The equation V/T = 2sN represents a family of preferred number series. Each series is a train of scales of increasing and integer scale number, S. The note number, N, of all terms within each scale also consists of a series of integers. Hence the values for N or V within each scale consist of a rational arithmetic series. Sonically applied, V/T is a frequency, e.g., cycles per second. One particular type series, which is incremental, is defined by the following value for any note number, N = S + K + N, where K is an integer constant for each series of the type, and N is the tone number within any single scale, viz., the integer series, 0, 1, 2, ⋯, S + K − 1, S + K. Each incremental scale possesses S + K + 1 notes, one more note or tone than the preceding scale. Each lowest numbered tone, N = 0, is the coupling tone of a pair of finite incremental scales. The frequency of the highest note is double that of the lowest note, so that the octave is completed within each finite incremental scale. Trains of finite incremental scales may find application in a new pure tone music, rich in harmonic partials and tonal possibilities. The number of incremental notes chosen to span seven octaves may vary from 18 upward. A train of incremental scales is an homology of scales, with new effects introduced in each higher scale. Composition and rendition should be relatively simple, since incremental bass scales contain comparatively few notes conforming to the fact that aural sensitivity to pitch progresses with frequency through most of the sonic range.