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	<h1 id="firstHeading" class="firstHeading" >Harmonic</h1>
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		<div id="mw-content-text" lang="en" dir="ltr" class="mw-content-ltr"><div class="mw-parser-output"><div role="note" class="hatnote navigation-not-searchable">This article is about the components of periodic signals. For other uses, see <a href="/wiki/Harmonic_(disambiguation)" class="mw-disambig" title="Harmonic (disambiguation)">Harmonic (disambiguation)</a>.</div>
<table class="box-More_citations_needed plainlinks metadata ambox ambox-content ambox-Refimprove" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><a href="/wiki/File:Question_book-new.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/50px-Question_book-new.svg.png" decoding="async" width="50" height="39" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/75px-Question_book-new.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/99/Question_book-new.svg/100px-Question_book-new.svg.png 2x" data-file-width="512" data-file-height="399" /></a></div></td><td class="mbox-text"><div class="mbox-text-span">This article <b>needs additional citations for <a href="/wiki/Wikipedia:Verifiability" title="Wikipedia:Verifiability">verification</a></b>.<span class="hide-when-compact"> Please help <a class="external text" href="https://en.wikipedia.org/w/index.php?title=Harmonic&amp;action=edit">improve this article</a> by <a href="/wiki/Help:Referencing_for_beginners" title="Help:Referencing for beginners">adding citations to reliable sources</a>. Unsourced material may be challenged and removed.<br /><small><span class="plainlinks"><i>Find sources:</i>&#160;<a rel="nofollow" class="external text" href="//www.google.com/search?as_eq=wikipedia&amp;q=%22Harmonic%22">"Harmonic"</a>&#160;–&#160;<a rel="nofollow" class="external text" href="//www.google.com/search?tbm=nws&amp;q=%22Harmonic%22+-wikipedia">news</a>&#160;<b>·</b> <a rel="nofollow" class="external text" href="//www.google.com/search?&amp;q=%22Harmonic%22+site:news.google.com/newspapers&amp;source=newspapers">newspapers</a>&#160;<b>·</b> <a rel="nofollow" class="external text" href="//www.google.com/search?tbs=bks:1&amp;q=%22Harmonic%22+-wikipedia">books</a>&#160;<b>·</b> <a rel="nofollow" class="external text" href="//scholar.google.com/scholar?q=%22Harmonic%22">scholar</a>&#160;<b>·</b> <a rel="nofollow" class="external text" href="https://www.jstor.org/action/doBasicSearch?Query=%22Harmonic%22&amp;acc=on&amp;wc=on">JSTOR</a></span></small></span>  <small class="date-container"><i>(<span class="date">August 2020</span>)</i></small><small class="hide-when-compact"><i> (<a href="/wiki/Help:Maintenance_template_removal" title="Help:Maintenance template removal">Learn how and when to remove this template message</a>)</i></small></div></td></tr></tbody></table>
<div class="thumb tright"><div class="thumbinner" style="width:252px;"><a href="/wiki/File:Moodswingerscale.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/250px-Moodswingerscale.svg.png" decoding="async" width="250" height="277" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/375px-Moodswingerscale.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Moodswingerscale.svg/500px-Moodswingerscale.svg.png 2x" data-file-width="512" data-file-height="568" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Moodswingerscale.svg" class="internal" title="Enlarge"></a></div>The <a href="/wiki/Node_(physics)" title="Node (physics)">nodes</a> of a vibrating string are harmonics.</div></div></div>
<div class="thumb tright"><div class="thumbinner" style="width:222px;"><a href="/wiki/File:Cello_natural_harmonics.png" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Cello_natural_harmonics.png/220px-Cello_natural_harmonics.png" decoding="async" width="220" height="140" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/1/19/Cello_natural_harmonics.png/330px-Cello_natural_harmonics.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/1/19/Cello_natural_harmonics.png/440px-Cello_natural_harmonics.png 2x" data-file-width="2204" data-file-height="1406" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Cello_natural_harmonics.png" class="internal" title="Enlarge"></a></div>Two different notations of natural harmonics on the cello. First as sounded (more common), then as fingered (easier to sightread).</div></div></div>
<p>A <b>harmonic</b> is any member of the <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a>. The term is employed in various disciplines, including music, physics, <a href="/wiki/Acoustics" title="Acoustics">acoustics</a>, electronic power transmission, radio technology, and other fields. It is typically applied to repeating signals, such as <a href="/wiki/Sine" title="Sine">sinusoidal</a> waves. A harmonic of such a <a href="/wiki/Wave" title="Wave">wave</a> is a wave with a <a href="/wiki/Frequency" title="Frequency">frequency</a> that is a positive <a href="/wiki/Integer" title="Integer">integer</a> multiple of the frequency of the original wave, known as the <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a>. The original <a href="/wiki/Wave" title="Wave">wave</a> is also called the 1st harmonic, the following harmonics are known as higher harmonics. As all harmonics are <a href="/wiki/Periodic_function" title="Periodic function">periodic</a> at the fundamental frequency, the sum of harmonics is also periodic at that frequency. For example, if the fundamental frequency is 50&#160;<a href="/wiki/Hertz" title="Hertz">Hz</a>, a common <a href="/wiki/Alternating_current" title="Alternating current">AC</a> power supply frequency, the frequencies of the first three higher harmonics are 100&#160;Hz (2nd harmonic), 150&#160;Hz (3rd harmonic), 200&#160;Hz (4th harmonic) and any addition of waves with these frequencies is periodic at 50&#160;Hz.
</p>
<style data-mw-deduplicate="TemplateStyles:r996844942">.mw-parser-output .templatequote{overflow:hidden;margin:1em 0;padding:0 40px}.mw-parser-output .templatequote .templatequotecite{line-height:1.5em;text-align:left;padding-left:1.6em;margin-top:0}</style><blockquote class="templatequote"><p>An <i>n</i><sup>th</sup> characteristic mode, for <i>n</i> &gt; 1, will have nodes that are not vibrating. For example, the 3rd characteristic mode will have nodes at <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\tfrac {1}{3}}}">
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    <annotation encoding="application/x-tex">{\displaystyle {\tfrac {2}{3}}}</annotation>
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</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/571a6ce6d697175e9e5e723b8c40eaa7efcfeaca" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\tfrac {2}{3}}"/></span><i>L</i>, where <i>L</i> is the length of the string. In fact, each <i>n</i><sup>th</sup> characteristic mode, for <i>n</i> not a multiple of 3, will <b>not</b> have nodes at these points. These other characteristic modes will be <i>vibrating</i> at the positions <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\tfrac {1}{3}}}">
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<p>In music, harmonics are used on string instruments and wind instruments as a way of producing sound on the instrument, particularly to play higher notes and, with strings, obtain notes that have a unique sound quality or "tone colour". On strings, bowed harmonics have a "glassy", pure tone. On stringed instruments, harmonics are played by touching (but not fully pressing down the string) at an exact point on the string while sounding the string (plucking, bowing, etc.); this allows the harmonic to sound, a pitch which is always higher than the fundamental frequency of the string.
