The Pierce 3579b scale

Abstract

A new scale, tentatively called the Pierce 3579b scale, has been invented, synthesized, and evaluated. The scale has nine notes spanning a new octave (3:1 frequency ratio). The nine notes are selected from a set of 13 equally tempered half steps, each of which has a frequency ratio of 133. The equal tempered scale gives an excellent approximation to the basic chords which have 3:5:7 and 5:7:9 frequency ratios, the average error being five cents. These chords provide a strong harmonic basis for music written in the new scale because they have high intonational sensitivity—that is, you can hear whether or not they are in tune. Some music has been composed in the new scale, using traditional musical forms such as chorals, canons, and minuets. Many of the compositional techniques used in the diatonic scale appear to have counterparts in the new scale including modulation from one key to another.