On the Institution of Music (De institutione musica)

...the Synemmenonoriginal: "smemenon," referring to the "conjunct" or connected tetrachord part and the Diezeugmenonthe "disjunct" or separated tetrachord. And the Synemmenon is that which is placed after the Mesethe central or "middle" note of the ancient Greek scale, that is:
the Trite and Paranete of the Synemmenon

the Trite Synemmenonliterally "the third string of the conjunct group". Next is the Licanos Synemmenonalso called the Paranete; "Licanos" refers to the index or "licking" finger used to play the string; this is the same in the Diatonic genus: the Diatonos Synemmenon. In the Chromatic genus, however, it is the Licanos Synemmenon Chromatic. In the Enharmonic genus, it is either the Diatonos Synemmenon Enharmonic or the Licanos Synemmenon Enharmonic. After these comes the Nete Synemmenonthe "last" or highest note of that group. But if the Mese note joins two together, it admits the Synemmenon tetrachord. However, after the Mese [in the disjunct system] is the Parameseliterally "next to the middle". Next is the Trite Diezeugmenon, which in the Diatonic is the Diatonos Diezeugmenon; in the Chromatic, the Diatonos Diezeugmenon Chromatic and the Licanos Diezeugmenon Chromatic; and in the Enharmonic, the Diatonos Diezeugmenon Enharmonic and the Licanos Diezeugmenon Enharmonic. This is also the Paranete, with the addition of either the Diatonic, Chromatic, or Enharmonic quality. Above these is the

Nete Diezeugmenon and the Trite Hyperbolaionthe "third" string of the "extreme" or highest group. And that which is the Paranete Hyperbolaion is the same in the Diatonic: the Diatonos Hyperbolaion; in the Chromatic: the Chromatic Hyperbolaion; and in the Enharmonic: the Enharmonic Hyperbolaion. The last of these is the Nete Hyperbolaion. Let there be a diagram of this kind so that it contains the arrangement of the three genera. In these, you will note both the similarity of the names and their differences, so that if the similar strings in all cases are joined with those that are different, there are twenty-eight in all. The following diagram shows this.

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What the proportions are between the notes in each of the genera. Chapter 24.

In this way, therefore, the division is made through each individual tetrachorda block of four notes into the specific properties of the genera. Thus, we will divide all five Diatonic tetrachords by two whole tones and a semitone; in this genus, the tone...