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,
Yo scale A - B. This is illustrated below. The Ryūkyū scale appears to be derived from the yo scale with pitches raised. More recent theory emphasizes that it is more useful in interpreting Japanese melody to view scales on the basis of "nuclear tones" located a fourth apart and containing notes between them, as in the "min'yō" scale used in folk music, and whose pitches are equivalent to the second mode of the "yo" scale: Yo scale The "yo" scale, which does not contain minor notes, according to a traditional theory is a pentatonic scale used in much Japanese music including