APOLOGY. 7

the laws it carries itself, so much goodness is judged to be in the craftsmanship. For example, the artist can establish short sounds in all the voices of polyphonic song original: cantus figurati; music where different voices move at different speeds; if, however, he assigns long measures to the Bass, and short ones to the Descant; here he looks to nature. For we have said that deep sounds, even in the formation of their very essence, are related to long durations of time, and sharp sounds to short ones. But if, on the contrary, he occasionally commands the Bass to flutter about in short measures, he devises an extraordinary seasoning, using a plan drawn from the flowers of his art and from his own arbitrary license. I touched upon this in Chapter 16, page 83, regarding the alternation of consonances.

When you have weighed these things, I will indeed be surprised if you can offer any further excuse as to why, in this Analysis, you denied that the various dimensions of Time, in length and brevity, are arbitrary. For you speak of this very respect of time as a measure.

As far as this respect of Time is concerned, which we are accustomed to call "Times" rather than "Time," I wonder in turn, Robert, why you wonder why I wrote nothing at all about times in my Harmonic work. These words you interpret to mean that I judge the investigation of Times to be frivolous.

For I ask you, when I was defining Song in Chapter 13, did I not insert a small part of the definition that embraced the measures of times? Can anything be judged frivolous which the one said to judge it so places in the very definition of the thing? Or did I not, in turn, in the explanation of that small part on page 63, in the paragraph on Measures, clearly enough indicate to the readers the cause of my brevity—namely, that it was not my purpose in this work to dispute about Measures? Why do you wonder that more was not disputed by me? Accept the reason: it was not my purpose. Although even in Book 4, page 125, I added a few things which Poetics The study of meter and rhythm in poetry shares in common with artificial Music regarding Measures; because in that place, it was my purpose to explain the variety of subjects in which Harmonies might exist.

The measure of the beat has no place in planetary Harmonies.

The arguments you bring forward to prove that one writing about the Harmonies of the Planets must dispute about time are drawn from a previous respect of time, of which we have no speech in the present part of our comparison. I certainly compare deep sounds to the motions of Saturn; as the slowest planet, it is the one that completes very little of its journey in a long time. But how long Saturn maintains that same depth of sound—that is, the same and uniform slowness of its motion—this has nothing to do with celestial Harmony. In that harmony, every degree of slowness (if we are acting most accurately) is momentary; thus it is not possible for a man to procure a uniform motion of Saturn lasting for any length of time; nor is it possible original: ενδεχόμενος (endechomenos), meaning admissible or possible within the natural order, once the continuous change of the interval between the Planet and the source of its motion has been established. This change of interval is necessarily followed by a continuous intensification and relaxation of motions, except at the Apsides The points in an orbit where a planet is closest to or farthest from the sun, where its speed momentarily stops increasing or decreasing. Therefore, the measure of time has no place in celestial motions contemplated Harmonically, insofar as they are contemplated harmonically. It does, however, have a place where it can be procured—namely, in the Harmony of the human voice, which is entirely occupied with the uniformity of sounds, as I explained in Book 4, page 125, number 10. For not all music, but at least the music of the human voice, is maimed and deficient without the measure of time. And as far as the music of the human voice is concerned, it was enough for me to have advised briefly on said page 63, since I was hurrying toward the celestial and astronomical harmonies, in which the temporary duration of uniform speed has no place. This is because the scope of my entire work was fixed not on that human harmony, but on this celestial Harmony; as I clearly professed on page 85 of Book 3.

In the meantime, as if stepping off the path, I thought I should warn you that I have been poorly understood by you regarding the Cube; I established that figure as being neither heavy in weight nor in sound; nor did I interpose it for the supreme planets because of the slowness of their motions, but rather to establish the figural interval between them.

Page 7. The harmonic proportions of the planets do not consist in the length of their periodic Times.

The same caution must be applied by me regarding your page 7 concerning the various motions of a single planet. For the periods The total time it takes for a planet to complete one full orbit will do nothing to demonstrate that harmonic proportions are found in the motions of the Planets; I carefully guarded against this in Book 5, Chapter 4, page 194, from the beginning. Moreover, the mean daily motions The average speed of a planet, which is a mathematical abstraction rather than its actual speed at any specific moment of the Planets are not suitable terms for Harmonies, as they are not true but only imaginary; I, however, in the real motions of the planets themselves...