Overtone

"Overtones" redirects here. For other uses, see Overtones (disambiguation).
"Superharmonic" redirects here. For functions in mathematics, see Superharmonic function.
Vibrational modes of an ideal string, dividing the string length into integer divisions, producing harmonic partials f, 2f, 3f, 4f, etc. (where f means fundamental frequency).

An overtone is any resonant frequency above the fundamental frequency of a sound. (An overtone may or may not be a harmonic)[1] In other words, overtones are all pitches higher than the lowest pitch within an individual sound; the fundamental is the lowest pitch. While the fundamental is usually heard most prominently, overtones are actually present in any pitch except a true sine wave.[2] The relative volume or amplitude of various overtone partials is one of the key identifying features of timbre, or the individual characteristic of a sound.[3]

Using the model of Fourier analysis, the fundamental and the overtones together are called partials. Harmonics, or more precisely, harmonic partials, are partials whose frequencies are numerical integer multiples of the fundamental (including the fundamental, which is 1 times itself). These overlapping terms are variously used when discussing the acoustic behavior of musical instruments.[4] (See etymology below.) The model of Fourier analysis provides for the inclusion of inharmonic partials, which are partials whose frequencies are not whole-number ratios of the fundamental (such as 1.1 or 2.14179).

Main tone (110 Hz) and first 15 overtones (16 harmonic partials) (listen)
Allowed and forbidden standing waves, and thus harmonics

When a resonant system such as a blown pipe or plucked string is excited, a number of overtones may be produced along with the fundamental tone. In simple cases, such as for most musical instruments, the frequencies of these tones are the same as (or close to) the harmonics. Examples of exceptions include the circular drum – a timpani whose first overtone is about 1.6 times its fundamental resonance frequency,[5] gongs and cymbals, and brass instruments. The human vocal tract is able to produce highly variable amplitudes of the overtones, called formants, which define different vowels.[6]

  1. ^ "Overtones and Harmonics". hyperphysics.phy-astr.gsu.edu. Retrieved 2020-10-26.
  2. ^ Fineberg, Joshua (2000). "Guide to the Basic Concepts and Techniques of Spectral Music" (PDF). Contemporary Music Review. 19 (2): 81–113. doi:10.1080/07494460000640271. S2CID 191456235. Archived (PDF) from the original on 2022-10-09. Retrieved 28 February 2021.
  3. ^ Hinds, Stuart (October 2010). "How to Teach Overtone Singing to Your Choir". The Choral Journal. 51 (3): 34–43. JSTOR 23560424.
  4. ^ Alexander J. Ellis (translating Hermann von Helmholtz): On the Sensations of Tone as a Physiological Basis for the Theory of Music, pp. 24, 25. 1885, reprinted by Dover Publications, New York, 1954.
  5. ^ Elena Prestini, The Evolution of Applied Harmonic Analysis: Models of the Real World, ISBN 0-8176-4125-4 (p140)
  6. ^ "Vowel Sounds". hyperphysics.phy-astr.gsu.edu. Retrieved 2021-02-28.