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Pitched musical instruments are usually based on some sort of harmonic oscillator, for example a string or a column of air, which can oscillate at a number of frequencies. The integer multiples of the lowest frequency make up the harmonic series.
The lowest of these frequencies is called the fundamental or first partial. This is the note created from the vibration of the full string length (the first transverse vibrational mode) of a stringed instrument or from air compression waves vibrating through the whole length of a woodwind instrument (the first longitudinal vibrational mode). All of the other frequencies in the harmonic series are integer multiples of the fundamental. The difference in terms of frequency (measured in Hertz (Hz)) is the same between all partials, but the ear responds in a logarithmic fashion, so the higher partials sound 'closer' together. Put another way: since the harmonic series is an arithmetic series (1f, 2f, 3f, 4f...), and the octave, or octave series, is a geometric series (f, 2×f, 4×f, 8×f...), this causes the overtone series to divide the octave into increasingly smaller parts as it ascends.
The second partial is twice the frequency of the fundamental, which makes it an octave higher. The third harmonic partial, at three times the frequency of the fundamental, is a perfect fifth above the second harmonic. Similarly, the fourth harmonic partial is four times the frequency of the fundamental; it is a perfect fourth above the third partial (two octaves above the fundamental). Note that double the partial number means double the frequency, which in turn means the 'pitch' is an octave higher. For example, the 6th partial is an octave higher than the 3rd partial.
After that the harmonics come thick and fast, getting closer and closer together. Some harmonics correspond very nearly to named pitches of the equal tempered scale; others, for example the 7th harmonic, are significantly off from the equal tempered tones. If you have a player capable of reading Vorbis files (for example Winamp 3), you can listen to A
For a fundamental of C', the first 16 harmonics are:
Since many instruments, and the fundamental intervals of Western harmonyThis article is about musical harmony. For other uses of the term, see Harmony (disambiguation) . Harmony is the art of using pitch simultaneity (or chords, actual or implied) in music. It is sometimes referred to as the "vertical" aspect of music, with m, are based on the harmonic series, many scale tuning systems (e.g. just intonationJust intonation is any musical tuning in which the frequencies of notes are related by whole number ratios. Any interval tuned in this way is called a just interval . Another way of considering just intonation is as being based on members of the harmonic) attempt to build the musical scale largely or entirely on the frequencies of the harmonic series. However, in modern equal temperament, many notes in the harmonic series are off pitch as indicated above.
Most instruments produce a number of frequencies in addition to the fundamental of the tone that is sounding. The amplitude and placement of different partials determine the timbreIn music, timbre is the quality of a musical note which distinguishes different types of musical instrument. See also: formant of speech, singing, and musical instruments. This is why, with a little practice, you can pick out the saxophone from the trumpe of different instruments. FormantA formant is a preferred resonating frequency of any acoustical system. It is most commonly invoked in phonetics or acoustics as the preferred vibrations of vocal tracts or musical instruments. However, it is equally valid to talk about the formant freques determine some of the character of the instrument, but the harmonic vibrations are probably the most important effect. For example, close ended reed instruments (e.g. the clarinetThe clarinet (sometimes historically spelled clarionet is a musical instrument in the woodwind family. A person who plays the clarinet is called a clarinettist. Professional clarinets are made from African hardwood, often grenadilla or (rarely) Honduran r, which is considered closed at the reed end) sound only odd numbered harmonics, giving each individual note a purer timbre than a stringed or brass instrument. It is the strength of higher harmonics in brass instruments that gives them their "brassy", rich, slightly dissonant timbre.
The placement of partials can also affect the perceived fundamental pitch. Not all musical instruments have partialsPartials could mean # in Music, Harmonics # in Mathematics, Partial derivatives. that exactly match the harmonic partials as described here. The partials of PianoPiano is a common abbreviation for pianoforte a large musical instrument with a keyboard (see keyboard instrument). Its sound is produced by strings stretched on a rigid frame. These vibrate when struck by felt-covered hammers, which are activated by the, and other, strings are increasingly sharper than perfect harmonics because the strings are stiff, leading to nonlinear, inharmonic effects. See Piano acoustics.
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