“Bringing back from the depths of his memory the basic notions, he first undertook to establish the difference between sound and musical sound, noting that the latter was distinguished from the pure physical phenomenon by the existence of a certain symmetry among its harmonics; in other words, the specificity of musical sound came from the fact that the so-called periodic waves of a single tone containing a sequence of vibrations could be expressed in a ratio of small whole numbers; then he observed the kinship between two sounds, the primary condition of harmonic concordance, and remarked that ‘pleasure,’ that is to say the musical perception of this phenomenon, appeared when the two sounds in question contained a maximum of consonant harmonics, that is, when a minimum of them were in a dangerous proximity to one another; this, in order simply to allow him to identify, without the slightest doubt, the very concept of a musical system and to study the increasingly pitiful stages of its evolution, a study that would very quickly lead him to a crucial discovery.
If he had once learned something about the matter, he no longer remembered the details, no doubt because of their apparent futility; this is why he had to refresh and enrich his memory, so that during those weeks of fervor his room became covered with a mountain of notes (in which functions and calculations, commas and equations, indices of frequency and resonance were lined up) that one had to step over in order to move about. He had to understand Pythagoras and his daemon of numbers, how this Greek master, surrounded by the admiration of his pupils, on the basis of dividing the length of a string, had devised an interval system highly impressive in its kind, and he was compelled to admire the ingenious discovery of Aristoxenus who, thanks to his practice of ancient music and his instinctive ingenuity, relied entirely on his ear and, since he heard the universe of natural harmonies, had the brilliant idea of tuning his instrument according to a harmonic scale founded on the famous Olympian tetrachord; in short, he had to understand and he had to admire this interesting fact: that the philosopher seeking the principles of the world’s cohesion and the humble servant of harmonic expression, starting from two radically different sensibilities, arrived at astonishingly similar conclusions.
At the same time, he had to study what happened afterward, namely the sad story of the scientific evolution of instrumental music, that is, how the limits of natural tuning, the restriction which, because of the difficulties of modulation, formally excluded the use of higher key signatures, became more and more unbearable; in other words, he was compelled to follow step by step the fatal process that gradually caused the fundamental question—the meaning and importance of restriction—to fall into oblivion.”
László Krasznahorkai, The Melancholy of Resistance, folio, p. 167–169 (automatic translation)
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