Chords from Tones Having Stretched Partials

Tones made up of partials having frequencies proportional to NS, where N is the partial number and S is the stretch exponent, have been generated on a digital computer and used to form scales and chords. The scales were constructed with the frequency ratio between “half steps” equal to (21/12)S. Chords analogous to the tonic, subdominant, and dominant were generated for S varying from 0.792481, which compressed the partials by a factor that made the frequency of the fourth partial three times that of the fundamental, to 1.261859, which made the frequency of the third partial four times that of the first. The sensation produced by the stretched chords was consistent with Helmholtz's criterion for dissonance. The quality of the individual tones, however, became more and more strange as the value of S increased.