Incremental Coupled Musical Scales
M. H. Gwynn · The Journal of the Acoustical Society of America · 1945
The equation V/T = 2SN represents a family of preferred number series. S and N are of integer value, V is a rational number. One particular type series, which is both incremental and coupled, is defined by the following proportion for the terminal terms, i.e., extreme notes, of each scale, Nmax/Nmin = 2(S+C)/(S+C). C is an integer constant for each series of the type. Each of several incremental coupled series is an homologous train of scales whose notes are interpreted as frequencies, the ratios thereof being rational. Each scale possesses one more note than the preceding scale, and the highest frequency in each scale is an overlapping member of two arithmetic progressions. An octave is spanned within each scale. The lower scales of these series are separated in four groups. The several lowest scales compose two primitive and subsonic groups relating to tone quality. The next or sonic group consists of nine audible scales. Harmonic potentialities with respect to a new pure tone music are tabulated. One half of the sonic group notes are members of at least one major chord. Composition and rendition should be extraordinarily simple, since bass scales contain relatively few notes conforming to the recent findings that aural sensitivity to pitch progresses with sonic frequency.