Pythagorean Tuning

Pythagorean tuning (Greek: Πυθαγόρεια κλίμακα) is a system of musical tuning in which the frequency relationships of all intervals are based on the ratio 3:2 (the perfect fifth), "found in the harmonic series." This interval is chosen because it is one of the most consonant. Attributed to Pythagoras (sixth century BC), "the Pythagorean system would appear to be ideal because of the purity, of the fifths, but other intervals, particularly the major third, are so badly out of tune that major chords a dissonance."

The Pythagorean scale is any scale which may be constructed from only perfect fifths and octaves or the gamut of twelve pitches constructed from only perfect fifths and octaves and from which specific scales may be drawn. See: generated collection. For example, the series of fifths generated above gives seven notes, a diatonic major scale on C in Pythagorean tuning, shown in notation on the top right. In Greek music it was used to tune tetrachords and the twelve tone Pythagorean system was developed by medieval music theorists using the same method of tuning in perfect fifths, however there is no evidence that Pythagoras himself went beyond the tetrachord.