</p>
<div id="toc" class="toc" role="navigation" aria-labelledby="mw-toc-heading"><input type="checkbox" role="button" id="toctogglecheckbox" class="toctogglecheckbox" style="display:none" /><div class="toctitle" lang="en" dir="ltr"><h2 id="mw-toc-heading">Contents</h2><span class="toctogglespan"><label class="toctogglelabel" for="toctogglecheckbox"></label></span></div>
<ul>
<li class="toclevel-1 tocsection-1"><a href="#Terminology"><span class="tocnumber">1</span> <span class="toctext">Terminology</span></a></li>
<li class="toclevel-1 tocsection-2"><a href="#Characteristics"><span class="tocnumber">2</span> <span class="toctext">Characteristics</span></a></li>
<li class="toclevel-1 tocsection-3"><a href="#Partials,_overtones,_and_harmonics"><span class="tocnumber">3</span> <span class="toctext">Partials, overtones, and harmonics</span></a></li>
<li class="toclevel-1 tocsection-4"><a href="#On_stringed_instruments"><span class="tocnumber">4</span> <span class="toctext">On stringed instruments</span></a>
<ul>
<li class="toclevel-2 tocsection-5"><a href="#Artificial_harmonics"><span class="tocnumber">4.1</span> <span class="toctext">Artificial harmonics</span></a></li>
</ul>
</li>
<li class="toclevel-1 tocsection-6"><a href="#Other_information"><span class="tocnumber">5</span> <span class="toctext">Other information</span></a></li>
<li class="toclevel-1 tocsection-7"><a href="#See_also"><span class="tocnumber">6</span> <span class="toctext">See also</span></a></li>
<li class="toclevel-1 tocsection-8"><a href="#References"><span class="tocnumber">7</span> <span class="toctext">References</span></a></li>
<li class="toclevel-1 tocsection-9"><a href="#External_links"><span class="tocnumber">8</span> <span class="toctext">External links</span></a></li>
</ul>
</div>

<h2><span class="mw-headline" id="Terminology">Terminology</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=1" title="Edit section: Terminology">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Harmonics may also be called "overtones", "partials" or "upper partials". The difference between "harmonic" and "overtone" is that the term "harmonic" includes all of the notes in a series, including the fundamental frequency (e.g., the open string of a guitar). The term "overtone" only includes the pitches above the fundamental. In some music contexts, the terms "harmonic", "overtone" and "partial" are used fairly interchangeably.
</p>
<h2><span class="mw-headline" id="Characteristics">Characteristics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=2" title="Edit section: Characteristics">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996844942"/><blockquote class="templatequote"><p>A whizzing, whistling tonal character, distinguishes all the harmonics both natural and artificial from the firmly stopped intervals; therefore their application in connection with the latter must always be carefully considered.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2">&#91;2&#93;</a></sup></p></blockquote>
<p>Most acoustic instruments emit complex tones containing many individual partials (component simple tones or sinusoidal waves), but the untrained human ear typically does not perceive those partials as separate phenomena. Rather, a musical note is perceived as one sound, the quality or <a href="/wiki/Timbre" title="Timbre">timbre</a> of that sound being a result of the relative strengths of the individual partials. Many acoustic <a href="/wiki/Oscillator" class="mw-redirect" title="Oscillator">oscillators</a>, such as the <a href="/wiki/Human_voice" title="Human voice">human voice</a> or a <a href="/wiki/Bow_(music)" title="Bow (music)">bowed</a> <a href="/wiki/Violin" title="Violin">violin</a> string, produce complex tones that are more or less <a href="/wiki/Periodic_function" title="Periodic function">periodic</a>, and thus are composed of partials that are near matches to integer multiples of the fundamental frequency and therefore resemble the ideal harmonics and are called "harmonic partials" or simply "harmonics" for convenience (although it's not strictly accurate to call a partial a harmonic, the first being real and the second being ideal).
</p><p>Oscillators that produce harmonic partials behave somewhat like one-dimensional <a href="/wiki/Resonator" title="Resonator">resonators</a>, and are often long and thin, such as a guitar string or a column of air open at both ends (as with the modern orchestral <a href="/wiki/Transverse_flute" title="Transverse flute">transverse flute</a>). Wind instruments whose air column is open at only one end, such as <a href="/wiki/Trumpet" title="Trumpet">trumpets</a> and <a href="/wiki/Clarinet" title="Clarinet">clarinets</a>, also produce partials resembling harmonics. However they only produce partials matching the <i>odd</i> harmonics, at least in theory. The reality of acoustic instruments is such that none of them behaves as perfectly as the somewhat simplified theoretical models would predict.
</p><p>Partials whose frequencies are not integer multiples of the fundamental are referred to as <a href="/wiki/Inharmonicity" title="Inharmonicity"><i>inharmonic partials</i></a>. Some acoustic instruments emit a mix of harmonic and inharmonic partials but still produce an effect on the ear of having a definite fundamental pitch, such as <a href="/wiki/Piano" title="Piano">pianos</a>, strings plucked <a href="/wiki/Pizzicato" title="Pizzicato">pizzicato</a>, vibraphones, marimbas, and certain pure-sounding bells or chimes. Antique <a href="/wiki/Singing_bowl" class="mw-redirect" title="Singing bowl">singing bowls</a> are known for producing multiple harmonic partials or <a href="/wiki/Multiphonics" class="mw-redirect" title="Multiphonics">multiphonics</a>.
<sup id="cite_ref-3" class="reference"><a href="#cite_note-3">&#91;3&#93;</a></sup>
<sup id="cite_ref-4" class="reference"><a href="#cite_note-4">&#91;4&#93;</a></sup> Other oscillators, such as <a href="/wiki/Cymbals" class="mw-redirect" title="Cymbals">cymbals</a>, drum heads, and other percussion instruments, naturally produce an abundance of inharmonic partials and do not imply any particular pitch, and therefore cannot be used melodically or harmonically in the same way other instruments can.
