {R, 2, 4, 5, 6, 7}
• On VI: {R, 2, 3, 5, 6, 7}
• On VII: {R, 2, 3, 4, 6, 7}
293
From VicDillahay.com
{R, 2, 3, 4, 5, 7}
11th built on I.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {5, 7}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {3, 4, 7}, {R, 4, 5}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {2, 3, 5}, {4, 5, 7}
• 7no3s: {R, 5, 7}, {2, 3, 7}, {R, 3, 4}, {2, 4, 5}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {2, 4, 5, 7}
• Add9s: {R, 2, 3, 5}, {3, 4, 5, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}
• Add4s: {R, 3, 4, 5}, {R, 2, 5, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {2, 3, 4, 5, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
294
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {6}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
295
From VicDillahay.com
{R, 2, 3, 4, 5, 6}
11th built on II.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {6}
• 4ths/5ths: {R, 4}, {2, 5}, {3, 6}, {R, 5}, {2, 6}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {4, 6}, {R, 6}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}
• Triads: {R, 3, 5}, {2, 4, 6}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {R, 4, 5}, {2, 5, 6}
• 7no5s: {R, 2, 4}, {2, 3, 5}, {3, 4, 6}, {R, 5, 6}
• 7no3s: {R, 2, 6}, {R, 3, 4}, {2, 4, 5}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {R, 4, 5, 6}
• 7sus4s: {R, 2, 5, 6}, {R, 2, 4, 5}, {2, 3, 5, 6}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}
• 9ths: {R, 2, 3, 4, 6}, {R, 3, 4, 5, 6}
• 6/9s: {R, 2, 3, 5, 6}, {R, 2, 4, 5, 6}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}
• 11ths: {R, 2, 3, 4, 5, 6}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
296
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 5, 6}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {7}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
297
From VicDillahay.com
{2, 3, 4, 5, 6, 7}
11th built on III.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {2}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {2, 4}, {3, 5}, {4, 6}, {5, 7}, {2, 7}
• 2nds/7ths: {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}
• Triads: {2, 4, 6}, {3, 5, 7}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {2, 3, 5}, {3, 4, 6}, {4, 5, 7}, {2, 6, 7}
• 7no3s: {2, 3, 7}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {2, 3, 4}, {3, 4, 5}, {4, 5, 6}, {5, 6, 7}
• 7s: {2, 3, 5, 7}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {3, 4, 5, 7}, {2, 5, 6, 7}
• 7sus4s: {2, 3, 6, 7}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {2, 4, 5, 6}, {3, 5, 6, 7}, {2, 3, 4, 7}
• 4 Note Clusters: {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}
• 9ths: {2, 3, 4, 5, 7}, {2, 4, 5, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}
• 11ths: {2, 3, 4, 5, 6, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
298
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {2, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {R}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
299
From VicDillahay.com
{R, 3, 4, 5, 6, 7}
11th built on IV.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {R, 5}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {4, 6}, {5, 7}, {R, 6}
• 2nds/7ths: {3, 4}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {R, 4, 6}, {R, 3, 6}
• Sus2s: {3, 4, 7}, {R, 4, 5}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {3, 4, 6}, {4, 5, 7}, {R, 5, 6}
• 7no3s: {R, 5, 7}, {R, 3, 4}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {3, 4, 5}, {4, 5, 6}, {5, 6, 7}, {R, 6, 7}
• 7s: {R, 3, 5, 7}, {R, 3, 4, 6}, {R, 3, 5, 6}
• Add9s: {3, 4, 5, 7}, {R, 4, 5, 6}, {R, 3, 6, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {3, 5, 6, 7}, {R, 4, 6, 7}
• 4 Note Clusters: {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}
• 9ths: {R, 3, 4, 5, 6}, {R, 3, 5, 6, 7}
• 6/9s: {R, 3, 4, 5, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}
• 11ths: {R, 3, 4, 5, 6, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
300
