Harmonics and Overtones
The tight relation between overtones and harmonics in music often leads to their being used synonymously in a strictly musical context, but they are counted differently leading to some possible confusion. This chart demonstrates how they are counted:
| Frequency | Order | Name 1 | Name 2 |
|---|---|---|---|
| 1 · f = 440 Hz | n = 1 | fundamental tone | 1st harmonic |
| 2 · f = 880 Hz | n = 2 | 1st overtone | 2nd harmonic |
| 3 · f = 1320 Hz | n = 3 | 2nd overtone | 3rd harmonic |
| 4 · f = 1760 Hz | n = 4 | 3rd overtone | 4th harmonic |
Harmonics are not overtones, when it comes to counting. Even numbered harmonics are odd numbered overtones and vice versa.
In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., recorder) this has the effect of making the note go up in pitch by an octave; but in more complex cases many other pitch variations are obtained. In some cases it also changes the timbre of the note. This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. The extended technique of playing multiphonics also produces harmonics. On string instruments it is possible to produce very pure sounding notes, called harmonics or flageolets by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. For example, lightly fingering the node found halfway down the highest string of a cello produces the same pitch as lightly fingering the node 1/3 of the way down the second highest string. For the human voice see Overtone singing, which uses harmonics.
While it is true that electronically produced periodic tones (e.g. square waves or other non-sinusoidal waves) have "harmonics" that are whole number multiples of the fundamental frequency, practical instruments do not all have this characteristic. For example higher "harmonics"' of piano notes are not true harmonics but are "overtones" and can be very sharp, i.e. a higher frequency than given by a pure harmonic series. This is especially true of instruments other than stringed or brass/woodwind ones, e.g., xylophone, drums, bells etc., where not all the overtones have a simple whole number ratio with the fundamental frequency.
The fundamental frequency is the reciprocal of the period of the periodic phenomenon.
This article incorporates public domain material from the General Services Administration document "Federal Standard 1037C".
Read more about this topic: Harmonic
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