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Ptolemy Harmonics: Translation and Commentary (Mnemosyne Supplements)

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Harmonics is not the science of music, and it is not the ability of the human ear to hear harmonics. Harmonics is a function of nature that allows humans to perceive, accept, digest, feel, emote, intuit, study, compute, hypothesize, and theorize the differences between highness and lowness in sounds, whether they are heard (or hearable) or not. Perception functions to differentiate things, among them sounds, and of sounds by how much they differ in highness and lowness, this highness being anywhere within the edge of the then-known, (by today's standard) microscopic universe at the end of Saturn's nested shell, the lowness being perhaps the 85:84 diesis, which Ptolemy so carefully avoids, played on a small lyre by a mere mortal musicologist here on earth. Harmonics begins when the proverbial tree falls in the forest and makes the air be beaten, and it ends when that abused bit of our atmosphere enters our ears, filters to the seat of reason, concords with the similarly calculable notes within us and in the distant heavens, and gives us pleasure in knowing that there is in the huge, sometimes audible, sometimes visible universe, a unified, predictable, divinely ordained order.