Chromatic scale common conception of the chromatic scale before the 13th century was the Pythagorean chromatic scale (). Due to a different tuning technique, the twelve semitones in this scale have two slightly different sizes. Thus, the scale is not perfectly symmetric. Many other tuning systems, developed in the ensuing centuries, share a similar asymmetry. In Pythagorean tuning (3-limit just intonation) the chromatic scale is tuned as follows, with sharps higher than their enharmonic flats: These are 17-EDO Pythagorean tuning approximations. In 5-limit just intonation the chromatic scale, Ptolemy's intense chromatic scale, is as follows, with flats higher than their enharmonic sharps,
Hexatonic scale a symmetric scale consisting of a repeated pattern of two semitones followed by a major third now used for improvisation and may substitute for any mode of the jazz minor scale. The scale originated in Nicolas Slonimsky's book "Thesaurus of Scales and Melodic Patterns" through the, "equal division of one octave into two parts," creating a tritone, and the, "interpolation of two notes," adding two consequent semitones after the two resulting notes. The scale is the fifth mode of Messiaen's list Hexatonic scale In music and music theory, a hexatonic scale is a scale with six pitches or notes per