The high octave original: Diapasō acuta with seven intermediate notes, which is called the whole song. The low octave original: Diapason grauis which is called the whole song, including the seven intermediate notes.

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paranete hyperbolaion The "next-to-highest" of the extreme notes in the Greek system. trite hyperbolaion The "third" note of the extreme notes. nete diezeugmenon The "highest" note of the disjoined tetrachord. paranete diezeugmenon The "next-to-highest" of the disjoined notes. paranete synemmenon The "next-to-highest" of the joined notes. trite diezeugmenon The "third" of the disjoined notes. paranete synemmenon A repetition indicating overlapping systems. paramese The "next-to-the-middle" note, equivalent to our B. trite synemmenon The "third" of the joined notes.

p (high a)
tone
o (g)
tone
n (f)
m (e)
tone
l (d)
tone
k (c)
semitone
□ The "square b" or B-natural.
i (b-flat)
[interval]
h (a)
tone
6 (g)
tone
f (f)
semitone
e (e)
tone
d (d)
[interval]
c (c)
the whole
b (B)
tone
a (A)

lichanos meson The "index-finger" note of the middle strings. parypate meson The "next-to-lowest" of the middle strings. hypate meson The "lowest" of the middle strings. lichanos hypaton The "index-finger" note of the principal strings. parypate hypaton The "next-to-lowest" of the principal strings. hypate hypaton The "lowest" of the principal strings.

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Chapter Three

Therefore, so that the arrangement of the figure where we have imprinted the Greek names of the strings and the Latin letters is not forgotten: although the whole range of music is contained within a single octave diapason; the interval of an eighth, we have nevertheless set down two, which are called the double octave bis diapason, so that we might imitate the teaching of Boethius and the Greeks. The handbook enchiridion; a common title for medieval music manuals, however, calls this the disdiapason. From this, the error of those who begin poorly is manifest, for they say there are twenty letters: Γ, A, B, C, D, E, F, G, a, b, c, d, e, f, g, aa, bb, cc, dd, ee. Since there are not twenty, but only seven diverse ones, after which no others but the same ones are reborn as if anew. But these people begin from the letter Gamma original: Γ and end at the third 'c', because they invent the story that Gregory Pope Gregory the Great, to whom Gregorian chant is traditionally attributed wished to place the first letter of his name there, and named it with the Greek name Gamma because the teachings of music were handed down by the Greeks.

But I respond that even if this were permitted to them, they wander greatly from the truth in their division when they say there are eight "grave" (low) notes, seven "acute" (high) notes, and five "super-acute" (very high) notes; for it has been shown that the eighth letter and the first differ only in pitch—that is, in height and depth. But further, they try to fortify themselves with the authority of Boethius, as they say; for they say the first high note is the Mese The "middle" note in the Greek system which is the letter 'h' [a], and 'a' is the second. It is gathered, therefore, among the low notes that Γ is placed by them. Even if it is said by Boethius, the placement of Γ among the low notes by Gregory was not well-said because of the addition of the letter Γ. Just as the first 'a' relates to 'b', or to the second 'a', so it relates to Γ. But the second 'a' differs from the first 'a' only in pitch; therefore Γ will also differ from 'a' only in pitch. Given twenty letters, the division ought to be made such that there are seven low, seven high, and six super-high notes. But the addition of the letter did not please Gregory, since he used only fifteen. Tinctoris Johannes Tinctoris (c. 1435–1511), a famous music theorist, however, being foreign to this reasoning, says the first Γ is the lowest, the second is low, and the third is high. Truly, we shall show a little later from where this error has invaded the singers. Now let us proceed to declare the teaching of others.

A subtle application of the aforementioned figure for the use of singers

All these twenty letters Guido the Monk Guido d'Arezzo (c. 991–1033), the inventor of modern musical notation—perhaps a better monk than a musician—embraced while using the four-string scale tetrachord as he composed the six-string scale hexachord. And he was compelled to this kind of hexachord for this reason: because the number six is called perfect by mathematicians, because its divisor parts [1, 2, 3] when taken together constitute that same six; namely, 1, 2, and 3, which together make six. And each string of this hexachord is named from the first six syllables of six words...

A faint woodcut illustration depicts a Guidonian hand, a mnemonic device used in medieval music to teach the notes and hexachords by mapping them to the joints of the human hand.