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Smith's Complete Book of Scales There are many books that claim to be complete yet are not, this is the only book of scales mathematically proven to be complete.
All
24,577 scales of the Twelve-Tone system are listed in this book and are
arranged in lexicographic order. The scales in this book are classified
by cardinality, not by arbitrary names or keys.
Smith's Complete Book of Scales gives you every possible scale
Included are over 24,000 scales!
cardinality combinations
Nulltonic 0 1
Unitonic 1 12
Bitonic 2 66
Tritonic 3 220
Tetratonic 4 495
Pentatonic 5 792
Hexatonic 6 924
Septatonic 7 792
Octatonic 8 495
Nonatonic 9 220
Decatonic 10 66
Undecatonic 11 12
Dodecatonic 12 1
An
easy three step method for counting scales is presented in this book.
The number of scales that exist in the Twelve-Tone system of tuning can
be answered by this relatively simple yet elegant algorithm. By using
this method a musician can learn every scale within minutes.
