Glossary
Evenness
Glossary
Set Theory
Nearly even or maximally even chords and scales are much more common in harmony because they are related to their involutions and transpositions by short voice leadings, whereas perfectly even chords and scales are limited in their voice leading possibilities.
Examples of perfectly even chords and scales are the diminished seventh, augmented triad, and hexatonic whole-tone scale. Examples of nearly even or maximally even chords and scales are major and minor triads, dominant seventh, half-diminished seventh, pentatonic scale, diatonic scale, etc.
See Evenness & Clusters and Tymoczko 2006 and 2011 for extended explanations of this.
Measure of Evenness v. Average Voice-Leading Distance. Distance (x-axis) of OPTIC-equivalent set class (prime form) to the perfectly even C-note chord (for cardinality C) versus average voice-leading distance (y-axis) of set class to its transpositions. (Regression lines ignore modes of limited transposition as outliers.)
Set Theory
Nearly even or maximally even chords and scales are much more common in harmony because they are related to their involutions and transpositions by short voice leadings, whereas perfectly even chords and scales are limited in their voice leading possibilities.
Examples of perfectly even chords and scales are the diminished seventh, augmented triad, and hexatonic whole-tone scale. Examples of nearly even or maximally even chords and scales are major and minor triads, dominant seventh, half-diminished seventh, pentatonic scale, diatonic scale, etc.
See Evenness & Clusters and Tymoczko 2006 and 2011 for extended explanations of this.
Measure of Evenness v. Average Voice-Leading Distance. Distance (x-axis) of OPTIC-equivalent set class (prime form) to the perfectly even C-note chord (for cardinality C) versus average voice-leading distance (y-axis) of set class to its transpositions. (Regression lines ignore modes of limited transposition as outliers.)