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 3, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {2}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
301
From VicDillahay.com
{R, 2, 4, 5, 6, 7}
11th built on V.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {4, 7}, {R, 5}, {2, 6}
• 3rds/6ths: {2, 4}, {4, 6}, {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {2, 5, 7}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {R, 4, 5}, {2, 5, 6}, {R, 4, 7}
• 7no5s: {R, 2, 4}, {4, 5, 7}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 4, 5}, {4, 6, 7}
• 3 Note Clusters: {4, 5, 6}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {2, 4, 5, 7}, {2, 4, 6, 7}
• Add9s: {R, 4, 5, 6}, {2, 5, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {R, 2, 4, 5}
• Add4s: {2, 4, 5, 6}, {R, 4, 6, 7}, {R, 2, 5, 7}
• 4 Note Clusters: {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7}
• 9ths: {2, 4, 5, 6, 7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 4, 5, 6}, {R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7}
• 11ths: {R, 2, 4, 5, 6, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
302
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 4, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {3}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
303
From VicDillahay.com
{R, 2, 3, 5, 6, 7}
11th built on VI.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {5}, {6}, {7}
• 4ths/5ths: {2, 5}, {3, 6}, {R, 5}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {3, 5}, {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {3, 5, 7}, {2, 5, 7}, {R, 3, 6}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {2, 5, 6}, {3, 6, 7}
• 7no5s: {R, 3, 7}, {2, 3, 5}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 3, 7}, {3, 5, 6}
• 3 Note Clusters: {R, 2, 3}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {2, 3, 5, 7}, {R, 3, 5, 6}
• Add9s: {R, 2, 3, 5}, {2, 5, 6, 7}, {R, 3, 6, 7}
• 7sus4s: {R, 2, 5, 6}, {2, 3, 6, 7}, {2, 3, 5, 6}
• Add4s: {3, 5, 6, 7}, {R, 2, 5, 7}, {R, 2, 3, 6}
• 4 Note Clusters: {R, 5, 6, 7}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 3, 5, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 5, 6, 7}
• 5 Note Clusters: {R, 2, 5, 6, 7}, {R, 2, 3, 6, 7}
• 11ths: {R, 2, 3, 5, 6, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
304
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 5, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {4}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
305
From VicDillahay.com
{R, 2, 3, 4, 6, 7}
11th built on VII.
Diatonic Interval Vector:
555
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {6}, {7}
• 4ths/5ths: {R, 4}, {3, 6}, {4, 7}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {4, 6}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {6, 7}, {R, 7}
• Triads: {2, 4, 6}, {R, 4, 6}, {R, 3, 6}, {2, 4, 7}
• Sus2s: {2, 3, 6}, {3, 4, 7}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {3, 4, 6}, {2, 6, 7}
• 7no3s: {R, 2, 6}, {2, 3, 7}, {R, 3, 4}, {4, 6, 7}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 2, 4, 6}, {R, 3, 4, 6}, {2, 4, 6, 7}
• Add9s: {2, 3, 4, 6}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {2, 3, 6, 7}, {R, 3, 4, 7}, {3, 4, 6, 7}
• Add4s: {R, 4, 6, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {R, 2, 6, 7}, {R, 2, 3, 7}
• 9ths: {R, 2, 3, 4, 6}, {R, 2, 4, 6, 7}
• 6/9s: {2, 3, 4, 6, 7}, {R, 3, 4, 6, 7}
• 5 Note Clusters: {R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 6, 7}
• 13ths: None
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
306
From VicDillahay.com
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: {5}
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
307
From VicDillahay.com
308
From VicDillahay.com
Set of 7 Notes • 13ths
309
From VicDillahay.com
310
From VicDillahay.com
13ths on Each Degree
• On I: {R, 2, 3, 4, 5, 6, 7}
• On II: {R, 2, 3, 4, 5, 6, 7}
• On III: {R, 2, 3, 4, 5, 6, 7}
• On IV: {R, 2, 3, 4, 5, 6, 7}
• On V: {R, 2, 3, 4, 5, 6, 7}
• On VI: {R, 2, 3, 4, 5, 6, 7}
• On VII: {R, 2, 3, 4, 5, 6, 7}
311
From VicDillahay.com
{R, 2, 3, 4, 5, 6, 7}
13th built on I.
