Factorial Thinking (Combinations applied to music)

Today’s’ tip has to do with mathematics applied to music…we have already seen how in the finger combinations exercises we have used all the possible combinations of 2,3 and 4 fingers of our left hand to make sure we cover every possible motion. This is not only a great warm up and technical exercise, but also a way to keep your brain connected.

Let’s see how we can now apply this to notes, chords, arpeggios, and so on. These are the combinations we have see in the previous post:

Finger combinations (combinations of all numbers from 1 to 4 as left hand fingers are numbered that way on guitar)

12 13 14
21 23 24
31 32 34
41 42 43

123 124 132 134 142 143
213 214 231 234 241 243
312 314 321 324 341 342
412 413 421 423 431 432

1234 1243 1324 1342 1423 1432
2134 2143 2314 2341 2413 2431
3124 3142 3214 3241 2413 2431
4123 4132 4213 4231 4312 4321

Let’s apply this to a 7th arpeggio: I will replace all the 2 with 3s, the 3 with 5s and the 4 with 7s.

Combinations applied to Chord Tones

13 15 17
31 35 37
51 53 57
71 73 75

135 137 153 157 173 175
315 317 351 357 371 375
513 517 531 537 571 573
713 715 731 735 751 753

1357 1375 1537 1573 1735 1753
3157 3175 3517 3571 3715 3751
5137 5173 5317 5371 3715 3751
7135 7153 7315 7351 7513 7531

Let’s make an example in the key of C: this is Cmaj7 every possible combination of the four notes.

Combinations applied to Chord Tones of Cmaj7

CE CG CB
EC EG EB
GC GE GB
BC BE BG

CEG CEB CGE CGB CBE CBG
ECG ECB EGC EGB EBC EBG
3GCE GCB GEC GEB GBC GBE
BCE BCG BEC BEG BGC BGE

CEGB CEBG CGEB CGBE CBEG CBGE
ECGB ECBG EGCB EGBC EBCG EBGC
GCEB GCBE GECB GEBC EBCG EBGC
BCEG BCGE BECG BEGC BGCE BGEC

Obviously this is not music as such, but I always find that incorporating things like these in your daily practice routine can lead you to discover new material, or just find faults to fix in your playing. As an example go through the combinations and find a combination you like and that sounds more musical to you…play in all 12 keys, apply it to a tune like ‘Autumn leaves’ taking it around the changes and modifying it to match the chord of the moment.

Good luck!

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