Four new scales based on nonsuccessive-integer-ratio chords
M. V. Mathews, Linda A. Roberts, John R. Pierce · The Journal of the Acoustical Society of America · 1984
Our previous work demonstrated that chords with frequency ratios 3:5:7: and 5:7:9: have many perceptual harmonic properties of major triads (4:5:6 ratios). The traditional diatonic scale can be constructed from three major chords, the tonic, the dominant, and the subdominant chords. Using analogous techniques with the new chords, we have constructed four new scales which we call the M579, M357a, M357b, and the P3579 scales. Pitches of the notes of these scales sound very different from the diatonic scale. All scales have clearly perceptable harmonic structure. All notes can be harmonized with consonant “major” chords. There are strong perceptual differences between consonant and dissonant chords. The M scales are based on an octave with a 2:1 frequency ratio. The P3579 scale has a 3:1 octave and was designed for timbres having only odd harmonics. In addition, P3579 is an equal tempered scale using a subset of 13 equal frequency divisions of the 3:1 octave. We believe these scales will be useful for nontraditional new music which has well defined and easily perceived harmonics. We also believe our techniques can be used to manufacture many additional scales.