</p>
<h2><span id="Partials.2C_overtones.2C_and_harmonics"></span><span class="mw-headline" id="Partials,_overtones,_and_harmonics">Partials, overtones, and harmonics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=3" title="Edit section: Partials, overtones, and harmonics">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>An <a href="/wiki/Overtone" title="Overtone">overtone</a> is any partial higher than the lowest partial in a compound tone. The relative strengths and frequency relationships of the component partials determine the timbre of an instrument. The similarity between the terms overtone and partial sometimes leads to their being loosely used interchangeably in a <a href="/wiki/Music" title="Music">musical</a> context, but they are counted differently, leading to some possible confusion. In the special case of instrumental timbres whose component partials closely match a harmonic series (such as with most strings and winds) rather than being inharmonic partials (such as with most pitched percussion instruments), it is also convenient to call the component partials "harmonics" but not strictly correct (because harmonics are numbered the same even when missing, while partials and overtones are only counted when present). This chart demonstrates how the three types of names (partial, overtone, and harmonic) are counted (assuming that the harmonics are present):
</p>
<table class="wikitable">

<tbody><tr class="hintergrundfarbe5">
<th>Frequency
</th>
<th>Order
</th>
<th>Name 1
</th>
<th>Name 2
</th>
<th>Name 3
</th>
<th><a href="/wiki/Standing_wave" title="Standing wave">Standing wave</a> representation
</th>
<th><a href="/wiki/Longitudinal_wave" title="Longitudinal wave">Longitudinal wave</a> representation
</th></tr>
<tr>
<td>1 × <i>f</i> = <span style="visibility:hidden;color:transparent;">0</span>440&#160;Hz
</td>
<td><i>n</i> = 1
</td>
<td>1st partial
</td>
<td><a href="/wiki/Fundamental_tone" class="mw-redirect" title="Fundamental tone">fundamental tone</a>
</td>
<td>1st harmonic
</td>
<td><a href="/wiki/File:Pipe001.gif" class="image"><img alt="Pipe001.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Pipe001.gif/220px-Pipe001.gif" decoding="async" width="220" height="66" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/5/54/Pipe001.gif/330px-Pipe001.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/5/54/Pipe001.gif/440px-Pipe001.gif 2x" data-file-width="640" data-file-height="192" /></a>
</td>
<td><a href="/wiki/File:Molecule1.gif" class="image"><img alt="Molecule1.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Molecule1.gif/220px-Molecule1.gif" decoding="async" width="220" height="116" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Molecule1.gif/330px-Molecule1.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Molecule1.gif/440px-Molecule1.gif 2x" data-file-width="576" data-file-height="304" /></a>
</td></tr>
<tr>
<td>2 × <i>f</i> = <span style="visibility:hidden;color:transparent;">0</span>880&#160;Hz
</td>
<td><i>n</i> = 2
</td>
<td>2nd partial
</td>
<td>1st overtone
</td>
<td>2nd harmonic
</td>
<td><a href="/wiki/File:Pipe002.gif" class="image"><img alt="Pipe002.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Pipe002.gif/220px-Pipe002.gif" decoding="async" width="220" height="66" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Pipe002.gif/330px-Pipe002.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a8/Pipe002.gif/440px-Pipe002.gif 2x" data-file-width="640" data-file-height="192" /></a>
</td>
<td><a href="/wiki/File:Molecule2.gif" class="image"><img alt="Molecule2.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Molecule2.gif/220px-Molecule2.gif" decoding="async" width="220" height="116" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/7/77/Molecule2.gif/330px-Molecule2.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/7/77/Molecule2.gif/440px-Molecule2.gif 2x" data-file-width="576" data-file-height="304" /></a>
</td></tr>
<tr>
<td>3 × <i>f</i> = 1320&#160;Hz
</td>
<td><i>n</i> = 3
</td>
<td>3rd partial
</td>
<td>2nd overtone
</td>
<td>3rd harmonic
</td>
<td><a href="/wiki/File:Pipe003.gif" class="image"><img alt="Pipe003.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Pipe003.gif/220px-Pipe003.gif" decoding="async" width="220" height="66" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Pipe003.gif/330px-Pipe003.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/a/a9/Pipe003.gif/440px-Pipe003.gif 2x" data-file-width="640" data-file-height="192" /></a>
</td>
<td><a href="/wiki/File:Molecule3.gif" class="image"><img alt="Molecule3.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Molecule3.gif/220px-Molecule3.gif" decoding="async" width="220" height="116" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/04/Molecule3.gif/330px-Molecule3.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/04/Molecule3.gif/440px-Molecule3.gif 2x" data-file-width="576" data-file-height="304" /></a>
</td></tr>
<tr>
<td>4 × <i>f</i> = 1760&#160;Hz
</td>
<td><i>n</i> = 4
</td>
<td>4th partial
</td>
<td>3rd overtone
</td>
<td>4th harmonic
</td>
<td><a href="/wiki/File:Pipe004.gif" class="image"><img alt="Pipe004.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Pipe004.gif/220px-Pipe004.gif" decoding="async" width="220" height="66" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Pipe004.gif/330px-Pipe004.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Pipe004.gif/440px-Pipe004.gif 2x" data-file-width="640" data-file-height="192" /></a>
</td>
<td><a href="/wiki/File:Molecule4.gif" class="image"><img alt="Molecule4.gif" src="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Molecule4.gif/220px-Molecule4.gif" decoding="async" width="220" height="116" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/0/03/Molecule4.gif/330px-Molecule4.gif 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/0/03/Molecule4.gif/440px-Molecule4.gif 2x" data-file-width="576" data-file-height="304" /></a>
</td></tr></tbody></table>
<p>In many <a href="/wiki/Musical_instruments" class="mw-redirect" title="Musical instruments">musical instruments</a>, it is possible to play the upper harmonics without the fundamental note being present. In a simple case (e.g., <a href="/wiki/Recorder_(musical_instrument)" title="Recorder (musical instrument)">recorder</a>) this has the effect of making the note go up in pitch by an <a href="/wiki/Octave" title="Octave">octave</a>, but in more complex cases many other pitch variations are obtained. In some cases it also changes the <a href="/wiki/Timbre" title="Timbre">timbre</a> of the note. This is part of the normal method of obtaining higher notes in <a href="/wiki/Wind_instruments" class="mw-redirect" title="Wind instruments">wind instruments</a>, where it is called <i><a href="/wiki/Overblowing" title="Overblowing">overblowing</a></i>. The <a href="/wiki/Extended_technique" title="Extended technique">extended technique</a> of playing <a href="/wiki/Multiphonic" title="Multiphonic">multiphonics</a> also produces harmonics. On <a href="/wiki/String_instruments" class="mw-redirect" title="String instruments">string instruments</a> it is possible to produce very pure sounding notes, called harmonics or <i>flageolets</i> by string players, which have an eerie quality, as well as being high in pitch. Harmonics may be used to check at a <a href="/wiki/Unison" title="Unison">unison</a> 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 <a href="/wiki/Cello" title="Cello">cello</a> produces the same pitch as lightly fingering the node &#x200b;<span class="frac nowrap"><sup>1</sup>&#8260;<sub>3</sub></span> of the way down the second highest string. For the human voice see <a href="/wiki/Overtone_singing" title="Overtone singing">Overtone singing</a>, which uses harmonics.
