Musical Intervals

Musical intervals in speech.

Throughout history and across cultures, humans have created music using pitch intervals that divide octaves into the 12 tones of the chromatic scale. Why these specific intervals in music are preferred, however, is not known. In the present study, we analyzed a database of individually spoken English vowel phones to examine the hypothesis that musical intervals arise from the relationships of t...

The Appreciation of Musical Intervals

Triadic comparisons of musical intervals.

An analysis is made of the perception of musical intervals. Two kinds of stimuli were used; intervals consisting of two simultaneous simple tones (sinusoids) and intervals consisting of two simultaneous complex tones (fundamental plus harmonics). Subjects judged the stimuli by the method of triadic comparisons in an incomplete balanced design. Multidimensional analysis was performed according t...

Musical Intervals And Special Linear Transformations

This paper presents a transformational approach to musical intervals with particular focus on their constitutive role for well-formed scales. These scales have the property that their binary step-interval pattern is maximally even. Transposition classes of well-formed scales are therefore characterized by two step intervals and their characteristic binary pattern, or more abstractly, by four nu...

Using Trajectory Mapping to Analyze Musical Intervals

Cognitive scientists have often pondered the question of perceptual spaces, that is, the question of how a certain gamut of familiar stimuli might be organized in the mind. We present Trajectory Mapping as an alternative clustering method to the traditional algorithm of Multi-Dimensional Scaling. We suggest that given data about the relationships among stimuli, Multi-Dimensional Scaling provide...