Science & Music
by Sir James Jeans, Cambridge University Press (1937)
Reprinted by Dover Books (1967), page 86:
The timbre depends only on the relative energies of the various harmonics and not on their phase-differences. Differences of phase produce no effect on the ear. This is known as "Ohmís law," having been discovered by G.S. Ohm (1787-1854), the discoverer of the still better known electrical law also called Ohm's Law.
The second harmonic adds clearness and brilliance but nothing else, it being a general principle that the addition of the octave can introduce no difference of timbre or characteristic musical quality. When the second harmonic is of equal strength with the first, it produces much of the same effect as adding the octave-coupler on an organ or harmonium or playing in octaves, instead of single notes on the piano.
The third harmonic again adds a certain amount of brilliance because of its high pitch, but it also introduces a difference of timbre, thickening the tone, and adding to it a certain hollow, throaty or nasal quality, which we may recognize as one of the main ingredients of clarinet tone.
The fourth harmonic, being two octaves above the fundamental, adds yet more brilliance, and perhaps even shrillness, but nothing more, for the reason already explained.
The fifth harmonic, apart from adding yet more brilliance, adds a rich, somewhat horn-like quality to the tone, while the sixth adds a delicate shrillness of nasal quality.
As the table on p. 73 shows, all these six harmonics form parts of the common chord of the fundamental note, and so are concordant with this note and with one another.
The seventh harmonic, however, introduces and element of discord; if the fundamental note is c, its pitch is approximately b, which forms a dissonance with c. The same is true of the ninth, eleventh, thirteenth, and all higher odd-numbered harmonics; these add dissonance as well as shrillness to the fundamental tone, and so introduce a roughness or harshness into the composite sound. The resultant quality of tone is often described as "metallic", since a piece of metal, when struck, emits a sound which is rich in discordant high tones.
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Last modified 16 Feb 2024