In acoustics and telecommunication, the harmonic of a wave is a component frequency of the signal that is an integer multiple of the fundamental frequency. Acoustics is the interdisciplinary science that deals with the study of Sound, Ultrasound and Infrasound (all mechanical waves in gases liquids and solids A wave is a disturbance that propagates through Space and Time, usually with transference of Energy. Frequency is a measure of the number of occurrences of a repeating event per unit Time. In Telecommunication, signalling (UK spelling or signaling (US spelling has the following meanings The use of signals for controlling communications The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. For example, if the frequency is f, the harmonics have frequency 2f, 3f, 4f, etc, as well as f itself. The harmonics have the property that they are all periodic at the signal frequency. Periodicity is the quality of occurring at regular intervals or periods (in Time or Space) and can occur in different contexts A Clock marks Also, due to the properties of Fourier series, the sum of the signal and its harmonics is also periodic at that frequency. In Mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions

Many oscillators, including the human voice, a bowed violin string, or a Cepheid variable star, are more or less periodic, and thus can be decomposed into harmonics. Oscillation is the repetitive variation typically in Time, of some measure about a central value (often a point of Equilibrium) or between two or more different states In Music, a bow is moved across some part of a Musical instrument, causing Vibration which the instrument emits as Sound. The violin is a bowed String instrument with four strings usually tuned in Perfect fifths It is the smallest and highest-pitched member A Cepheid variable (pron ˈse-f(ē-id or ˈsē-f(ē-id or Cepheid is a member of a particular class of Variable stars notable for a fairly tight correlation

Most passive oscillators, such as a plucked guitar string or a struck drum head or struck bell, naturally oscillate at several frequencies known as overtones. An overtone is a natural resonance or vibration frequency of a system When the oscillator is long and thin, such as a guitar string, a trumpet, or a chime, the overtones are still integer multiples of the fundamental frequency. Hence, these devices can mimic the sound of singing and are often incorporated into music. Overtones whose frequency is not an integer multiple of the fundamental are called inharmonic and are sometimes perceived as unpleasant. In music inharmonicity is the degree to which the frequencies of Overtones (known as partials partial tones or Harmonics depart from whole

The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the timbre of the tone. In Music, timbre (ˈtæm-bər' like timber, or, from Fr timbre tɛ̃bʁ is the quality of a Musical note or sound that distinguishes different In a musical context, overtones that are not exactly integer multiples of the fundamental are known as inharmonics. In music inharmonicity is the degree to which the frequencies of Overtones (known as partials partial tones or Harmonics depart from whole Inharmonics that are not close to harmonics are known as partials. Bells have more clearly perceptible partials than most instruments. A bell is a simple Sound -making device The bell is a Percussion instrument and an Idiophone. Antique singing bowls are well known for their unique quality of producing multiple harmonic overtones or multiphonics. Singing bowls (also known as 'Himalayan bowls' or 'rin' or Suzu gongs in Japan are a type of bell, specifically classified as a standing bell Multiphonics is an Extended technique in instrumental music in which a monophonic instrument (one which generally produces only one note at a time is made to produce

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. Music is an Art form in which the medium is Sound organized in Time. This chart demonstrates how they are counted:

In many musical instruments, it is possible to play the upper harmonics without the fundamental note being present. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. A musical instrument is a device constructed or modified for the purpose of making Music. 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. The recorder is a woodwind Musical instrument of the family known as Fipple Flutes ' or internal duct flutes &mdash whistle-like In Music, an octave ( is the the use of which is "common in most musical systems In some cases it also changes the timbre of the note. In Music, timbre (ˈtæm-bər' like timber, or, from Fr timbre tɛ̃bʁ is the quality of a Musical note or sound that distinguishes different This is part of the normal method of obtaining higher notes in wind instruments, where it is called overblowing. A wind instrument is a Musical instrument that contains some type of Resonator (usually a tube in which a column of air is set into vibration by the player blowing Overblowing is a technique used in playing a Wind instrument to produce a different pitch by changing the direction and/or force of the air stream The extended technique of playing multiphonics also produces harmonics. Extended techniques are performance techniques used in Music to describe unconventional unorthodox or "improper" techniques of Singing, or of Multiphonics is an Extended technique in instrumental music in which a monophonic instrument (one which generally produces only one note at a time is made to produce On string instruments it is possible to produce very pure sounding notes, called harmonics by string players, which have an eerie quality, as well as being high in pitch. A string instrument (or stringed instrument) is a Musical instrument that produces Sound by means of Vibrating strings In the Hornbostel-Sachs Harmonics may be used to check at a unison the tuning of strings that are not tuned to the unison. In Music, a unison () is an interval, the ratio of 11 or 0 half steps and zero cents. For example, lightly fingering the node found half way 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. The violoncello (abbreviated to cello, or 'cello, plural cellos or celli —the c is tʃ For the human voice see Overtone singing, which uses harmonics. Overtone singing, also known as throat singing, overtone chanting, or harmonic singing, is a type of singing in which the Singer manipulates

Harmonics may be either used or considered as the basis of just intonation systems. In music just intonation is any Musical tuning in which the frequencies of Notes are related by Ratios of Whole numbers Any interval Composer Arnold Dreyblatt is able to bring out different harmonics on the single string of his modified double bass by slightly altering his unique bowing technique halfway between hitting and bowing the strings. Arnold Dreyblatt (b New York City, 1953 is an American Composer and visual artist The double bass is the largest and lowest-pitched bowed String instrument used in the modern symphony orchestra. In Music, a bow is moved across some part of a Musical instrument, causing Vibration which the instrument emits as Sound. Composer Lawrence Ball uses harmonics to generate music electronically. Lawrence Ball is an English musician and composer who currently lives in North London.

The fundamental frequency is the reciprocal of the period of the periodic phenomenon. The fundamental tone, often referred to simply as the fundamental and abbreviated fo, is the lowest frequency in a harmonic series. In Mathematics, a multiplicative inverse for a number x, denoted by 1&frasl x or x &minus1 is a number which Frequency is a measure of the number of occurrences of a repeating event per unit Time.

Harmonics on stringed instruments

playing a harmonic on a string (click to enlarge)

The following table displays the stop points on a stringed instrument, such as the guitar, at which gentle touching of a string will force it into a harmonic mode when vibrated. The guitar is a Musical instrument with ancient roots that is used in a wide variety of musical styles

Table of harmonics

Table of harmonics of a stringed instrument with colored dots indicating which positions can be lightly fingered to generate just intervals up to the 7th harmonic

Audio Samples

See also