Pythagorean tuning


Audio: pythagorean tuning (0:04)

Pythagorean tuning
Figure: pythagorean tuning

Perfect unison1:1Perfect octave2:1
Perfect fifth3:2Perfect fourth4:3
Major second9:8Minor seventh16:9
Major sixth27:16Minor third32:27
Major third81:64Minor sixth128:81
Major seventh243:128Minor second256:243
Augmented fourth729:512Diminished fifth1024:729
Table: pythagorean tuning

pythagorean tuning plays a melody in Pythagorean tuning. It consists of twelve different notes in succession followed by a note an octave above the first note. The frequency ratio between each pair of notes is either 3:2 or 2:3. The pythagorean tuning figure shows the score and the table lists the names of the intervals and their frequency ratios in Pythagorean tuning.

Pythagorean tuning is a system of tuning which constructs notes using a frequency ratio of 3:2.

Around 540BC in Greece, Pythagoras started to systematically construct the tuning system which now bears his name. The frequency ratio of the octave, 2:1, was already known, so the starting point for Pythagorean tuning was to divide the octave in half. Half an octave is the frequency ratio 3:2. Using this simple ratio results in the set of intervals shown in the Pythagorean tuning table.