</p><p>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 <a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">harmonic series</a>. 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 <a href="/wiki/Fundamental_frequency" title="Fundamental frequency">fundamental frequency</a> is the <a href="/wiki/Reciprocal_(mathematics)" class="mw-redirect" title="Reciprocal (mathematics)">reciprocal</a> of the <a href="/wiki/Period_(physics)" class="mw-redirect" title="Period (physics)">period</a> of the periodic phenomenon.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5">&#91;5&#93;</a></sup>
</p>
<h2><span class="mw-headline" id="On_stringed_instruments">On stringed instruments</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=4" title="Edit section: On stringed instruments">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<div class="thumb tright"><div class="thumbinner" style="width:202px;"><a href="/wiki/File:Flageolette.svg" class="image"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Flageolette.svg/200px-Flageolette.svg.png" decoding="async" width="200" height="227" class="thumbimage" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/61/Flageolette.svg/300px-Flageolette.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/61/Flageolette.svg/400px-Flageolette.svg.png 2x" data-file-width="600" data-file-height="680" /></a>  <div class="thumbcaption"><div class="magnify"><a href="/wiki/File:Flageolette.svg" class="internal" title="Enlarge"></a></div>Playing a harmonic on a string</div></div></div><div role="note" class="hatnote navigation-not-searchable">Main article: <a href="/wiki/String_harmonic" title="String harmonic">String harmonic</a></div>
<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r996844942"/><blockquote class="templatequote"><p>Harmonics may be singly produced [on stringed instruments] (1) by varying the point of contact with the bow, or (2) by slightly pressing the string at the nodes, or divisions of its aliquot parts (<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\tfrac {1}{2}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mstyle displaystyle="false" scriptlevel="0">
            <mfrac>
              <mn>1</mn>
              <mn>2</mn>
            </mfrac>
          </mstyle>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{2}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/edef8290613648790a8ac1a95c2fb7c3972aea2f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="{\tfrac {1}{2}}"/></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\tfrac {1}{3}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mstyle displaystyle="false" scriptlevel="0">
            <mfrac>
              <mn>1</mn>
              <mn>3</mn>
            </mfrac>
          </mstyle>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{3}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9efc37d09854a3f8fb997e7de4331876bc49c2c0" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.338ex; width:1.658ex; height:3.676ex;" alt="{\tfrac {1}{3}}"/></span>, <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML"  alttext="{\displaystyle {\tfrac {1}{4}}}">
  <semantics>
    <mrow class="MJX-TeXAtom-ORD">
      <mstyle displaystyle="true" scriptlevel="0">
        <mrow class="MJX-TeXAtom-ORD">
          <mstyle displaystyle="false" scriptlevel="0">
            <mfrac>
              <mn>1</mn>
              <mn>4</mn>
            </mfrac>
          </mstyle>
        </mrow>
      </mstyle>
    </mrow>
    <annotation encoding="application/x-tex">{\displaystyle {\tfrac {1}{4}}}</annotation>
  </semantics>
</math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/4825cd2a1ca51dfc4d53042434f6d3733370a57f" class="mwe-math-fallback-image-inline" aria-hidden="true" style="vertical-align: -1.171ex; width:1.658ex; height:3.509ex;" alt="\tfrac{1}{4}"/></span>, etc.). (1) In the first case, advancing the bow from the usual place where the fundamental note is produced, towards the bridge, the whole scale of harmonics may be produced in succession, on an old and highly resonant instrument. The employment of this means produces the effect called '<a href="/wiki/Sul_ponticello" class="mw-redirect" title="Sul ponticello">sul ponticello</a>.' (2) The production of harmonics by the slight pressure of the finger on the open string is more useful. When produced by pressing slightly on the various nodes of the open strings they are called 'Natural harmonics.' ... Violinists are well aware that the longer the string in proportion to its thickness, the greater the number of upper harmonics it can be made to yield.</p><div class="templatequotecite">—&#8201;<cite><i><a href="/wiki/Grove%27s_Dictionary_of_Music_and_Musicians" class="mw-redirect" title="Grove&#39;s Dictionary of Music and Musicians">Grove's Dictionary of Music and Musicians</a></i> (1879)<sup id="cite_ref-6" class="reference"><a href="#cite_note-6">&#91;6&#93;</a></sup></cite></div></blockquote>
<p>The following table displays the stop points on a stringed instrument at which gentle touching of a string will force it into a harmonic mode when vibrated. String harmonics (flageolet tones) are described as having a "flutelike, silvery quality" that can be highly effective as a special color or tone color (<a href="/wiki/Timbre" title="Timbre">timbre</a>) when used and heard in <a href="/wiki/Orchestration" title="Orchestration">orchestration</a>.<sup id="cite_ref-7" class="reference"><a href="#cite_note-7">&#91;7&#93;</a></sup> It is unusual to encounter natural harmonics higher than the fifth partial on any stringed instrument except the double bass, on account of its much longer strings.<sup id="cite_ref-8" class="reference"><a href="#cite_note-8">&#91;8&#93;</a></sup>
</p>
<table class="wikitable">

<tbody><tr>
<th>Harmonic
</th>
<th><a href="/wiki/Stop_note" class="mw-redirect" title="Stop note">Stop note</a>
</th>
<th>Sounded note relative to open string
</th>
<th width="50"><a href="/wiki/Cent_(music)" title="Cent (music)">Cents</a> above open string
</th>
<th width="50">Cents reduced to one octave
</th>
<th>Audio
</th></tr>
<tr>
<td>2
</td>
<td>octave
</td>
<td><a href="/wiki/Octave" title="Octave">octave</a> (P8)
</td>
<td style="text-align:right;">1,200.0
</td>
<td style="text-align:right;">0.0
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Perfect_octave_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/f/f0/Perfect_octave_on_C.mid" class="internal" title="Perfect octave on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Perfect_octave_on_C.mid" title="File:Perfect octave on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>3
</td>
<td>just perfect fifth
</td>
<td>P8 + just <a href="/wiki/Perfect_fifth" title="Perfect fifth">perfect fifth</a> (P5)
</td>
<td style="text-align:right;">1,902.0
</td>
<td style="text-align:right;">702.0
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Just_perfect_fifth_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/5/5c/Just_perfect_fifth_on_C.mid" class="internal" title="Just perfect fifth on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Just_perfect_fifth_on_C.mid" title="File:Just perfect fifth on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>4
</td>
<td>just <a href="/wiki/Perfect_fourth" title="Perfect fourth">perfect fourth</a>
</td>
<td>2P8
</td>
<td style="text-align:right;">2,400.0
</td>
<td style="text-align:right;">0.0
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Just_perfect_fourth_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/b/be/Just_perfect_fourth_on_C.mid" class="internal" title="Just perfect fourth on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Just_perfect_fourth_on_C.mid" title="File:Just perfect fourth on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>5
</td>
<td>just major third
</td>
<td>2P8 + <a href="/wiki/Just_major_third" class="mw-redirect" title="Just major third">just major third</a> (M3)
</td>
<td style="text-align:right;">2,786.3
</td>
<td style="text-align:right;">386.3
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Just_major_third_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/2/2a/Just_major_third_on_C.mid" class="internal" title="Just major third on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Just_major_third_on_C.mid" title="File:Just major third on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>6
