Scale (music) identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a chromatic scale. It is assumed that the scale is tuned using 12-tone equal temperament (so that, for instance, C is the same as D), and that the tonic is in the leftmost position. For example, the binary number 101011010101, equivalent to the decimal number 2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from 100000000000 (2048) to 111111111111 (4095), providing a total of 2048 possible species, but only 351 unique scales containing from 1 to 12
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