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In ancient Greek music theory, the diatonic genus (Greek: διατονικό γένος) is the division of the tetrachord from which the modern diatonic scale evolved. The distinguishing characteristic of the diatonic genus is that its largest interval is about the size of a major second. The other two intervals vary among different tunings.
The word is derived either from the Greek, dia (διά) and tonos (τόνος), meaning "proceeding by whole tones" (Drabkin n.d.), or "through, at the interval of" a "tone" (OED), or from Greek dia and tonikos, meaning "at intervals of a tone" (Dunsby 2002).
Tunings of the diatonic 
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
Byzantine music 
In Byzantine music most of the modes of the Octoechos are based on the diatonic genus, apart from the 2nd mode (both authentic and plagal) which is based on the chromatic genus. Byzantine music theory distinguishes between two tunings of the diatonic genus, the so-called hard diatonic on which the 3rd mode and two of the grave modes are based, and the soft diatonic on which the 1st mode (both authentic and plagal) and the 4th mode (both authentic and plagal) are based. The hard tuning of the diatonic genus in Byzantine music may also be referred to as the enharmonic genus; an unfortunate name that persisted, since it can be confused with the ancient enharmonic genus.
See also 
- Drabkin, William. n.d. "Diatonic". Grove Music Online, edited by Deane Root (Accessed 14 January 2011)
- Dunsby, Jonathan. 2002. "Diatonic". The Oxford Companion to Music, edited by Alison Latham. Oxford and New York.