</td>
<td>just <a href="/wiki/Minor_third" title="Minor third">minor third</a>
</td>
<td>2P8 + P5
</td>
<td style="text-align:right;">3,102.0
</td>
<td style="text-align:right;">702.0
</td>
<td>
</td></tr>
<tr>
<td>7
</td>
<td>septimal minor third
</td>
<td>2P8 + <a href="/wiki/Harmonic_seventh" title="Harmonic seventh">septimal minor seventh</a> (m7)
</td>
<td style="text-align:right;">3,368.8
</td>
<td style="text-align:right;">968.8
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Harmonic_seventh_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/d/dd/Harmonic_seventh_on_C.mid" class="internal" title="Harmonic seventh on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Harmonic_seventh_on_C.mid" title="File:Harmonic seventh on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>8
</td>
<td><a href="/wiki/Septimal_major_second" class="mw-redirect" title="Septimal major second">septimal major second</a>
</td>
<td>3P8
</td>
<td style="text-align:right;">3,600.0
</td>
<td style="text-align:right;">0.0
</td>
<td>
</td></tr>
<tr>
<td>9
</td>
<td>Pythagorean major second
</td>
<td>3P8 + <a href="/wiki/Pythagorean_interval" title="Pythagorean interval">Pythagorean major second</a> (M2)
</td>
<td style="text-align:right;">3,803.9
</td>
<td style="text-align:right;">203.9
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Major_tone_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/7/7b/Major_tone_on_C.mid" class="internal" title="Major tone on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Major_tone_on_C.mid" title="File:Major tone on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>10
</td>
<td>just minor <a href="/wiki/Whole_tone" class="mw-redirect" title="Whole tone">whole tone</a>
</td>
<td>3P8 + just M3
</td>
<td style="text-align:right;">3,986.3
</td>
<td style="text-align:right;">386.3
</td>
<td>
</td></tr>
<tr>
<td>11
</td>
<td>greater undecimal <a href="/wiki/Neutral_second" class="mw-redirect" title="Neutral second">neutral second</a>
</td>
<td>3P8 + lesser undecimal <a href="/wiki/Tritone" title="Tritone">tritone</a>
</td>
<td style="text-align:right;">4,151.3
</td>
<td style="text-align:right;">551.3
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Eleventh_harmonic_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/2/2a/Eleventh_harmonic_on_C.mid" class="internal" title="Eleventh harmonic on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Eleventh_harmonic_on_C.mid" title="File:Eleventh harmonic on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>12
</td>
<td>lesser undecimal neutral second
</td>
<td>3P8 + P5
</td>
<td style="text-align:right;">4,302.0
</td>
<td style="text-align:right;">702.0
</td>
<td>
</td></tr>
<tr>
<td>13
</td>
<td>tridecimal 2/3-tone
</td>
<td>3P8 + tridecimal <a href="/wiki/Neutral_sixth" title="Neutral sixth">neutral sixth</a> (n6)
</td>
<td style="text-align:right;">4,440.5
</td>
<td style="text-align:right;">840.5
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Tridecimal_neutral_sixth_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/9/95/Tridecimal_neutral_sixth_on_C.mid" class="internal" title="Tridecimal neutral sixth on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Tridecimal_neutral_sixth_on_C.mid" title="File:Tridecimal neutral sixth on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>14
</td>
<td>2/3-tone
</td>
<td>3P8 + septimal m7
</td>
<td style="text-align:right;">4,568.8
</td>
<td style="text-align:right;">968.8
</td>
<td>
</td></tr>
<tr>
<td>15
</td>
<td>septimal (or major) <a href="/wiki/Diatonic_semitone" class="mw-redirect" title="Diatonic semitone">diatonic semitone</a>
</td>
<td>3P8 + just <a href="/wiki/Major_seventh" title="Major seventh">major seventh</a> (M7)
</td>
<td style="text-align:right;">4,688.3
</td>
<td style="text-align:right;">1,088.3
</td>
<td><span class="unicode haudio"><span class="fn"><span style="white-space:nowrap;margin-right:.25em;"><a href="/wiki/File:Just_major_seventh_on_C.mid" title="About this sound"><img alt="About this sound" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/11px-Loudspeaker.svg.png" decoding="async" width="11" height="11" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/17px-Loudspeaker.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/8a/Loudspeaker.svg/22px-Loudspeaker.svg.png 2x" data-file-width="20" data-file-height="20" /></a></span><a href="//upload.wikimedia.org/wikipedia/commons/a/a4/Just_major_seventh_on_C.mid" class="internal" title="Just major seventh on C.mid">Play</a></span>&#160;<small class="metadata audiolinkinfo" style="cursor:help;">(<a href="/wiki/Wikipedia:Media_help" class="mw-redirect" title="Wikipedia:Media help"><span style="cursor:help;">help</span></a>·<a href="/wiki/File:Just_major_seventh_on_C.mid" title="File:Just major seventh on C.mid"><span style="cursor:help;">info</span></a>)</small></span>
</td></tr>
<tr>
<td>16
</td>
<td>just (or minor) diatonic semitone
</td>
<td>4P8
</td>
<td style="text-align:right;">4,800.0
</td>
<td style="text-align:right;">0.0
</td>
<td>
</td></tr></tbody></table>
<h3><span class="mw-headline" id="Artificial_harmonics">Artificial harmonics</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=5" title="Edit section: Artificial harmonics">edit</a><span class="mw-editsection-bracket">]</span></span></h3>
<p>Occasionally a score will call for an <a href="/wiki/Artificial_harmonic" class="mw-redirect" title="Artificial harmonic">artificial harmonic</a>, produced by playing an overtone on an already stopped string. As a performance technique, it is accomplished by using two fingers on the fingerboard, the first to shorten the string to the desired fundamental, with the second touching the node corresponding to the appropriate harmonic.
</p>
<h2><span class="mw-headline" id="Other_information">Other information</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=6" title="Edit section: Other information">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<p>Harmonics may be either used in or considered as the basis of <a href="/wiki/Just_intonation" title="Just intonation">just intonation</a> systems. Composer <a href="/wiki/Arnold_Dreyblatt" title="Arnold Dreyblatt">Arnold Dreyblatt</a> is able to bring out different harmonics on the single string of his modified <a href="/wiki/Double_bass" title="Double bass">double bass</a> by slightly altering his unique <a href="/wiki/Bow_(music)" title="Bow (music)">bowing</a> technique halfway between hitting and bowing the strings. Composer <a href="/wiki/Lawrence_Ball" title="Lawrence Ball">Lawrence Ball</a> uses harmonics to generate music electronically.
</p>
<h2><span class="mw-headline" id="See_also">See also</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=7" title="Edit section: See also">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<table role="presentation" class="mbox-small noprint" style="background-color:#f9f9f9;border:1px solid #aaa;color:#000;">
<tbody><tr>
<td class="mbox-image"><div class="center"><div class="floatnone"><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/50px-Gnome-mime-sound-openclipart.svg.png" decoding="async" width="50" height="50" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/75px-Gnome-mime-sound-openclipart.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/8/87/Gnome-mime-sound-openclipart.svg/100px-Gnome-mime-sound-openclipart.svg.png 2x" data-file-width="160" data-file-height="160" /></div></div></td>
<td class="mbox-text plainlist" style="line-height:1.1em"><div class="haudio">
<div style="padding:4px 0"><a href="/wiki/File:Violin_harmonics.ogg" title="File:Violin harmonics.ogg">Violin harmonics</a></div>
<div><div class="mediaContainer" style="width:220px"><audio id="mwe_player_0" controls="" preload="none" style="width:220px" class="kskin" data-durationhint="9.9613605442177" data-startoffset="0" data-mwtitle="Violin_harmonics.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/7/7d/Violin_harmonics.ogg" type="audio/ogg; codecs=&quot;vorbis&quot;" data-title="Original Ogg file (134 kbps)" data-shorttitle="Ogg source" data-width="0" data-height="0" data-bandwidth="133929" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/7/7d/Violin_harmonics.ogg/Violin_harmonics.ogg.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="188224" /></audio></div></div>
