On the Institution of Music (De institutione musica)

there will be no need to dwell on this work.

Which strings are compared to which stars. Chapter [27].

That much, meanwhile, needs to be added to the previous [discussion] of the twenty-seventh [chapter].

It seems something must be added to the tetrachords the four-note scales that form the basis of the Greek system, because from the hypate melon original: hypate melon; the principal note of the "middle" tetrachord up to the nete original: nete; the last or highest-pitched note of the system, there is, as it were, a certain celestial model in its order and distinction. For the hypate melon is attributed to Saturn. The parhypate the note "next to" the hypate, however, is similar to the circle of Jupiter. They have assigned the lichanos melon the "forefinger" note of the middle tetrachord to Mars. The Sun occupies the mese the "middle" note, often considered the most important. Venus holds the trite synemmenon the third note of the "conjunct" tetrachord. Mercury rules the paramese synemmenon the note next to the middle in the conjunct system. Moreover, the nete holds the model of the lunar circle.

But Marcus Cicero Tullius Cicero original: M. Tullius; the Roman statesman and philosopher makes the order contrary. For in the sixth book of The Republic specifically from the "Dream of Scipio," a famous text on the harmony of the spheres, he says thus: "And nature brings it about that the extremes sound low on one side and high on the other. Wherefore that highest starry course of heaven, whose revolution is more rapid, is moved by a high and excited sound; while this lunar and lowest one [is moved] by the deepest." For the Earth, the ninth [sphere], remaining immobile, always clings to one seat.

Here, therefore, Tully [Cicero] places the Earth as if it were a silence, but immobile. After this, to that which is nearest to silence, he gives the deepest sound to the Moon, so that the Moon is the proslambanomenos original: proslambanomenos; the "added note" at the very bottom of the Greek scale; Mercury is the hypate hypaton; Venus the parhypate hypaton; the Sun the lichanos hypaton; Mars the hypate melon; Jupiter the parhypate melon; Saturn the lichanos meson; and the highest heaven is the mese.

Which of these strings are truly immobile, which are entirely mobile, or which consist of both immobile and mobile parts, will be much more clearly explained when you treat the regular division of the monochord a single-stringed instrument used to demonstrate musical ratios and intervals.

What the nature of consonance is. Chapter 28.

Large blue ornamental initial 'C' with red pen-flourishing extending into the margin and an internal yellow circular detail. Consonance, although the sense of the ear judges it, nonetheless reason weighs it. For when two strings are stretched with one tension, and being struck together, they return a somewhat mixed and sweet sound, and the two voices

coalesce as if mixed into one, then that which is called consonance from the Latin con-sonantia, meaning "sounding together" occurs. But when, being struck together, each [sound] desires to go its own way, nor do they blend into a sweet and single sound composed of the two, then it is that which is called dissonance. Where consonance is found

How it may be aided by these comparisons. Chapter 29.

and by aid it is necessary that these dissonances likely a scribal error or specific technical usage, as the context describes the math of consonances be found which are commensurate with one another—that is, which can have a common measure. Just as in multiples, the "double" [ratio of 2:1] is that part which is measured by the difference between two terms; for instance, between 2 and 4, the number two [the binary] measures both. Between 2 and 6, which is a "triple" ratio [3:1], the number two measures both. Between 8 and 8, the same unit is what measures both.

Again, in superparticulars ratios where the larger number contains the smaller plus one part of it, like 3:2 or 4:3, if there is a sesquialtera proportion original: sesquialtera; a 3:2 ratio, which creates a musical fifth, such as 4 to 6, it is the number two that measures both, which is clearly the difference of both. But if it is a sesquitertia proportion original: sesquitertia; a 4:3 ratio, which creates a musical fourth, as if 8 were compared to 6, the same number two measures both.

This, however, does not happen in the other kinds of inequalities which we rejected above, such as in the superpartient ratios where the larger number contains the smaller plus more than one part of it, like 5:3. For if we compare 4 to 3, the number two, which is their difference, measures neither. For compared once to 3, it is smaller; but doubled [to 4], it exceeds it. Likewise, compared twice to 5, it is smaller; but the third time, it surpasses it. And therefore this first kind of inequality is separated from the nature of consonance.

Furthermore, in those things that form consonances, many things are similar; in the others, however, not at all. This is proven in this way: for the "double" is nothing other than twice the simple; the "triple" is nothing other than thrice the simple; the "quadruple" is the same as four times the simple. But the sesquialtera is twice a half; the sesquitertia is a third part, which is certainly not the case in other inequalities...