Microtones and projective planes
Carlton Gamer, Robin J. Wilson · 2003
Abstract For hundreds of years mathematicians and musicians have been intrigued by the musical systems obtained when an octave is divided up, not into the usual twelve tones with which we are all familiar, but into a smaller or larger number of tones. Certain of these systems, such as the 19-tone, 31-tone and 53-tone equal-tempered systems, have been much investigated, since they give rise to tunings that more closely approximate particular intervals in the harmonic series (‘just’ tunings) than does the 12-tone equally tempered system; a table comparing these tunings is given below.