Diatonic Interval Vector:
777
Subsets:
• Silence: {}
• Scale Degrees: {R}, {2}, {3}, {4}, {5}, {6}, {7}
• 4ths/5ths: {R, 4}, {2, 5}, {3, 6}, {4, 7}, {R, 5}, {2, 6}, {3, 7}
• 3rds/6ths: {R, 3}, {2, 4}, {3, 5}, {4, 6}, {5, 7}, {R, 6}, {2, 7}
• 2nds/7ths: {R, 2}, {2, 3}, {3, 4}, {4, 5}, {5, 6}, {6, 7}, {R, 7}
• Triads: {R, 3, 5}, {2, 4, 6}, {3, 5, 7}, {R, 4, 6}, {2, 5, 7}, {R, 3, 6}, {2, 4, 7}
• Sus2s: {R, 2, 5}, {2, 3, 6}, {3, 4, 7}, {R, 4, 5}, {2, 5, 6}, {3, 6, 7}, {R, 4, 7}
• 7no5s: {R, 3, 7}, {R, 2, 4}, {2, 3, 5}, {3, 4, 6}, {4, 5, 7}, {R, 5, 6}, {2, 6, 7}
• 7no3s: {R, 5, 7}, {R, 2, 6}, {2, 3, 7}, {R, 3, 4}, {2, 4, 5}, {3, 5, 6}, {4, 6, 7}
• 3 Note Clusters: {R, 2, 3}, {2, 3, 4}, {3, 4, 5}, {4, 5, 6}, {5, 6, 7}, {R, 6, 7}, {R, 2, 7}
• 7s: {R, 3, 5, 7}, {R, 2, 4, 6}, {2, 3, 5, 7}, {R, 3, 4, 6}, {2, 4, 5, 7}, {R, 3, 5, 6}, {2, 4, 6, 7}
• Add9s: {R, 2, 3, 5}, {2, 3, 4, 6}, {3, 4, 5, 7}, {R, 4, 5, 6}, {2, 5, 6, 7}, {R, 3, 6, 7}, {R, 2, 4, 7}
• 7sus4s: {R, 4, 5, 7}, {R, 2, 5, 6}, {2, 3, 6, 7}, {R, 3, 4, 7}, {R, 2, 4, 5}, {2, 3, 5, 6}, {3, 4, 6, 7}
• Add4s: {R, 3, 4, 5}, {2, 4, 5, 6}, {3, 5, 6, 7}, {R, 4, 6, 7}, {R, 2, 5, 7}, {R, 2, 3, 6}, {2, 3, 4, 7}
• 4 Note Clusters: {R, 2, 3, 4}, {2, 3, 4, 5}, {3, 4, 5, 6}, {4, 5, 6, 7}, {R, 5, 6, 7}, {R, 2, 6, 7},
{R, 2, 3, 7}
• 9ths: {R, 2, 3, 5, 7}, {R, 2, 3, 4, 6}, {2, 3, 4, 5, 7}, {R, 3, 4, 5, 6}, {2, 4, 5, 6, 7}, {R, 3, 5, 6,
7}, {R, 2, 4, 6, 7}
• 6/9s: {R, 2, 3, 5, 6}, {2, 3, 4, 6, 7}, {R, 3, 4, 5, 7}, {R, 2, 4, 5, 6}, {2, 3, 5, 6, 7}, {R, 3, 4, 6, 7},
{R, 2, 4, 5, 7}
• 5 Note Clusters: {R, 2, 3, 4, 5}, {2, 3, 4, 5, 6}, {3, 4, 5, 6, 7}, {R, 4, 5, 6, 7}, {R, 2, 5, 6, 7},
{R, 2, 3, 6, 7}, {R, 2, 3, 4, 7}
• 11ths: {R, 2, 3, 4, 5, 7}, {R, 2, 3, 4, 5, 6}, {2, 3, 4, 5, 6, 7}, {R, 3, 4, 5, 6, 7}, {R, 2, 4, 5, 6, 7},
{R, 2, 3, 5, 6, 7}, {R, 2, 3, 4, 6, 7}
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Supersets:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
312
From VicDillahay.com
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: {R, 2, 3, 4, 5, 6, 7}
Sets Without Common Tones:
• Scale Degrees: None
• 4ths/5ths: None
• 3rds/6ths: None
• 2nds/7ths: None
• Triads: None
• Sus2s: None
• 7no5s: None
• 7no3s: None
• 3 Note Clusters: None
• 7s: None
• Add9s: None
• 7sus4s: None
• Add4s: None
• 4 Note Clusters: None
• 9ths: None
• 6/9s: None
• 5 Note Clusters: None
• 11ths: None
• 13ths: None
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From VicDillahay.com
Diatonic Interval Vectors for Each Set Type • Scale Degrees: 000
• 4ths/5ths: 001
