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

What a ditone is.

Semiditone.
Pythagoras.
Chromatic.
Enharmonic.

For a ditone is a collection of two tones. A semiditone, however, is a mixture of a tone and a minor semitone, called "semi-" as if an imperfect or diminished ditone; Boethius places this as an incomposite trihemitone in chromatic tetrachords, naturally harmonious. For by Pythagorean inquiry, in each diatonic and natural tetrachord, there is a certain incomposite interval, dissonant to the ears but naturally consonant, found by the loosening of the middle strings. For since it is detected by a double consideration—that is, by the ditone and the trihemitone—those two genera, Chromatic and Enharmonic, are placed between the natural diatonic. But we will discuss these more broadly in instrumental harmony. Therefore, the "fa" sound departs from "re" into the acute by the interval of a semitone, and "re" is likewise loosened from "fa" into the grave, also in two ways: composite, and incomposite, as anyone can perceive for themselves from these descriptions:

Musical staff showing notes ascending and descending by semitone intervals.

The "sol" sound, however, is again sharper than "mi" by the interval of a semitone, and "mi" is lower than "sol," and it is also considered composite and incomposite. This differs from that which is deduced between "re" and "fa." For that one is a semitone sharper than a tone; this one keeps the tone sharper than a semitone, which is proven by these notes:

Musical staff showing notes ascending and descending by tone and semitone intervals.

The "fa" sound, however, from "ut" in a single hexachord is raised into the acute by the diatessaron fourth consonance or epitrite interval, and the sound of the syllable "ut" is pressed from "fa" by a similar distance into the grave, which happens in four ways. For it is disposed and proceeds either by three distinct intervals surrounded by four notes—that is, two tones and a semitone—or by two intervals, namely a tone and a semitone, or again by two intervals of a ditone and a semitone, or by a single and incomposite interval of the extreme sounds, which is deduced by these examples:

Musical staff showing notes ascending and descending by diatessaron intervals.

The sound "sol," however, is sustained from "ut" into the acute by the diapente fifth interval—that is, by three tones and a semitone—which is tended through different intervals by varied notes, as is considered by these deductions:

Musical staff showing notes ascending and descending by diapente intervals.