<div class="description" style="padding:2px 0 0 0">Violin natural harmonic stop points on the A string</div></div><hr /><div class="haudio">
<div style="padding:4px 0"><a href="/wiki/File:Harmonics_110x16.ogg" title="File:Harmonics 110x16.ogg">Harmonics 110x16</a></div>
<div><div class="mediaContainer" style="width:220px"><audio id="mwe_player_1" controls="" preload="none" style="width:220px" class="kskin" data-durationhint="5.3834013605442" data-startoffset="2.6165986394558" data-mwtitle="Harmonics_110x16.ogg" data-mwprovider="wikimediacommons"><source src="//upload.wikimedia.org/wikipedia/commons/9/9d/Harmonics_110x16.ogg" type="audio/ogg; codecs=&quot;vorbis&quot;" data-title="Original Ogg file (24 kbps)" data-shorttitle="Ogg source" data-width="0" data-height="0" data-bandwidth="23708" /><source src="//upload.wikimedia.org/wikipedia/commons/transcoded/9/9d/Harmonics_110x16.ogg/Harmonics_110x16.ogg.mp3" type="audio/mpeg" data-title="MP3" data-shorttitle="MP3" data-transcodekey="mp3" data-width="0" data-height="0" data-bandwidth="92136" /></audio></div></div>
<div class="description" style="padding:2px 0 0 0">Demonstration of 16 harmonics using electronic sine tones, starting with 110 Hz fundamental, 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</div></div></td></tr>
<tr><td colspan="2" class="mbox-text" style="line-height:1.1em"><hr /><i class="selfreference">Problems playing these files? See <a href="/wiki/Help:Media" title="Help:Media">media help</a>.</i></td></tr>
</tbody></table>
<ul><li><a href="/wiki/Aristoxenus" title="Aristoxenus">Aristoxenus</a></li>
<li><a href="/wiki/Electronic_tuner" title="Electronic tuner">Electronic tuner</a></li>
<li><a href="/wiki/Formant" title="Formant">Formant</a></li>
<li><a href="/wiki/Fourier_series" title="Fourier series">Fourier series</a></li>
<li><a href="/wiki/Guitar_harmonic" class="mw-redirect" title="Guitar harmonic">Guitar harmonic</a></li>
<li><a href="/wiki/Harmonic_analysis" title="Harmonic analysis">Harmonic analysis</a></li>
<li><a href="/wiki/Harmonics_(electrical_power)" title="Harmonics (electrical power)">Harmonics (electrical power)</a></li>
<li><a href="/wiki/Harmonic_oscillator" title="Harmonic oscillator">Harmonic oscillator</a></li>
<li><a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">Harmonic series (music)</a></li>
<li><a href="/wiki/Harmony" title="Harmony">Harmony</a></li>
<li><a href="/wiki/Pure_tone" title="Pure tone">Pure tone</a></li>
<li><a href="/wiki/Pythagorean_tuning" title="Pythagorean tuning">Pythagorean tuning</a></li>
<li><a href="/wiki/Scale_of_harmonics" title="Scale of harmonics">Scale of harmonics</a></li>
<li><a href="/wiki/Spherical_harmonics" title="Spherical harmonics">Spherical harmonics</a></li>
<li><a href="/wiki/Stretched_octave" class="mw-redirect" title="Stretched octave">Stretched octave</a></li>
<li><a href="/wiki/Subharmonic" class="mw-redirect" title="Subharmonic">Subharmonic</a></li>
<li><a href="/wiki/Xenharmonic_music" title="Xenharmonic music">Xenharmonic music</a></li></ul>
<h2><span class="mw-headline" id="References">References</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=8" title="Edit section: References">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<style data-mw-deduplicate="TemplateStyles:r1011085734">.mw-parser-output .reflist{font-size:90%;margin-bottom:0.5em;list-style-type:decimal}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist">
<div class="mw-references-wrap"><ol class="references">
<li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r999302996">.mw-parser-output cite.citation{font-style:inherit}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .id-lock-free a,.mw-parser-output .citation .cs1-lock-free a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited a,.mw-parser-output .id-lock-registration a,.mw-parser-output .citation .cs1-lock-limited a,.mw-parser-output .citation .cs1-lock-registration a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription a,.mw-parser-output .citation .cs1-lock-subscription a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-subscription,.mw-parser-output .cs1-registration{color:#555}.mw-parser-output .cs1-subscription span,.mw-parser-output .cs1-registration span{border-bottom:1px dotted;cursor:help}.mw-parser-output .cs1-ws-icon a{background:linear-gradient(transparent,transparent),url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}.mw-parser-output code.cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;font-size:100%}.mw-parser-output .cs1-visible-error{font-size:100%}.mw-parser-output .cs1-maint{display:none;color:#33aa33;margin-left:0.3em}.mw-parser-output .cs1-format{font-size:95%}.mw-parser-output .cs1-kern-left,.mw-parser-output .cs1-kern-wl-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right,.mw-parser-output .cs1-kern-wl-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}</style><cite id="CITEREFRussell_Walker2019" class="citation journal cs1">Russell Walker, Russell Walker (2019-06-14). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1287/7648739e-8e59-466e-82cb-3ded22bbebf6">"Russell Walker"</a>. <i>Authors group</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1287%2F7648739e-8e59-466e-82cb-3ded22bbebf6">10.1287/7648739e-8e59-466e-82cb-3ded22bbebf6</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Authors+group&amp;rft.atitle=Russell+Walker&amp;rft.date=2019-06-14&amp;rft_id=info%3Adoi%2F10.1287%2F7648739e-8e59-466e-82cb-3ded22bbebf6&amp;rft.aulast=Russell+Walker&amp;rft.aufirst=Russell+Walker&amp;rft_id=http%3A%2F%2Fdx.doi.org%2F10.1287%2F7648739e-8e59-466e-82cb-3ded22bbebf6&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span>
</li>
<li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://imslp.org/wiki/Category:Scholz,_Richard">"Category:Scholz, Richard – IMSLP"</a>. <i>imslp.org</i><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=imslp.org&amp;rft.atitle=Category%3AScholz%2C+Richard+%E2%80%93+IMSLP&amp;rft_id=https%3A%2F%2Fimslp.org%2Fwiki%2FCategory%3AScholz%2C_Richard&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span>
</li>
<li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><a rel="nofollow" class="external text" href="http://www.acoustics.org/press/134th/galembo.htm">Acoustical Society of America –  Large grand and small upright pianos</a> <a rel="nofollow" class="external text" href="https://web.archive.org/web/20120209050929/http://www.acoustics.org/press/134th/galembo.htm">Archived</a> 2012-02-09 at the <a href="/wiki/Wayback_Machine" title="Wayback Machine">Wayback Machine</a> by Alexander Galembo and Lola L. Cuddly</span>
</li>
<li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFRademacherRademacherRademacherRademacher1927" class="citation journal cs1">Rademacher, Hanna; Rademacher, Hanna; Rademacher, Hanna; Rademacher, Hanna (1927). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.2307/40043442">"Golo und Genovefa"</a>. <i>Books Abroad</i>. <b>1</b> (2): 34. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F40043442">10.2307/40043442</a>. <a href="/wiki/ISSN_(identifier)" class="mw-redirect" title="ISSN (identifier)">ISSN</a>&#160;<a rel="nofollow" class="external text" href="//www.worldcat.org/issn/0006-7431">0006-7431</a>. <a href="/wiki/JSTOR_(identifier)" class="mw-redirect" title="JSTOR (identifier)">JSTOR</a>&#160;<a rel="nofollow" class="external text" href="//www.jstor.org/stable/40043442">40043442</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Books+Abroad&amp;rft.atitle=Golo+und+Genovefa&amp;rft.volume=1&amp;rft.issue=2&amp;rft.pages=34&amp;rft.date=1927&amp;rft.issn=0006-7431&amp;rft_id=%2F%2Fwww.jstor.org%2Fstable%2F40043442%23id-name%3DJSTOR&amp;rft_id=info%3Adoi%2F10.2307%2F40043442&amp;rft.aulast=Rademacher&amp;rft.aufirst=Hanna&amp;rft.au=Rademacher%2C+Hanna&amp;rft.au=Rademacher%2C+Hanna&amp;rft.au=Rademacher%2C+Hanna&amp;rft_id=http%3A%2F%2Fdx.doi.org%2F10.2307%2F40043442&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span> <span class="cs1-visible-error error citation-comment">Missing <code class="cs1-code">&#124;author2=</code> (<a href="/wiki/Help:CS1_errors#missing_name" title="Help:CS1 errors">help</a>)</span></span>
