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Pythagorean Plato: Prelude to the Song Itself
In essence, the book is pointing out that Plato borrowed a great deal from Pythagoras, more specifically his interest in harmony. The argument in the book is that Plato's Dialogues are saturated in this cryptic harmony. The author caught on to occult symmetry in Plato's writings, illustrating that the soul can be tuned to perfection just like an instrument and how the lives of societies even can be composed and performed like the perfect symphony.
- GenresMusicPhilosophy
192 pages, Paperback
First published January 1, 1978
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About the author
Ernest G. McClain
7 books2 followersErnest G. McClain is Professor Emeritus of Music, Brooklyn College of the City University of New York, retired since 1982 and living presently in Washington, D.C.. Clarinetist, band director, author of three books and more than thirty related essays in various professional journals, his degrees from Oberlin, Northwestern, and Columbia are in Music Education.
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January 26, 2021
When McClain promised in this book that, “the allegories are musical and… involve one octave, ten numbers,” I was hopeful I’d be able to fully comprehend the math. Sadly, that was not the case. I’m not a numbers person, and McClain’s math — which was not limited to simply ten numbers — often eluded me.
But I am a musician, more or less. I studied piano and violin when I was young. At one time in my life, I could play four-octave scales in any key and my experience with scales helped me to eventually penetrate the point of this book.
Ultimately, McClain's point was that Plato based good governance on good musical tuning. This metaphor, though, requires understanding a complex backstory.
Prior to Plato, Pythagoras developed a system of musical tuning in which he built a scale using fifths (intervals of five). This tuning system would create a problem central to both music and, for Plato, political theory. When you calculate a scale using perfect fifths (which you can do with a calculator: simply start with a frequency in Hz of your root note and multiply it seven times by 1.5 or the ratio 3:2)... let's start again: When you calculate a scale using perfect fifths, you will not reach the exact frequency of the next octave above your root note. In fact, the eighth note of your scale will be ever so slightly sharp. The gap between the expected octave note and the one you arrive at by stacking fifths is called the Pythagorean Comma, and to solve for this problem, musicians have been mis-tuning their instruments for centuries.
Today we call that mis-tuning “equal temperament” and it’s the process of shaving off a few “cents” of frequency from each note in the diatonic scale. This allows you to squish the notes together and end up at the proper frequency for the next octave note. This solution is what allows harmonies to “work.” It also precludes the need for musicians to have to re-tune their instruments every time they change key.
But this solution is a trade-off. For a workable, harmonious scale that can be expanded into neighboring octaves, you give up “pure” intervals that give individual notes their richness and beauty. For the sake of the scale, temperament penalizes the note.
Plato saw the same necessary trade-off in governing a society. Allowing individuals to go about according to their true natures caused a "gap" in Plato's understanding of justice. Individuals, like notes of a scale, required temperament.
But temperament, whether musical or political, isn’t a neutral activity. It results in a winner and a loser. For the sake of the city, government penalizes the individual.
“In Plato's ideal city,” writes McClain, “which the planets model, justice does not mean giving each man… ‘exactly what he is owed,’ but rather moderating such demands in the interests of ‘what is best for the city.’” Good governance requires that the individual, whether a man or the tone of a scale, should be tempered with a mis-tuning for the greater good.
It's a fascinating subject and my only complaint is that McClain made the ideas rather difficult for the lay-person to follow and comprehend.
But I am a musician, more or less. I studied piano and violin when I was young. At one time in my life, I could play four-octave scales in any key and my experience with scales helped me to eventually penetrate the point of this book.
Ultimately, McClain's point was that Plato based good governance on good musical tuning. This metaphor, though, requires understanding a complex backstory.
Prior to Plato, Pythagoras developed a system of musical tuning in which he built a scale using fifths (intervals of five). This tuning system would create a problem central to both music and, for Plato, political theory. When you calculate a scale using perfect fifths (which you can do with a calculator: simply start with a frequency in Hz of your root note and multiply it seven times by 1.5 or the ratio 3:2)... let's start again: When you calculate a scale using perfect fifths, you will not reach the exact frequency of the next octave above your root note. In fact, the eighth note of your scale will be ever so slightly sharp. The gap between the expected octave note and the one you arrive at by stacking fifths is called the Pythagorean Comma, and to solve for this problem, musicians have been mis-tuning their instruments for centuries.
Today we call that mis-tuning “equal temperament” and it’s the process of shaving off a few “cents” of frequency from each note in the diatonic scale. This allows you to squish the notes together and end up at the proper frequency for the next octave note. This solution is what allows harmonies to “work.” It also precludes the need for musicians to have to re-tune their instruments every time they change key.
But this solution is a trade-off. For a workable, harmonious scale that can be expanded into neighboring octaves, you give up “pure” intervals that give individual notes their richness and beauty. For the sake of the scale, temperament penalizes the note.
Plato saw the same necessary trade-off in governing a society. Allowing individuals to go about according to their true natures caused a "gap" in Plato's understanding of justice. Individuals, like notes of a scale, required temperament.
But temperament, whether musical or political, isn’t a neutral activity. It results in a winner and a loser. For the sake of the city, government penalizes the individual.
“In Plato's ideal city,” writes McClain, “which the planets model, justice does not mean giving each man… ‘exactly what he is owed,’ but rather moderating such demands in the interests of ‘what is best for the city.’” Good governance requires that the individual, whether a man or the tone of a scale, should be tempered with a mis-tuning for the greater good.
It's a fascinating subject and my only complaint is that McClain made the ideas rather difficult for the lay-person to follow and comprehend.
Displaying 1 of 1 review