It had never occurred to me before that music and thinking are so much alike. In fact you could say music is another way of thinking, or maybe thinking is another kind of music.
—
Ursula K. Le Guin (1929– )Solution to Harmonics and
Music Exercise 4.27.
It had never occurred to me before that music and
thinking are so much alike. In fact you could say music is another way of
thinking, or maybe thinking is another kind of music.
—Ursula K. Le Guin (1929– )
Exercise 4.27. A different scale called the equal temperament scale is used in tuning pianos. The frequency ratios are 1.000 (C) : 1.122 (D) : 1.260 (E) : 1.335 (F) : 1.498 (G) : 1.682 (A) : 1.888 (B). If a string is tuned to C (as with the example above) and the equal temperament scale is used, investigate whether or not the major triad C, E, and G determines a harmonic set H(OE, CG).
The O, E, C, G do not form a harmonic set H(OE,CG). Consider the construction of G1, the harmonic conjugate of C with respect to O and E in the diagram. G and G1 are distinct points, since the length of OG does not equal the length of OG1. Since the harmonic conjugate is a unique point, H(OE,CG) is not valid.
It is only by introducing the
young to great literature, drama and music, and to the excitement of great
science that we open to them the possibilities that lie within the human
spirit—enable them to see visions and dream dreams.
—Eric Anderson
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© Copyright 2005, 2006 - Timothy Peil |
