Practica Musicae utriusque cantus, excellentis Franchini Gaffori Laudensis quatuor libris modulatissima

What a tone is.

...in the acute direction. The fifth hexachord, however, is joined to the first tetrachord of the fourth hexachord. But the sixth hexachord, which can be called synemmenon joined, is connected to the first tetrachord of this fifth hexachord. The seventh hexachord is separated from the first tetrachord of the fifth hexachord by the distance of a tone in the acute direction. For a tone is the legitimate space of a sesquioctave dimension, circumscribed by two sounds. It sustains two nearby parts only by section, one of which is smaller, the other larger. They call the latter an apotome major semitone and the former a minor semitone. When the minor semitone is abstracted from the tone itself, an apotome remains, through which a discordant transition proceeds in voices with great difficulty, unlike the minor semitone; for the latter provides a concordant and sweet temperament to the tones themselves and the consonances, as I shall prove most notably in instrumental harmony, when it is known to be deducted naturally—especially in the diatonic introduction—before, after, or between two tones. Hence, the semitone itself may be defined as an interval which, when added to two sesquioctaves, creates a sesquitertia 4:3 ratio proportion, or a space that, when joined to two tones, completes the diatessaron fourth consonance at its extreme limits. An interval or space, in this way, can be understood as the distance between an acute and a grave sound. A sonorous concept of the mind is declared by certain notes, whose extension, intension, and remission, arranged by the variety of lines and spaces, must be followed by the voice itself, and for this reason, the notes themselves are called signs of the voice. And because voices cannot be written, they are committed to memory through use and exercise, so they do not perish. For they flow into the past time by their pronunciation. Thus, a triple description of notes occurs: simple, composite, and mediocre. A simple note is one that is not joined to another note, and it is figured with a square body in this manner A square musical note symbol, and sometimes it is also described with a stem descending on its right side in the mode of a measurable long, as here: A square musical note with a descending stem. A composite note is one that is sewn onto another note, which then follows a different description. For when a ligature ascends—that is, having the second note higher—the first requires no ascending or descending stem on either of its sides, as here. But when the ligature descends—having the second note, that is, lower—a descending stem is ascribed to the first on the left side, whether it be oblique or square, in this manner:

What a semitone is.

What an interval is.

Musical notation showing a descending ligature

The authority of the ancients established that this ligature, at the beginnings, should be called a property. Therefore, a property is the description of the beginnings of ligatures, established by musical authors. But to the final notes of the commission—since the perfection of all things, as the Philosopher testifies, is attributed to the end—they ascribed perfection. For this denotes in three ways. For either the last note of the ligature is described with a square body under the penultimate, as here: Musical notation showing a ligature with a descending stem

Philosopher.

ligature