D E F E N S E

How irrelevantly the times attributed to the periods of the planets The time it takes for a planet to complete one full orbit around the Sun. are compared with one another. For these times are nothing but a number; they do not measure the duration of a motion that is uniform in all its parts. You are mistaken here, Robert, and you cling more stubbornly to the uniformity of motions taught by ancient astronomy than is helpful for this investigation. This is why you judge the speed of each planet based on the time it takes to return to its starting point. Therefore, you are not dealing with the actual bodies of the planets as I am, but rather with the writers of theoretical systems and with Aristotle, remaining focused on the concentric sphere The ancient Aristotelian model where planets were fixed on nested, perfectly circular crystalline spheres. which encloses and carries each system from the outside.

But in this, the whole heaven is misunderstood: these fictitious "orbs" must be cast out of the mind. Instead, one must embrace the sixth axiom from Chapter III of the fifth book of my work (page 188). I say this not because the axiom is mine, but because the most certain logic of celestial observations, when reduced to calculations, testifies that this axiom is true regarding the actual bodies of the planets. Therefore, even if I had said absolutely nothing about the measurement of time in my explanation of human song, no error would flow from that into my fifth book or into the contemplation of the Harmonic celestial motions Kepler’s theory that the speeds of planets correspond to musical intervals..

REGARDING ANALYSIS VI

The smallest intervals of song ought not to be called consonant

I am not the only one, Robert, who has pronounced the smallest intervals to be dissonant Sounds that create tension or "clash," requiring resolution.. Ptolemy and indeed all writers on Harmony said the same before me. See to it that you do not claim to be a defender of the ancients in vain, since you are here attacking them of your own accord.

But explain your contrary arguments. 1. You say a Tone is consonant with an equally tempered Tone, as in a unison. You are playing with an ambiguity of terms: for you, "Tone" here means "sound" original: sonus, using the term for the interval. When two strings produce a unison Two voices or instruments playing the exact same pitch., there is no interval at all, and thus it cannot be called a "Tone," for a Tone is one of the intervals. But Harmonic theorists call a Tone a dissonant interval, because two voices separated by a tone clash with each other.

2. You say a semitone added to certain harmonies makes another harmony; therefore, it is a consonant interval. Robert, you are incorrectly viewing the effect as the cause. There are intervals that distinguish between harmonies, and for this duty they are usually called fitting original: εμμελῆ (emmele); sounds that fit in a scale but aren't necessarily pleasant on their own., but not consonant original: σύμφωνα (symphona); sounds that blend harmoniously together.. I warn my reader not to listen to you here, if they wish to avoid confusion, for you indiscriminately call the same things both consonant and dissonant.

REGARDING ANALYSIS VII

Page 9.

One of the reasons why I did not touch upon the practice of musical composition is, without a doubt, that I am ignorant of it and unpracticed in this kind of work. But by what marks in my works will you prove this without my own confession? Show me the songs composed by Pythagoras, Ptolemy, or Porphyry. Do you then also drive these men away from Theory? O, poor little philosophers, who obtrude their speculations on the work of creation when they have created nothing themselves! Surely Theory finds its support even in the eyes and in the experience of the work of others. As for the rest, I forgive your bitterness in taking up and exaggerating my own self-deprecations, for you clearly wrote while angry. You indeed, as appears here and in what came before, make much of proportions—even those that men have established in musical notes. There are many such in the fourth book of my work (page 125). Certainly, these are not sound proportions simply because they were chosen a few centuries ago by Guido of Arezzo A medieval music theorist often credited with inventing modern musical notation and the "Do-Re-Mi" system. and his associates for writing song, but because they imitate certain other works of Nature or of God the Creator.

REGARDING ANALYSIS VIII

Who are you striking at here, Robert? Or what is the cause of such great emotion for you? For I have hidden myself in a corner, far from your blows. Indeed, my text gave you no cause for this, as it contains nothing besides a frank confession intended to let readers know what they should not expect to find in my book.

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