Harmonic 41232 213990258 2008-05-21T17:42:59Z 216.189.190.221 the phrase that inharmonic sounds are "often" unpleasant is too general and often does not apply {{Otheruses1|the components of sound}} In [[acoustics]] and [[telecommunication]], the '''harmonic''' of a [[wave]] is a component [[frequency]] of the [[Signalling (telecommunication)|signal]] that is an [[integer]] multiple of the [[fundamental frequency]]. For example, if the frequency is ''f'', the harmonics have frequency 2''f'', 3''f'', 4''f'', etc, as well as ''f'' itself. The harmonics have the property that they are all [[periodicity|periodic]] at the signal frequency. Also, due to the properties of [[Fourier series]], the sum of the signal and its harmonics is also periodic at that frequency. Many [[oscillator]]s, including the [[human voice]], a [[Bow (music)|bowed]] [[violin]] string, or a [[Cepheid variable star]], are more or less periodic, and thus can be decomposed into harmonics. 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]]. 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. The untrained human ear typically does not perceive harmonics as separate notes. Instead, they are perceived as the [[timbre]] of the tone. In a musical context, overtones that are not exactly integer multiples of the fundamental are known as [[inharmonic]]s. Inharmonics that are not close to harmonics are known as partials. [[bell (instrument)|Bells]] have more clearly perceptible partials than most instruments. Antique [[singing bowl]]s are well known for their unique quality of producing multiple harmonic overtones or [[multiphonics]]. 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: {| class="wikitable" ! ''1f'' | 440 Hz | [[fundamental frequency]] | first harmonic |- ! ''2f'' | 880 Hz | first overtone | second harmonic |- ! ''3f'' | 1320 Hz | second overtone | third harmonic |- ! ''4f'' | 1760 Hz | third overtone | fourth harmonic |} 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 [[multiphonic]]s also produces harmonics. 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. 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 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. For the human voice see [[Overtone singing]], which uses harmonics. Harmonics may be either used or considered as the basis of [[just intonation]] systems. Composer [[Arnold Dreyblatt]] is able to bring out different harmonics on the single string of his modified [[double bass]] by slightly altering his unique [[bow (music)|bow]]ing technique halfway between hitting and bowing the strings. Composer [[Lawrence Ball]] uses harmonics to generate music electronically. The [[fundamental frequency]] is the [[Reciprocal (mathematics)|reciprocal]] of the [[period (physics)|period]] of the periodic phenomenon. {{FS1037C}} == Harmonics on stringed instruments == [[Image:Flageolette.svg|thumb|200px|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. {| class="wikitable" ! harmonic ! stop note ! harmonic noteing !width="50"| cents !width="50"| reduced<br />cents |- | 2 | [[octave]] | P8 |align="right" | 1200.0 |align="right" | 0.0 |- | 3 | just [[perfect fifth]] | P8 + P5 |align="right" | 1902.0 |align="right" | 702.0 |- | 4 | just [[perfect fourth]] | 2P8 |align="right" | 2400.0 |align="right" | 0.0 |- | 5 | just [[major third]] | 2P8 + just M3 |align="right" | 2786.3 |align="right" | 386.3 |- | 6 | just [[minor third]] | 2P8 + P5 |align="right" | 3102.0 |align="right" | 702.0 |- | 7 | [[septimal minor third]] | 2P8 + septimal m7 |align="right" | 3368.8 |align="right" | 968.8 |- | 8 | [[septimal major second]] | 3P8 |align="right" | 3600.0 |align="right" | 0.0 |- | 9 | [[Pythagorean interval|Pythagorean major second]] | 3P8 + pyth M2 |align="right" | 3803.9 |align="right" | 203.9 |- | 10 | just minor [[whole tone]] | 3P8 + just M3 |align="right" | 3986.3 |align="right" | 386.3 |- | 11 | greater unidecimal [[neutral second]] | 3P8 + just M3 + GUN2 |align="right" | 4151.3 |align="right" | 551.3 |- | 12 | lesser unidecimal [[neutral second]] | 3P8 + P5 |align="right" | 4302.0 |align="right" | 702.0 |- | 13 | tridecimal 2/3-tone | 3P8 + P5 + T23T |align="right" | 4440.5 |align="right" | 840.5 |- | 14 | 2/3-tone | 3P8 + P5 + septimal m3 |align="right" | 4568.8 |align="right" | 968.8 |- | 15 | septimal (or major) [[diatonic semitone]] | 3P8 + P5 + just M3 |align="right" | 4688.3 |align="right" | 1088.3 |- | 16 | just (or minor) [[diatonic semitone]] | 4P8 |align="right" | 4800.0 |align="right" | 0.0 |- |} ===Table of harmonics=== [[Image:Table_of_Harmonics.jpg|thumb|centre|700px|Table of harmonics of a stringed instrument with colored dots indicating which positions can be lightly fingered to generate [[Just intonation|just intervals]] up to the 7th harmonic]] == Audio Samples == {{Multi-listen start}} {{Multi-listen item|filename=Violin harmonics.ogg|title=Violin harmonics|description=Violin natural harmonic stop points on the A string|format=[[Ogg]]}} {{Multi-listen item|filename=Harmonics 110x16.ogg|title=Harmonics 110x16|description=Demonstration of harmonics using electronic sine tones - fundamental and 15 harmonics of 110 Hz, 0.5s each. Note that each harmonic is presented at the same signal level as the fundamental; the sample tones sound louder as they increase in frequency|format=[[Ogg]]}} {{Multi-listen end}} == See also == <div style="-moz-column-count:3; column-count:3;"> *[[Aristoxenus]] *[[Artificial harmonic]] *[[Formant]] *[[Fourier series]] *[[Fundamental frequency]] *[[Harmonic oscillator]] *[[Harmonic series (music)]] *[[Harmony]] *[[Inharmonic]] *[[Just intonation]] *[[Overtones]] *[[Pinch harmonic]] *[[Pure tone]] *[[Singing bowl]] *[[Stretched octave]] *[[Tap harmonic]] *[[Xenharmonic]] == External links == *[http://www.sengpielaudio.com/calculator-harmonics.htm Calculations of harmonics from fundamental frequency] *[http://www.newmusicbox.org/chatter/chatter.nmbx?id=5556 Discussion of [[Sciarrino]]'s violin etudes and notation issues] [[Category:Acoustics]] [[de:Harmonische]] [[et:Harmoonik]] [[es:Armónico]] [[eo:Harmono]] [[fr:Courants_harmoniques]] [[nl:Harmonische]] [[ja:倍音]] [[nn:Harmonisk bølgje]] [[pl:Składowa harmoniczna]] [[pt:Harmônica]]