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<li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><span class="citation 1037C"><img alt="" src="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/12px-PD-icon.svg.png" decoding="async" width="12" height="12" srcset="//upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/18px-PD-icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/6/62/PD-icon.svg/24px-PD-icon.svg.png 2x" data-file-width="196" data-file-height="196" />&#160;This article incorporates&#160;<a href="/wiki/Copyright_status_of_works_by_the_federal_government_of_the_United_States" title="Copyright status of works by the federal government of the United States">public domain material</a> from the <a href="/wiki/General_Services_Administration" title="General Services Administration">General Services Administration</a>&#32;document: <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://www.its.bldrdoc.gov/fs-1037/fs-1037c.htm">"Federal Standard 1037C"</a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Federal+Standard+1037C&amp;rft_id=https%3A%2F%2Fwww.its.bldrdoc.gov%2Ffs-1037%2Ffs-1037c.htm&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span></span>
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<li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFGeorge_alikeGeorge_alikeGeorge_alikeGeorge_alike2011" class="citation journal cs1">George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike; George alike, George alike (2011-01-21). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.4016/26742.01">"MyFavoritegamez.com - Free Online Games For Kids"</a>. <i>SciVee</i>. <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.4016%2F26742.01">10.4016/26742.01</a><span class="reference-accessdate">. Retrieved <span class="nowrap">2020-12-21</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=SciVee&amp;rft.atitle=MyFavoritegamez.com+-+Free+Online+Games+For+Kids&amp;rft.date=2011-01-21&amp;rft_id=info%3Adoi%2F10.4016%2F26742.01&amp;rft.aulast=George+alike&amp;rft.aufirst=George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft.au=George+alike%2C+George+alike&amp;rft_id=http%3A%2F%2Fdx.doi.org%2F10.4016%2F26742.01&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span>
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<li id="cite_note-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-7">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFMarrocco2001" class="citation cs2">Marrocco, W. Thomas (2001), <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1093/gmo/9781561592630.article.14882">"Kennan, Kent"</a>, <i>Oxford Music Online</i>, Oxford University Press, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgmo%2F9781561592630.article.14882">10.1093/gmo/9781561592630.article.14882</a><span class="reference-accessdate">, retrieved <span class="nowrap">2020-12-21</span></span></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Oxford+Music+Online&amp;rft.atitle=Kennan%2C+Kent&amp;rft.date=2001&amp;rft_id=info%3Adoi%2F10.1093%2Fgmo%2F9781561592630.article.14882&amp;rft.aulast=Marrocco&amp;rft.aufirst=W.+Thomas&amp;rft_id=http%3A%2F%2Fdx.doi.org%2F10.1093%2Fgmo%2F9781561592630.article.14882&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span>
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<li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFMarrocco2001" class="citation cs2">Marrocco, W. Thomas (2001), <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1093/gmo/9781561592630.article.14882">"Kennan, Kent"</a>, <i>Oxford Music Online</i>, Oxford University Press, <a href="/wiki/Doi_(identifier)" class="mw-redirect" title="Doi (identifier)">doi</a>:<a rel="nofollow" class="external text" href="https://doi.org/10.1093%2Fgmo%2F9781561592630.article.14882">10.1093/gmo/9781561592630.article.14882</a><span class="reference-accessdate">, retrieved <span class="nowrap">2020-12-21</span></span></cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=article&amp;rft.jtitle=Oxford+Music+Online&amp;rft.atitle=Kennan%2C+Kent&amp;rft.date=2001&amp;rft_id=info%3Adoi%2F10.1093%2Fgmo%2F9781561592630.article.14882&amp;rft.aulast=Marrocco&amp;rft.aufirst=W.+Thomas&amp;rft_id=http%3A%2F%2Fdx.doi.org%2F10.1093%2Fgmo%2F9781561592630.article.14882&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></span>
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<h2><span class="mw-headline" id="External_links">External links</span><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Harmonic&amp;action=edit&amp;section=9" title="Edit section: External links">edit</a><span class="mw-editsection-bracket">]</span></span></h2>
<ul><li><a rel="nofollow" class="external text" href="https://feynmanlectures.caltech.edu/I_50.html">The Feynman Lectures on Physics: Harmonics</a></li>
<li><a rel="nofollow" class="external text" href="http://www.sengpielaudio.com/calculator-harmonics.htm">Harmonics, partials and overtones from fundamental frequency</a></li>
<li><a rel="nofollow" class="external text" href="http://www.newmusicbox.org/chatter/chatter.nmbx?id=5556">Discussion of Sciarrino's violin etudes and notation issues</a></li>
<li><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r999302996"/><cite id="CITEREFChisholm1911" class="citation encyclopaedia cs1">Chisholm, Hugh, ed. (1911). <span class="cs1-ws-icon" title="s:1911 Encyclopædia Britannica/Harmonic"><a class="external text" href="https://en.wikisource.org/wiki/1911_Encyclop%C3%A6dia_Britannica/Harmonic">"Harmonic"&#160;</a></span>. <i><a href="/wiki/Encyclop%C3%A6dia_Britannica_Eleventh_Edition" title="Encyclopædia Britannica Eleventh Edition">Encyclopædia Britannica</a></i> (11th&#160;ed.). Cambridge University Press.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=bookitem&amp;rft.atitle=Harmonic&amp;rft.btitle=Encyclop%C3%A6dia+Britannica&amp;rft.edition=11th&amp;rft.pub=Cambridge+University+Press&amp;rft.date=1911&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3AHarmonic" class="Z3988"></span></li>
<li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20091229052719/http://www.dranetz-bmi.com/pdf/harmonicsall.pdf">Harmonics</a></li>
<li><a rel="nofollow" class="external text" href="http://harmonicviewerforpiano.com/">Hear and see harmonics on a Piano</a></li></ul>
<div role="navigation" class="navbox" aria-labelledby="Acoustics" style="padding:3px"><table class="nowraplinks mw-collapsible autocollapse navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="navbox-title" colspan="3"><style data-mw-deduplicate="TemplateStyles:r992953826">.mw-parser-output .navbar{display:inline;font-size:88%;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:114%;margin:0 7em}.mw-parser-output .navbar-ct-mini{font-size:114%;margin:0 4em}.mw-parser-output .infobox .navbar{font-size:100%}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Acoustics" title="Template:Acoustics"><abbr title="View this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Acoustics" title="Template talk:Acoustics"><abbr title="Discuss this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">t</abbr></a></li><li class="nv-edit"><a class="external text" href="https://en.wikipedia.org/w/index.php?title=Template:Acoustics&amp;action=edit"><abbr title="Edit this template" style=";;background:none transparent;border:none;box-shadow:none;padding:0;">e</abbr></a></li></ul></div><div id="Acoustics" style="font-size:114%;margin:0 4em"><a href="/wiki/Acoustics" title="Acoustics">Acoustics</a></div></th></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Acoustical_engineering" title="Acoustical engineering">Acoustical engineering</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/wiki/Architectural_acoustics" title="Architectural acoustics">Architectural acoustics</a></li>
