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,
Jazz scale scales add a single chromatic passing tone to the 7 note major scale (Ionian and Mixolydian modes). The added passing tone creates an 8 tone scale that fits rhythmically evenly within a 4/4 measure of eight 8th notes, thus making it useful in practicing. When an 8th note bebop scale run starts on the beat from a chord tone (Root, 3rd, 5th or 7th) the other chord notes will also fall on the beats. As a result, all of the "non-chord tones" will fall on the upbeats (the "ands" when counting "one and two and three and four and") and