APPENDIX ON HARMONICS

...I call "motions," Kepler is likely quoting Fludd's accusation that Kepler attributes divine power to created things. to take this title away from the Creator and grant it to the creature. I fear, as the nation is so perverse today, that this injustice may extend beyond words into actual deeds, if some readers rashly believe you without inspecting my own text.

ON ANALYSIS XII.

Page 14. In response to my six lines, and short ones at that, you pour back more than six full pages. I wish I could draw out and explain most of these for the reader's benefit.

First, you reproach me for boasting, as you often do. I do not fear that the reader will believe this. Since I am occupied with teaching, the distinctions between our books had to be set forth, of which this one is not the least. When asked what the difference is, I reply: my purpose is one thing, yours is another. You take from the ancients and use what is taken; I see to it that nothing is taken that is contrary to nature. You have not thought about things that are confused; I, moreover, wished to arrange them. With these words, the reason is suggested to readers why we do not agree in all things—this, too, is for the reader's use.

Next, you complain that I am attempting to expose your ignorance and lack of skill to the World: you are clearly mistaken, or you are deceiving. As I said, I compare my work with yours to educate the reader, who I know gains nothing from anyone's ignorance or lack of skill. You go on to say that I attribute nothing to your own invention. If you pay close attention to the matters I deal with in this text, you will admit that very thing. Why, then, would I say anything false about you? The question is: what harmonic proportions proportions: the mathematical ratios that define musical intervals do you hand down? By what numbers are they encompassed? What is a tone to you? What is a semitone? You take all these from the ancients. I, even though some things are also found among the ancients, do not take them as from the ancients, but—setting aside the authors—I dig them out from the very foundations. Do you resist and point out what you have discovered? What are those things? Hieroglyphic pictures Fludd’s famous symbolic and mystical engravings.. But here you may win without me fighting; I was not speaking here except about the proportions of intervals. Nor did I mock you for following the ancients, even if they were in error, as long as this was hidden from you. Not everything can or should be treated everywhere.

Do you ask for an instance of incorrectness and confusion? Look: you define the semitone with Plato original: "Semitonium cum Platone" ordinarily by the numbers 243 and 256. This is incorrect. For two major tones major tone: the musical interval defined by the ratio 8:9 are not given in succession such that their sum (64 to 81) subtracted from the fourth (3 to 4) leaves 243 to 256. And let this now be an example of confusion: that you hold two tones with Ptolemy Claudius Ptolemy, an ancient astronomer and music theorist. as 8 to 9 and 9 to 10, and to these you add the semitone 243 to 256. But if there are two tones in succession, one 8 to 9 and the other 9 to 10, their sum—8 to 10 or 32 to 40—subtracted from the fourth (3 to 4 or 30 to 40) leaves the semitone 30 to 32, which is 15 to 16. Therefore, the semitone of Plato is confused with the tones of Ptolemy. Many such things occur, which are not to be blamed in one who uses them if his purpose was to follow the ancients; but they are to be avoided by the reader if he aspires to a corrected knowledge of Harmony. Therefore, they must be pointed out by the teacher if he wishes to be seen as having done his duty. Thus, the reproach of dog-like envy original: "invidiæ caninæ"—a common idiom for snarling or biting criticism. cast at me does not stick. Nor do you prove the crime you charge: that I accuse you for imitating the opinions of others. For I consider it a credit to myself to follow the ancients when they are not in error; and I congratulate human happiness whenever I feel I am able to do so. Likewise, whenever I cannot do this, I desert the ancients and flee to nature. There is no inconsistency here; for I have it as my purpose to strive constantly toward the Truth by either path.

Therefore, as for why you prefer the intervals of Pythagoras and Boethius Pythagoras and Boethius were the traditional authorities on mathematical music theory based on whole-number ratios. to mine: you will not persuade me until you dissolve the objections I have raised against them and demolish my own foundations, and do so with words and quantitative diagrams. For it would cost me too much to run across the sea Kepler lived in mainland Europe; Fludd lived in England. with your "sons of wisdom" to drink these things from your mouth under a pledge of silence, and to understand the things presented in your riddles through the expressed picture of your temple.

It is consistent with what has been said that I should thank you for seeking out places in my books where I have imitated the ancients—though I could have done it more correctly myself, and without the risk of hallucination. However, whatever you heap up here regards other matters. But the part of the comparison we are now dealing with concerns the origin of Harmonies in particular. Here, I am that same man who imitates the ancients so many other times, but now I reject them and consult the nature of things. There is no inconsistency in my assertions here.