 | Harmonic series music: Encyclopedia II - Harmonic series music - Description of the harmonic series
Harmonic series music - Description of the harmonic series
The lowest possible frequency of a harmonic oscillator is called its fundamental frequency. This frequency determines the musical pitch or note that is created by vibration over the full length of the string or air column.
In nearly every musical instrument, the fundamental note is always accompanied by other, higher-frequency tones that are generally called overtones. In pitched (i.e., non-percussion) instruments, these shorter, faster waves are reflected between the two ends of the string or air column. As the reflected waves interact, frequencies whose wavelengths do not divide evenly into the length of the string or air column are suppressed, and the vibrations that persist are called harmonics. Their wavelengths are 1, 1/2, 1/3, 1/4, 1/5, 1/6, etc. of the length of the string or air column. To better understand this, see node.
Theoretically, these wavelengths produce vibrations at frequencies that are 2, 3, 4, 5, 6, etc. times the fundamental frequency. Physical characteristics of the vibrating medium and/or the resonator against which it vibrates often alter these frequencies. (See inharmonicity and stretched tuning for alterations specific to wire-stringed instruments and certain electric pianos.) However, those alterations are small, and except for precise, highly specialized tuning, it is reasonable to think of the frequencies of the harmonic series as integer multiples of the fundamental frequency.
The harmonic series is an arithmetic series (2×f, 3×f, 4×f, 5×f, ...). In terms of frequency (measured in cycles per second, or hertz (Hz)), the difference between consecutive harmonics is therefore constant. But because our ears respond to sound logarithmically, we perceive higher harmonics as "closer together" than lower ones. On the other hand, the octave series is a geometric progression (2×f, 4×f, 8×f, 16×f, ...), and we hear these distances as "the same" in all ranges. In terms of what we hear, each octave in the harmonic series is divided into increasingly "smaller" and more numerous intervals.
The second harmonic, twice the frequency of the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher). The combined oscillation of a string with several of its lowest harmonics can be seen clearly in an interactive animation at Edward Zobel's "Zona Land".
For a fundamental of C1, the first 16 harmonics are notated as shown. You can listen to A2 (110 Hz) and 15 of its partials if you have a media player capable of playing Vorbis files. You can also hear a sweep of the first 20 harmonics of A1 (55 Hz) in Quicktime format by clicking here.
Other related archivesAdditive synthesis, FM synthesis, Harmony, Mathematics of musical scales, Missing fundamental, Overtone singing, Paul Hindemith, Pedal tone, Physics of music, Vorbis, a media player capable, amplitudes, arithmetic series, bassoon, brass instruments, bugle, bugle calls, clarinet, dissonance, flugelhorn, formants, fundamental frequency, geometric progression, harmonic oscillator, harmonic series (mathematics), hertz, inharmonic, inharmonicity, just noticeable difference, logarithmically, mouthpieces, musical instruments, node, oboe, octave, octave key, overtone, overtones, pedal tones, perfect fifth, perfect fourth, piano, piano acoustics, pitch, reeds, resonance, saxophone, semitones, stretched tuning, timbre, transposed, trombone, trumpet, tuba, tuning, waves, woodwind instruments
 Adapted from the Wikipedia article "Description of the harmonic series", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
