This paper discusses non–octave-based microtonal scales which can express a septimal minor triad formed by the 6th, 7th and 9th partials of the harmonic series. Three methods are proposed for modulating or transferring between each scale:... more
This paper discusses non–octave-based microtonal scales which can express a septimal minor triad formed by the 6th, 7th and 9th partials of the harmonic series. Three methods are proposed for modulating or transferring between each scale: by pivoting on common tones, building joint chords with pitches unique to each scale, or dynamically changing the sizes of generator and period to transform one scale into another. Motivation for this project was to shed light on two relatively unexplored possibilities in microtonality: scales without octaves, and multiple scales within a single piece of music. With today's computers and synthesizers these areas can be explored more easily. The author borrows a goodness-of-fit strategy for a 6:7:9 chord and chooses three scales that divide the perfect fifth into 8, 13 and 18 equal steps. In addition to septimal triads other common tones are identified, e.g. a major seventh 1/6th-tone sharp, and the paper touches on less obvious manners of modulation. This project may be of interest to composers wishing to explore new facets of microtonality in their work.