On the Syllabic Names of Sounds and Their Distances.

Chapter Two

Decorative drop cap 'S'The authority of Virgil in the sixth book of the Aeneid original: "aeneidos" celebrated the seven essential strings, described by seven letters as written by Gregory in this poem: "The Trojan priest, with his long robe, speaks back in numbers, seven distinct voice-intervals." From this, Guido himself completed the introductory work using seven mixed hexachords six-note musical scales. A hexachord is a collection of six strings arranged in a diatonic dimension, whose names are: ut, re, mi, fa, sol, la. For "ut" and "re" are grave, "sol" and "la" are acute, and "mi" and "fa" are intermediate. It is the custom of ecclesiastics, however, to call "ut" and "re" grave, and "mi" and "fa" super-acute. Guido himself arranged these so that he defined each interval of the perfect and diatonic system by only two syllables of this kind. For between "ut" and "re" the interval is closed by a sesquioctave a ratio of 9:8 dimension of a tone. The same applies between "re" and "mi". But between "mi" and "fa" is the distance of a minor semitone. Between "fa" and "sol", and between "sol" and "la", a whole tone is extended. Wherefore "re" is higher than "ut" by a tone, and likewise "ut" is lower than "re" by a tone. "Re" is surpassed by "mi" in acuteness by a tone, and "mi" is beneath it in gravity by a tone. "Fa" is lower than "sol" by a tone, and "sol" exceeds "fa" in acuteness by a tone. "La" is overcome by "sol" in gravity by the interval of a tone, but "la" exceeds "sol" in acuteness by a sesquioctave original: "epogdoa" distance. However, "fa" is known to be sharper than "mi" by the space of a minor semitone. Hence, by that same interval, it is necessary for "mi" to be lower than "fa". It is therefore evident that in every hexachord, four tones viewed through different notes enclose a minor and natural semitone in the middle place, which can be considered to have been done by necessity. For when you wish to consider the three forms of the diatessaron fourth according to the variety of tetrachords, you will nowhere be able to find them diatonically in a single hexachord unless those four tones have enclosed a middle semitone, which anyone can easily verify for themselves through these things we are doing. And for this reason, the individual semitones, naturally and diatonically arranged in the perfect system, are known to be cut by those two syllables, "mi" and "fa"; such was Guido's attention to the arrangement of the seven mixed hexachords. For he joined the beginning of each hexachord either to the tetrachord of the preceding hexachord, or he established it as separated from it by the interval of a tone. From this fact, in the heptachord, the first tetrachords of two hexachords are proven. But where the first tetrachord of the second hexachord ends, the third hexachord—called b-molle B-flat, which can also be called "joined"—takes its beginning, being added so that the harshness of the tritone in the modulation might become sweeter, and the composition of several tones might be able to proceed in a mixed and acquired manner through varied species of consonances. The fourth hexachord is separated from the first tetrachord of the second hexachord by the interval of a tone in the acute direction.

Gregory

Virgil
Guido

In praise

of Guido