Harmonic scale It was invented by Wendy Carlos and used on three pieces on her album "Beauty in the Beast" (1986): "Just Imaginings", "That's Just It", and "Yusae-Aisae". Versions of the scale have also been used by Ezra Sims and Frans Richter Herf. Though described by Carlos as containing "144 [= 12] distinct pitches to the octave", the twelve scales include 78 (= ) notes per octave. Technically there should then be duplicates and thus 57 (= 78 − 21) pitches (21 = ). For example, a perfect fifth above G (D) is the major tone above C. Harmonic scale The Harmonic
Symmetric scale degrees are symmetrical if read from the "top" (end) or "bottom" (beginning) of the scale (mirror symmetry). Examples include the Ukrainian Dorian b9 scale (sixth mode of the Hungarian Major scale), the Jazz Minor b5 scale (fifth mode of the involution of Hungarian Major), the Neapolitan Major scale (fourth mode of the Major Locrian scale), the Javanese slendro, the chromatic scale, whole-tone scale, Dorian scale, the Aeolian Dominant scale (fifth mode of the melodic minor), and the double harmonic scale. Asymmetric scales are "far more common" than symmetric scales and this may be accounted for by the inability of symmetric