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,
Double harmonic scale harmonic minor scales respectively, each of which, unlike the double harmonic minor scale, has a full diminished chord backbone. This scale (and its modes like the Hungarian minor scale) is the only seven-note scale (in 12-tone equal temperament) that is "perfectly balanced"; this means that when its pitches are represented as points on a circle (whose full circumference represents an octave), their average position (or "centre of mass") is the centre of the circle. Like most heptatonic (seven-pitch) scales, the double harmonic scale has a mode for each of its individual scale degrees. The most commonly known of these modes