Chapter Three

If a species is added, a perfect fifth original: diapente; from the Greek for "through five." is created, so named because it consists of five voices or notes. It is also called a pentachord because it consists of five strings or four intervals: three whole tones and one semitone, such as the span from a to e. But if a semitone is subtracted from a perfect fifth, a tritone An interval of three whole tones, notorious in medieval music as the "devil in music" for its dissonance. is produced, as seen between f and b-natural original: b ♮, represented here by the "square b" or b quadratum.. After the perfect fifth, the previous intervals are added back to the fourth in this manner: a perfect fifth with a semitone added, as from a to f A minor sixth; a perfect fifth with a whole tone, as from e to h A major sixth; 'h' was often used in Germanic notation for B-natural; a perfect fifth with a minor third original: semitonio, likely a scribal error for semiditono (minor third), as from a to g A minor seventh; and a perfect fifth with a major third original: ditono, as from e to b-natural original: b. qdr..

But when a perfect fifth is joined with a perfect fourth original: diatessaron, it composes the species called the octave original: dyapason; from the Greek dia pason, meaning "through all [the notes].". This name signifies "through the whole" or "concerning the total" in Latin, because every melody—which the Greeks call a symphony—and every harmonic variation is contained within it. For this reason, it was rightly said by the ancients that after the octave, there is always a repetition. The seven intermediate notes each have their own distinction; hence the poet Virgil wisely wrote in the sixth book of the Aeneid:

The eighth note is indeed similar to the first. Therefore, Gregory Pope Gregory I, traditionally credited with organizing the plainchant of the church. did not establish more than seven different letters, but repeats them and places them again, because between the first and the eighth, the greatest affinity and likeness is found. They are so similar that they are not perceived to differ except in their sharpness original: acuminis; high pitch or heaviness original: grauitatis; low pitch. Thus, the lower octave was labeled a. b., while the higher was labeled b. p.

The same letters used for the low notes were also used to mark the high notes of the octave. However, it should be noted that while the musical tones original: phthongi are equal to each other in sound, they vary in the size of their physical representation in the diagram. Depending on whether they have more or less heaviness, they occupy larger or smaller spaces. Consequently, the whole tone a. b. has double the physical interval when compared to the tone b. b-natural. Similarly, c. d. is compared to k. k. The same must be said for the semitones and other larger species, as demonstrated in the figure. But hereafter, they shall not be placed in this way, lest the understanding of beginners be obscured; instead, just as whole tones are equal to each other in sound, we shall place the gaps between them as equal. We will, however, diminish the intervals of the semitones so that it is clearly evident that a semitone is less than a whole tone. All these aforementioned points will be made clear by the figure placed below.

Faint, large circular diagrams illustrate musical theory concepts. These "figura" serve as a visual aid to help the student see how musical intervals—the gaps between notes—relate to one another mathematically and physically on an instrument like the monochord.