Didymos

Didymos Greek: Δίδυμος) was an ancient Greek music theorist in the last century before the common era. He was a predecessor of Ptolemy at the library at Alexandria.

We know of his theory only indirectly from the works of Porphyry and Ptolemy. There one finds examples of his tetrachords as measured string lengths from which the following proportions can be calculated:

• diatonic Tetrachord: (16:15)(10:9)(9:8)
• chromatic Tetrachord: (16:15)(25:24)(6:5)
• enharmonic Tetrachord:(32:31)(31:30)(5:4)

Like Archytas he used a major third, but appears to have been the first to use it in the diatonic as sum of the large and small whole tones as for the proportions (10:9)•(9:8)=5:4 obtains.The difference of these whole tones is the so-called syntonic comma, also referred to as Didymos' comma