Diatonic Genus - Tunings of The Diatonic

Tunings of The Diatonic

The traditional Pythagorean tuning of the diatonic, also known as Ptolemy's "ditonic diatonic", has two identical 9/8 tones in succession, making the other interval 256/243:

hypate parhypate lichanos mese | 256/243 | 9/8 | 9/8 | -498 -408 -204 0 cents Play

However, the most common tuning in practice from about the 4th century BC to the 2nd century AD appears to have been Archytas's diatonic, or Ptolemy's "tonic diatonic", which has the superparticular 28/27 instead of the complex 256/243 for the lowest interval:

hypate parhypate lichanos mese | 28/27 | 8/7 | 9/8 | -498 -435 -204 0 cents

Ptolemy described his "equable" or "even diatonic" as sounding foreign or rustic, and its neutral seconds are reminiscent of scales used in Arab music. It is based on an equal division of string lengths, which implies a harmonic series of pitch frequencies:

hypate parhypate lichanos mese | 12/11 | 11/10 | 10/9 | -498 -347 -182 0 cents