<li><a href="/wiki/Monochord" title="Monochord">Monochord</a></li>
<li><a href="/wiki/Reverberation" title="Reverberation">Reverberation</a></li>
<li><a href="/wiki/Soundproofing" title="Soundproofing">Soundproofing</a></li>
<li><a href="/wiki/String_vibration" title="String vibration">String vibration</a>
<ul><li><a href="/wiki/String_resonance" title="String resonance">String resonance</a></li></ul></li></ul>
</div></td><td class="noviewer navbox-image" rowspan="5" style="width:1px;padding:0px 0px 0px 2px"><div><div class="plainlist"><ul><li><a href="/wiki/File:Spectrogram_showing_shared_partials.png" class="image"><img alt="A spectrogram of a violin playing a note and then a perfect fifth above it. The shared partials are highlighted by the white dashes." src="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/80px-Spectrogram_showing_shared_partials.png" decoding="async" width="80" height="67" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/120px-Spectrogram_showing_shared_partials.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/2/26/Spectrogram_showing_shared_partials.png/160px-Spectrogram_showing_shared_partials.png 2x" data-file-width="300" data-file-height="250" /></a></li><li><span style="font-size:90%;"><a href="/wiki/Spectrogram" title="Spectrogram">Spectrogram</a></span></li></ul></div></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Psychoacoustics" title="Psychoacoustics">Psychoacoustics</a></th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/wiki/Bark_scale" title="Bark scale">Bark scale</a></li>
<li><a href="/wiki/Combination_tone" title="Combination tone">Combination tone</a></li>
<li><a href="/wiki/Equal-loudness_contour" title="Equal-loudness contour">Equal-loudness contour</a>
<ul><li><a href="/wiki/Fletcher%E2%80%93Munson_curves" class="mw-redirect" title="Fletcher–Munson curves">Fletcher–Munson curves</a></li></ul></li>
<li><a href="/wiki/Mel_scale" title="Mel scale">Mel scale</a></li>
<li><a href="/wiki/Missing_fundamental" title="Missing fundamental">Missing fundamental</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/Frequency" title="Frequency">Frequency</a> and <a href="/wiki/Pitch_(music)" title="Pitch (music)">pitch</a></th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/wiki/Beat_(acoustics)" title="Beat (acoustics)">Beat</a></li>
<li><a href="/wiki/Formant" title="Formant">Formant</a></li>
<li><a href="/wiki/Fundamental_frequency" title="Fundamental frequency">Fundamental frequency</a></li>
<li><a href="/wiki/Frequency_spectrum" class="mw-redirect" title="Frequency spectrum">Frequency spectrum</a>
<ul><li><a href="/wiki/Harmonic_spectrum" title="Harmonic spectrum">harmonic spectrum</a></li></ul></li>
<li><a class="mw-selflink selflink">Harmonic</a>
<ul><li><a href="/wiki/Harmonic_series_(music)" title="Harmonic series (music)">Series</a></li>
<li><a href="/wiki/Inharmonicity" title="Inharmonicity">Inharmonicity</a></li></ul></li>
<li><a href="/wiki/Mersenne%27s_laws" title="Mersenne&#39;s laws">Mersenne's laws</a></li>
<li><a href="/wiki/Overtone" title="Overtone">Overtone</a></li>
<li><a href="/wiki/Acoustic_resonance" title="Acoustic resonance">Resonance</a></li>
<li><a href="/wiki/Standing_wave" title="Standing wave">Standing wave</a>
<ul><li><a href="/wiki/Node_(physics)" title="Node (physics)">Node</a></li></ul></li>
<li><a href="/wiki/Undertone_series" title="Undertone series">Subharmonic</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Acousticians</th><td class="navbox-list navbox-even hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/wiki/John_Backus_(acoustician)" title="John Backus (acoustician)">John Backus</a></li>
<li><a href="/wiki/Jens_Blauert" title="Jens Blauert">Jens Blauert</a></li>
<li><a href="/wiki/Ernst_Chladni" title="Ernst Chladni">Ernst Chladni</a></li>
<li><a href="/wiki/Hermann_von_Helmholtz" title="Hermann von Helmholtz">Hermann von Helmholtz</a></li>
<li><a href="/wiki/Carleen_Hutchins" title="Carleen Hutchins">Carleen Hutchins</a></li>
<li><a href="/wiki/Franz_Melde" title="Franz Melde">Franz Melde</a></li>
<li><a href="/wiki/Marin_Mersenne" title="Marin Mersenne">Marin Mersenne</a></li>
<li><a href="/wiki/Werner_Meyer-Eppler" title="Werner Meyer-Eppler">Werner Meyer-Eppler</a></li>
<li><a href="/wiki/John_Strutt,_3rd_Baron_Rayleigh" class="mw-redirect" title="John Strutt, 3rd Baron Rayleigh">Lord Rayleigh</a></li>
<li><a href="/wiki/Joseph_Sauveur" title="Joseph Sauveur">Joseph Sauveur</a></li>
<li><a href="/wiki/D._Van_Holliday" title="D. Van Holliday">D. Van Holliday</a></li>
<li><a href="/wiki/Thomas_Young_(scientist)" title="Thomas Young (scientist)">Thomas Young</a></li></ul>
</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">Related topics</th><td class="navbox-list navbox-odd hlist" style="text-align:left;border-left-width:2px;border-left-style:solid;width:100%;padding:0px"><div style="padding:0em 0.25em">
<ul><li><a href="/wiki/Echo_(phenomenon)" class="mw-redirect" title="Echo (phenomenon)">Echo</a></li>
<li><a href="/wiki/Infrasound" title="Infrasound">Infrasound</a></li>
<li><a href="/wiki/Sound" title="Sound">Sound</a></li>
<li><a href="/wiki/Ultrasound" title="Ultrasound">Ultrasound</a></li>
<li><a href="/wiki/Musical_acoustics" title="Musical acoustics">Musical acoustics</a>
<ul><li><a href="/wiki/Piano_acoustics" title="Piano acoustics">Piano</a></li>
<li><a href="/wiki/Violin_acoustics" title="Violin acoustics">Violin</a></li></ul></li></ul>
</div></td></tr><tr><td class="navbox-abovebelow hlist" colspan="3"><div>
<ul><li><img alt="Category" src="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" title="Category" width="16" height="16" srcset="//upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/en/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /> <a href="/wiki/Category:Acoustics" title="Category:Acoustics">Category</a></li></ul>
</div></td></tr></tbody></table></div>
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href="https://ht.wikipedia.org/wiki/Amoni" title="Amoni – Haitian Creole" lang="ht" hreflang="ht" class="interlanguage-link-target">Kreyòl ayisyen</a></li><li class="interlanguage-link interwiki-nl"><a href="https://nl.wikipedia.org/wiki/Harmonische" title="Harmonische – Dutch" lang="nl" hreflang="nl" class="interlanguage-link-target">Nederlands</a></li><li class="interlanguage-link interwiki-ja"><a href="https://ja.wikipedia.org/wiki/%E9%AB%98%E8%AA%BF%E6%B3%A2" title="高調波 – Japanese" lang="ja" hreflang="ja" class="interlanguage-link-target">日本語</a></li><li class="interlanguage-link interwiki-nn"><a href="https://nn.wikipedia.org/wiki/Harmonisk_b%C3%B8lgje" title="Harmonisk bølgje – Norwegian Nynorsk" lang="nn" hreflang="nn" class="interlanguage-link-target">Norsk nynorsk</a></li><li class="interlanguage-link interwiki-oc"><a href="https://oc.wikipedia.org/wiki/Armonica_(musica)" title="Armonica (musica) – Occitan" lang="oc" hreflang="oc" 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href="https://sv.wikipedia.org/wiki/Harmonisk_v%C3%A5g" title="Harmonisk våg – Swedish" lang="sv" hreflang="sv" class="interlanguage-link-target">Svenska</a></li><li class="interlanguage-link interwiki-th"><a href="https://th.wikipedia.org/wiki/%E0%B8%AE%E0%B8%B2%E0%B8%A3%E0%B9%8C%E0%B8%A1%E0%B8%AD%E0%B8%99%E0%B8%B4%E0%B8%81" title="ฮาร์มอนิก – Thai" lang="th" hreflang="th" class="interlanguage-link-target">ไทย</a></li><li class="interlanguage-link interwiki-uk"><a href="https://uk.wikipedia.org/wiki/%D0%93%D0%B0%D1%80%D0%BC%D0%BE%D0%BD%D1%96%D0%BA%D0%B8" title="Гармоніки – Ukrainian" lang="uk" hreflang="uk" class="interlanguage-link-target">Українська</a></li><li class="interlanguage-link interwiki-zh"><a href="https://zh.wikipedia.org/wiki/%E8%B0%90%E6%B3%A2" title="谐波 – Chinese" lang="zh" hreflang="zh" class="interlanguage-link-target">中文</a></li></ul>
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