ANALYTICAL DISCOURSE

The entire mystery of musical durations cannot be contained in a single volume. Undoubtedly, since this vocal and instrumental music is a kind of image and shadow of that true Music which thunders secondarily in the heavens, and primarily in the supersubstantial heavenA Neo-Platonic term for a realm of pure being above the physical or even the standard celestial spheres itself (according to that divine sentiment of IamblichusA Syrian Neoplatonist philosopher who wrote on the divinity of numbers and music: The soul in the intelligible world heard divine harmony, which it remembers here when it hears melodies possessing a divine trace; remembering it, the soul is vehemently moved toward it, if it is among the number of souls who especially contemplated the idea of harmony itself in their true homeland), it is necessary to imagine that there is no "variable" music in the heavens where a variety of times is also not found, since the proportions of both intervals and durations are the same. Indeed, it will be hidden from no one versed in Astronomy that the motion of the stars is distinguished by number and time. Consequently, we say that if the true proportions of celestial times and intervals are rightly compared with one another, a great understanding of mundane harmony may be drawn and derived from them. For motion can never leave its companion, Time, behind. Hence it is certain that just as PanIn Fludd’s philosophy, Pan represents the "All" or universal nature—the universal nature whose act is the moving soul—is said to be the son of Chaos, so also Time itself is the son of Eternity, without which Pan cannot endure or move for even a moment of space. From these things it is clear that if Time and Interval behave this way in this lower Music, it is necessary that they observe the same relationship to each other in the heavens. For just as the DiapasonAn octave, DiapenteA perfect fifth, and DiatesseronA perfect fourth are the harmonic intervals of artificial Music, so also they perform this same role in celestial things, and even in the Archetype itself. But truly, since motion does not happen without time—passing from one interval, as from a starting point, to another—it follows that times are found among the Planets in unknown proportions as well as known ones. Therefore, we conclude against the intention of the author [Kepler], who estimated the inquiry into durations to be frivolous, that the length and brevity of musical Time, or all its differences, require great investigation and are very necessary to his history of harmony. And therefore (as it seems to me), his greatest error lies in the fact that he said nothing about Durations or the length and brevity of sounds; and so the matter is far different than if the various dimensions of Time in length and brevity were merely arbitrary—rather, it follows that they require an investigation of their causes.

TEXT VI

He calls certain intervals "simple," which to me are the smallest dissonant concords: the Major Tone, Minor Tone, Semitone, and diesisA very small musical interval, smaller than a semitone. He wants others to be composed of these, which I call consonances. And yet, this opinion of the ancients—that consonances are composed of smaller intervals as if they were prior by nature—I expressly refuted in Chapter 4 of my third book, showing that, on the contrary, the smaller intervals arise from the larger consonances.

ANALYSIS

If I called the smaller intervals "simple" according to the opinion of the ancients, it was certainly not done without consideration; and when I said that the larger consonances were composed of them, I did not do that without a reason of great weight. Insofar as a whole is usually forged from its parts, and a multitude from its smaller members (the unit of which is sound), and a line from its points, and mathematical bodies from their plane figures (whose origin is the Triangle), so things that come after are formed from things that come before. I shall speak of these things below in their proper place, where I will strive to defend this assertion of the Ancients with irrefragable arguments, and I will attempt to refute the arguments brought forward by the Author.

But truly, because in this context he calls the smallest intervals—namely the Tone and Semitone—dissonant and not consonant, it seems that the matter turns out quite differently. Experience teaches that the tone of one string, corresponding to another by identity of proportion, is called "unison" in SymphoniaThe sounding together of voices or instruments. Hence, without doubt, the Tone is a consonant interval, although it can also be called dissonant in another respect. Furthermore, we also find that the space of the minor semitone is the cause of the difference between "soft song" and "hard song" original: "cantus mollis" (using B-flat) and "cantus durus" (using B-natural). Hence, if the b-flat signoriginal: "signaculum b. mollis" is expressed in the bass in B mi, it is certain that if the same sign is also placed in the same interval of the Tenor, it produces a most exact consonant voice. From this it is clear that since the Semitone makes a consonance with its voice, it is a consonant interval. But this is also clear in the pronunciation of the voice in B mi of different strings: where if the flat sign is expressed on the second line of one melody and not the other, the sound will be dissonant and incomplete; but if the flat is depicted in both intervals, the agreement of both will be consonant. And for this reason, the smaller intervals can be called consonant as much as