“To truly perceive the voices mi and fa with the eyes and mind, one must clearly target them as to avoid indiscriminately situating one in place of the other, for all Music depends on these two voices.” It is with this final piece of advice for singers that book 5 of Hermann Finck's 1556 Practica musica culminates. Such consideration and esteem for these two voces musicales (musical voices), mi and fa, forming the semitone at the nexus of the hexachord, lays the foundation for this discussion, which takes practical music as its point of departure into the speculative. Practicing musicians of the Middle Ages and Renaissance attributed to each note one of seven possible letter names (litterae), A through G, and up to three of six possible “voices” or vocables (voces) that formed the hexachord, ut–re–mi–fa–sol– la. If the letter name determined a fixed position (locus) for any given note within an absolute system, whether on the musical staff, the musical hand, or a musical instrument, the voices determined the place of that note in a relative system of intervallic relationships. The vocable assigned to a given note determined its place and function relative to the surrounding notes, where ut was attributed to the letters C, F, or G and would run for six rising steps to la on A, D, or E, respectively, in a repeating and overlapping latticework extending over the gamut from Γ ut to eʺ la. This entire system was known as musica recta or vera—“straight,” “proper,” or “true” music (see figures 1.1a–1.1d).

Every hexachord had a similar, symmetrical construction, consisting of two whole tones (ut–re–mi), a semitone (mi–fa), and two more whole tones (fa–sol–la). Due to the proximity of the hexachords on F and G beginning one note apart, the note B had to be split, sharing two distinct qualities and sounds as B fa B mi (sounding B-flat and B-natural, respectively). This division was established in order to preserve the pattern of tones and semitone within each of the two hexachords, F–G–A–B♭–C–D and G–A–B♮–C–D–E, both voiced ut–re–mi–fa–sol–la. Although their construction was comparable, they each possessed a unique propriety (proprietas).