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
Jazz scale scales add a single chromatic passing tone to the 7 note major scale (Ionian and Mixolydian modes). The added passing tone creates an 8 tone scale that fits rhythmically evenly within a 4/4 measure of eight 8th notes, thus making it useful in practicing. When an 8th note bebop scale run starts on the beat from a chord tone (Root, 3rd, 5th or 7th) the other chord notes will also fall on the beats. As a result, all of the "non-chord tones" will fall on the upbeats (the "ands" when counting "one and two and three and four and") and