• 3rds/6ths: 010
• 2nds/7ths: 100
• Triads: 021
• Sus2s: 102
• 7no5s: 111
• 7no3s: 111
• 3 Note Clusters: 210
• 7ths: 132
• Add9s: 222
• 7sus4s: 213
• Add4s: 222
• 4 Note Clusters: 321
• 9ths: 343
• 6/9s: 334
• 5 Note Clusters: 433
• 11ths: 555
• 13ths: 777
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From VicDillahay.com
Diatonic Steps in Each Set Type The are the number of 2nds between each note, listed in order. A7 is {R, 3, 5, 7} and has two steps
from R to 3, two steps from 3 to 5, two steps from 5 to 7, and one step from 7 to R so it is listed here as
{2, 2, 2, 1}.
A few sets have inverted to form a more common chord. The most compact form for each of these
cases is written in parenthesis.
• Scale Degrees: 7
• 4ths/5ths: 3, 4
• 3rds/6ths: 2, 5
• 2nds/7ths: 1, 6
• Triads: 2, 2, 3
• Sus2s: 1, 3, 3
• 7no5s: 2, 4, 1 (Most compact form is 1, 2, 4)
• 7no3s: 4, 2, 1 (Most compact form is 2, 1, 4)
• 3 Note Clusters: 1, 1, 5
• 7ths: 2, 2, 2, 1
• Add9s: 1, 1, 2, 3
• 7sus4s: 3, 1, 2, 1 (most compact form is 1, 2, 1, 3)
• Add4s: 2, 1, 1, 3
• 4 Note Clusters: 1, 1, 1, 4
• 9ths: 1, 1, 2, 2, 1 (most compact form is 1, 1, 1, 2, 2)
• 6/9s: 1, 1, 2, 1, 2
• 5 Note Clusters: 1, 1, 1, 1, 3
• 11ths: 1, 1, 1, 1, 2, 1
• 13ths: 1, 1, 1, 1, 1, 1, 1
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From VicDillahay.com
Ideas for Using This Book in Jazz
Reharmonizing Standards with 4 note chords:
• Select a mode for each chord and decide how many substitute chords will be based on it.
• For the first chord from each mode, look up any 4 note subset of {R, 2, 3, 4, 5, 6, 7}.
• For the next chord, find the 3 note set under "No Common Tones" and turn to its page. Select
any of its 4 note supersets for the 2nd chord.
• Continue this process for each additional substitute chord.
Using this system, Gmaj7 / Gmaj7 / Gmin7 / C7 with 2 chords per measure becomes Gmaj7 A(add9) /
D(add4) F7sus4 / Gm(add9) Bm7 / D7sus4 Bbmaj7sus4.
Modal Comping:
• Select any set from the mode.
• Look up the set with no common tones and use any of its subsets or superesets.
A possible modal vamp on D Dorian is Dm9 G7no5 / Am(add11) Cmaj7sus4.
Generic Modality Compression
If you would like to quickly find sets for use in Generic Modality Compression (outlined in Creative
Chordal Harmony for Guitar by Mick Goodrick and Tim Miller, Berklee Press 2012), look up the
mode minus the root. Goodrick and Miller use only the 3 note subsets, but any other subsets may be
used.
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