On the Institution of Music (De institutione musica)

4,384 will become 4,382 original: ".iiii. ccclxxxiiii" and ".iiii. ccclxxxii". These numbers represent the lengths of a string on the monochord used to measure musical pitches.. Let this be marked as "P. hypate" and as the letter for the enharmonic trite synemmenon: The "third" note of the conjunct (synemmenon) tetrachord.. There will be a semitone original: "semitonium" maintained between the enharmonic paranete synemmenon: The note "next to the last" (nete) in the conjunct tetrachord. and the mese mese: The central "middle" note and primary tuning reference of the ancient Greek musical system.. This same interval is found between the values 4,384 and 4,632. Having set aside the enharmonic paranete synemmenon, specifically the one located at 4,382, the rest of the logic for this tetrachord is now explained. Now, however, we must create a diagram joined with the others, namely the hyperboleon hyperboleon: The "highest" tetrachord in the Greater Perfect System. and the diezeugmenon diezeugmenon: The "disjunct" tetrachord, which is separated from the central note by a whole tone., so that the arranged progression may be formed step by step.

A circular diagram in the upper right quadrant represents the enharmonic genus. The word "ENHARMONIC" is written around the outer edge. The diagram contains concentric arcs labeling the "Enharmonic Conjunct Tetrachord." Within the segments, musical notes are identified: the "Middle Note" (Mese), "Third Conjunct Note" (Trite synemmenon), "Next-to-last Conjunct Note" (Paranete synemmenon), and the "Last Conjunct Note" (Nete synemmenon). Each is paired with specific numerical values like 4,384 and 4,632. To the right of the circle, a rectangular table lists Greek musical notation symbols in columns.

A large, complex diagram fills the bottom half of the page. It consists of two interlinked circular systems that form a double-lobed or heart-like shape. The left system is labeled "CHROMATIC" and the right is labeled "ENHARMONIC." Each side features three concentric arcs representing different groups of four notes: the "Conjunct Tetrachord," the "Disjunct Tetrachord," and the "Highest Tetrachord." Inside these arcs, specific notes are named, such as the "Highest of the Highest" (Nete hyperboleon) and the "Middle Note" (Mese). These are shown alongside numerical ratios written in medieval numerals, such as 5,184 and 9,362. A central vertical rectangle bridges the two systems, containing columns of musical notation characters. Dozens of thin, curved lines and arrows connect the notes across the diagram to illustrate the mathematical and tonal relationships between the chromatic and enharmonic musical scales.