Chromatic scale and new notes between E/F and B/C: The fractions and , and , and , and , and many other pairs are interchangeable, as (syntonic comma) is tempered out. These are 19-EDO just intonation approximations. The ancient Chinese chromatic scale is called "Shí-èr-lǜ". However, "it should not be imagined that this gamut ever functioned as a scale, and it is erroneous to refer to the 'Chinese chromatic scale', as some Western writers have done. The series of twelve notes known as the twelve "lü" were simply a series of fundamental notes from which scales could be constructed." The Indian solfège,
Scale (music) notes. A more mathematically flexible schema for binary representation, espoused by theorist Ian Ring in his study of musical scales, has bits representing ascending tones, with the smaller bits representing lower pitches and higher bits representing higher pitches. This causes the bits to appear reversed compared with Duncan's system. Under this schema, a major scale is 101010110101 = (2741), a single root tone is 1, and a chromatic scale is still 111111111111 (4095). All the tone possibilities that begin with a root tone, and are thus scale-like, are odd-numbered. Scales may also be shown as semitones from the tonic. For