Melodic Scales
Roel C.H. Vermeulen · The Journal of the Acoustical Society of America · 1948
An attempt is made to give a derivation of musical scales on melodic rather than harmonic principles. Starting from the hypothesis that the scale shall contain, at most, two different intervals and shall contain a perfect fifth, all possible scales have been investigated. Only a few satisfy some rather obvious conditions. With three exceptions these can be recognized as existing scales. The intervals of the customary scale prove to be those of Pythagoras. It is pointed out that the differences between this scale and the equally tempered one are only slight while the latter one lies in between the Pythagorean and the just scales.