A study of stretched harmonies

Abstract

A class of nonharmonic sounds was synthesized by stretching normal harmonic sounds. Stretching means uniformly expanding the logarithmic frequency ratios between the fundamental frequencies of the tones in a scale and between the fundamental of each tone and its overtones. Stretched passages were studied to see what properties are invariant to stretching. Stretched cords have the same coincidence of overtones as unstretched chords; hence, harmonic perceptions, which depend on overtone coincidence, should be invariant. By contrast, perceptions which depend on periodicity pitch or on the Rameau fundamental bass should be destroyed by stretching. A number of traditional pieces and chords were synthesized in stretched and unstretched forms. These samples were evaluated by (1) informal listening, (2) tests of the identification of the key of the material, and (3) tests of the perception of cadences. Results showed both similarities and differences between stretched and unstretched materials. We believe stretched sounds have perceivable structures that can be utilized in musical compositions.