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,
Chromatic circle major (Ionian mode), minor (Aeolian mode) and Mixolydian - include these pitches. Symmetric scales have simple representations in this scheme. More exotic scales - such as the pentatonic, blues and octatonic - can also be drawn and related to the common scales. A more complete list of musical scales and modes In previous sections we saw how various overlays (scale degrees, semi-tone numbering, notes) can be used to notate the circumference of the constellation. Various other overlays can be laid around the constellation. For example: Note that once a pitch constellation has been determined, any number of overlays (notes, solfège,