Pyknon

[2] Although in modern usage, a tetrachord may be any four-note segment of a scale, or indeed any (unordered) collection of four pitch classes, in ancient Greek music theory a tetrachord consists of a four-note segment of the Greater and Lesser Perfect Systems bounded by the interval of a perfect fourth, the outer notes of which remain fixed in all genera and therefore are called "standing notes" (Greek: ἑστῶτες φθόγγοι).

The existence of a pyknon therefore depends on the uppermost interval being larger than half of a perfect fourth, which occurs only in the chromatic and enharmonic genera.

[8] In the enharmonic genus, the large incomposite interval was originally a ditone (the major third of Pythagorean tuning), leaving a pyknon with a total width of just a semitone.

14) that two other theorists, Archytas and Didymus, replaced the ditone with the smaller, just major third with the number ratio of 5:4, making the pyknon correspondingly larger.

[14] In the chromatic genus, the largest interval was called a Greek: τριημιτόνιόν ἀσύνθετον, Latin: triemitonium incompositum—translated as "incomposite" (or "noncomposite") "trihemitone" (Bower, Hagel, Levin, and Barker prefer a descriptive translation, "an individed interval of three semitones";[15][16][17][18] Strunk uses "trisemitone"[19]), the modern term being "minor third"—leaving a pyknon of some type of whole tone to be divided into two semitones.

Up to the beginning of the 4th century BC the chromatic pyknon spanned a major whole tone with a 9:8 ratio, and this was divided by Gaudentius into ascending semitone intervals of 256:243 and 2187:2048.

[13] According to Aristoxenus' Elementa harmonica (Elements of Harmony, book 2), whenever tetrachords are combined to form a scale filling an octave, "Two consecutive pycna may not occur in ascent or descent.