Symmetric scale


In music, a symmetric scale is a music scale which equally divides the octave. The concept and term appears to have been introduced by Joseph Schillinger and further developed by Nicolas Slonimsky as part of his famous Thesaurus of Scales and Melodic Patterns. In twelve-tone equal temperament, the octave can only be equally divided into two, three, four, six, or twelve parts, which consequently may be filled in by adding the same exact interval or sequence of intervals to each resulting note.
Examples include the octatonic scale and the two-semitone tritone scale:
gaps with two semitones.
As explained above, both are composed of repeating sub-units within an octave. This property allows these scales to be transposed to other notes, yet retain exactly the same notes as the original scale.
This may be seen quite readily with the whole tone scale on C:
If transposed up a whole tone to D, contains exactly the same notes in a different permutation:
In the case of inversionally symmetrical scales, the inversion of the scale is identical. Thus the intervals between scale degrees are symmetrical if read from the "top" or "bottom" of the scale. Examples include the Ukrainian Dorian b9 scale, the Jazz Minor b5 scale, the Neapolitan Major scale, the Javanese slendro, the chromatic scale, whole-tone scale, Dorian scale, the Aeolian Dominant scale, and the double harmonic scale.
s of five symmetric scales.
Asymmetric scales are "far more common" than symmetric scales and this may be accounted for by the inability of symmetric scales to possess the property of uniqueness which assists with determining the location of notes in relation to the first note of the scale.