Harmonics

The character of an audible sound is determined by several features. The volume of the sound, its loud-ness, is determined by the amplitude of the oscillations in the sound wave, the distance individual air molecules oscillate as the wave travels. A larger amplitude produces a louder sound and transmits more energy. The pitch of a note is the frequency or number of oscillations per second. A higher frequency produces a higher pitched note. The richness or quality of a sound is produced by the harmonics.

A pure note, that is, one consisting of a perfect sinusoidal wave (single frequency), tends to sound boring. A musical instrument that only produced such pure notes would not be pleasing. For a tone to be perceived as rich, the human ear demands harmonics. These are tones whose frequencies are integer multiples of the fundamental frequency of the sound. For example, the first harmonic is the fundamental frequency, 264 cycles per second for middle C. The second harmonic will be twice this frequency, 528 cycles per second, which is an octave higher. The third harmonic will be three times the fundamental frequency, 792 cycles per second, and so on. These harmonics are also called overtones—the second harmonic is the first overtone, the third harmonic the second overtone, and so on. Tones at simple fractional multiples of the fundamental frequency, such 3/4, are called inharmonics. These are also present in musical sounds. The sound we hear is a single sound wave, but it can be considered as being constructed by summing a fundamental note and a number of harmonics and inharmonics, each present at a different amplitude or loudness.

The violin, piano, and guitar all produce sounds by vibrating strings. Playing the same note, say middle C, will produce a tone with a fundamental frequency of 264 cycles per second. Yet all three instruments sound different because they have different harmonics. The amount of each harmonic present is what gives each musical instrument its own unique sound. A well-made instrument will sound richer than a poorly made one because it will have better harmonics. An instrument with no harmonics will sound like a tuning fork with only one fundamental frequency present.

For reasons that we do not completely understand, sounds composed of harmonics whose frequencies are integer multiples of each other sound pleasing to the human ear. They are musical. On the other hand, musical composed of frequencies that are not integer multiples of each other are dissonant to the human ear.

The foregoing is a simplification of the facts of sound perception: pleasing human voices are not simple combinations of harmonic tones, for example, and a certain amount of distortion or nonharmonic, nonlinear noise (as in some electric guitar sounds) can be pleasing to listeners. Indeed, few musical instruments— the French horn is one—produce tones that can be closely approximated as sums of pure harmonics.

Harmonics

What makes a note from a musical instrument sound rich? The volume of the sound is determined by the amplitude of the oscillations in a sound wave, the distance individual molecules oscillate. A larger amplitude produces a louder sound and transmits more energy . The pitch of a note is the frequency or number of oscillations per second. A higher frequency produces a higher pitched note. The richness or quality of a sound is produced by the harmonics.

A pure note consisting entirely of one frequency will sound boring. A musical instrument that only produced such pure notes would not sound pleasing. The harmonics are missing. The harmonics are integer multiples of the fundamental frequency. The first harmonic is the fundamental frequency, 264 cycles per second for middle C. The second harmonic will be twice this frequency, 528 cycles per second, which is an octave higher. The third harmonic will be three times the fundamental frequency, 792 cycles per second, and so on. These harmonics are also called overtones—the second harmonic is the first overtone, the third harmonic the second overtone, and so on.

The violin, piano, and guitar all produce sounds by vibrating strings. Playing the same note, say middle C, will produce a tone with a fundamental frequency of 264 cycles per second. Yet all three instruments sound different because they have different harmonics. The amount of each harmonic present is what gives each musical instrument its own unique sound. A well made instrument will sound richer than a poorly made one because it will have better harmonics. An instrument with no harmonics will sound like a tuning fork with only one fundamental frequency present.

For reasons that we do not completely understand, sounds composed of harmonics whose frequencies are integer multiples of each other sound pleasing to the human ear . They are music. On the other hand, sounds composed of frequencies that are not integer multiples of each other are dissonant noise to the human ear.

harmonics. Any note prod. by an instr. is accompanied by a number of other notes at fixed intervals above it. These are heard as the constituents of the single note, but can be prod. separately. On str. instrs. this is done by touching the string lightly at various points (‘nodes’) so splitting up the vibrations and producing notes of a flute-like purity (in Ger. and Fr. harmonics are indeed called flageolet). The lowest tone of the harmonic series (the ‘fundamental’) is the 1st harmonic, the next lowest the 2nd harmonic, and so on. Other tones are the ‘upper partials’ or ‘overtones’, at fixed intervals above the fundamental, an octave, then a perfect 5th, etc. On an open str. the result is a ‘natural’ harmonic; on a ‘stopped’ str. (a finger used to stop and another lightly placed) it is an ‘artificial’ harmonic. In brass instrs. harmonics are produced by varying the method of blowing. Every note of normal mus. instr. is a combination of the fundamental and certain upper partials. The only exception is the tuning-fork.

harmonics (overtones) In acoustics, additional notes whose frequencies are multiples of a basic (fundamental) note. When a violin string is plucked, the sounds correspond to vibrations of the string. The loudest note corresponds to the fundamental mode of vibration. Other weaker notes, corresponding to subsidiary vibrations, sound at the same time. Together these notes make up a harmonic series.