Octatonic scale out, the cascading arpeggios played on the celesta in the "Sugar Plum Fairy" from "The Nutcracker" ballet are made up of dominant seventh chords a minor third apart. "Hagens Watch", one of the darkest and most sinister scenes in Richard Wagner's opera "Götterdämmerung" features chromatic harmonies using eleven of the twelve chromatic notes, within which the eight notes of the octatonic scale may be found in bars 9–10 below:] The scale also may be found in the music of Claude Debussy and Maurice Ravel. Melodic phrases that move by alternating tones and semitones frequently appear in the works of both
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