Enumeration of Synthetic Musical Scales by Matrix Algebra and a Catalogue of Busoni Scales
Robert M. Mason · Journal of Music Theory · 1970
I have made an attempt to exhaust the possibilities of the arrangement of degrees within the seven-tone scale; and succeeded, by raising and lowering the intervals, in establishing one hundred and thirteen different scales. These 113 scales (within the octave C-C) comprise the greater part of our familiar twenty-four keys, and, furthermore, a series of new keys of peculiar character. But with these the mine is not exhausted, for we are at liberty to transpose each of these 113, besides the blending of two such keys in harmony and melody. *1