My previous book, the Thesaurus of Diatonic Sets, describes the relationships between the content of the subsets of the diatonic or other seven-note scales. It served that purpose well, but I soon found a basic flaw in its approach to pandiatonisim. It is careful about the set content but woefully lacking in concern about how sets move, treating all sets with similar content relationships the same. Resolving to the tonic triad from V {2, 5, 7} and IV {R, 4, 6} are the same in terms of set content, as both of these cadential pairs share one common tone while two differ. They are quite different in sound and practice, however, and it is an odd system that cannot distinguish between authentic and plagal cadences. The sets’ content does not tell the whole story, since the paths between sets are a large part of what define their relationships.

I had created a map with every possible destination but no roads. This book adds the roads. It lists the possible movements between any two subsets of a heptatonic scale in a simple to read diatonic movement vector.


Thesaurus of Diatonic Sets
(Curious Automata, 2013)

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The Thesaurus of Diatonic Sets is a guide to all of the sets formed by the diatonic or any other seven note scale. Every possible set is listed along with their descriptions, diatonic interval vectors, subsets, supersets, and sets which contain no common tones.

This book is ordered logically, starting by number of notes. Sets of the same number of notes are then grouped by intervallic content and each group is named for a common chord formed by it. These chords are then placed in order from those with the most evenly distributed intervals to those with the least. Finally, the sets in each group are listed by the root of their chord in order of scale degree, from I through VII.