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<button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">move to sidebar</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">hide</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">From Wikipedia, the free encyclopedia</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Relative unit corresponding to doubling of frequency</div> <p>In <a href="/wiki/Electronics" title="Electronics">electronics</a>, an <b>octave</b> (symbol: <b>oct</b>) is a <a href="/wiki/Logarithmic_unit" class="mw-redirect" title="Logarithmic unit">logarithmic unit</a> for <a href="/wiki/Ratio" title="Ratio">ratios</a> between <a href="/wiki/Frequency" title="Frequency">frequencies</a>, with one octave corresponding to a doubling of frequency. For example, the frequency one octave above 40 Hz is 80 Hz. The term is derived from the <a href="/wiki/Scale_(music)#Western_music" title="Scale (music)">Western musical scale</a> where an <a href="/wiki/Octave" title="Octave">octave</a> is a doubling in frequency.<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>note 1<span class="cite-bracket">]</span></a></sup> Specification in terms of octaves is therefore common in <a href="/wiki/Audio_electronics" class="mw-redirect" title="Audio electronics">audio electronics</a>. </p><p>Along with the <a href="/wiki/Decade_(log_scale)" title="Decade (log scale)">decade</a>, it is a <a href="/wiki/Unit_of_measurement" title="Unit of measurement">unit</a> used to describe <a href="/wiki/Frequency_band" class="mw-redirect" title="Frequency band">frequency bands</a> or <a href="/wiki/Interval_ratio" title="Interval ratio">frequency ratios</a>.<sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Ratios_and_slopes">Ratios and slopes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Octave_(electronics)&action=edit&section=1" title="Edit section: Ratios and slopes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>A frequency ratio expressed in octaves is the base-2 <a href="/wiki/Logarithm" title="Logarithm">logarithm</a> (<a href="/wiki/Binary_logarithm" title="Binary logarithm">binary logarithm</a>) of the ratio: </p> <dl><dd><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 {\text{number of octaves}}=\log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>number of octaves</mtext> </mrow> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <msub> <mi>f</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>1</mn> </mrow> </msub> </mfrac> </mrow> <mo>)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7dc41cb457c10a14b6dbd717b7213423410b803c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:31.806ex; height:6.176ex;" alt="{\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {f_{2}}{f_{1}}}\right)}"></span></dd></dl> <p>An amplifier or filter may be stated to have a frequency response of ±6 dB per octave over a particular frequency range, which signifies that the power gain changes by ±6 <a href="/wiki/Decibels" class="mw-redirect" title="Decibels">decibels</a> (a factor of 4 in power), when the frequency changes by a factor of 2. This slope, or more precisely 10 log<sub>10</sub>(4) ≈ 6 decibels per octave, corresponds to an amplitude gain proportional to frequency, which is equivalent to ±20 dB per <a href="/wiki/Decade_(log_scale)" title="Decade (log scale)">decade</a> (factor of 10 amplitude gain change for a factor of 10 frequency change). This would be a <a href="/wiki/Roll-off#First-order_roll-off" title="Roll-off">first-order filter</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Example">Example</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Octave_(electronics)&action=edit&section=2" title="Edit section: Example"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The distance between the frequencies 20 Hz and 40 Hz is 1 octave. An amplitude of 52 dB at 4 kHz decreases as frequency increases at −2 dB/oct. What is the amplitude at 13 kHz? </p> <dl><dd><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 {\text{number of octaves}}=\log _{2}\left({\frac {13}{4}}\right)=1.7}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtext>number of octaves</mtext> </mrow> <mo>=</mo> <msub> <mi>log</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msub> <mo>⁡</mo> <mrow> <mo>(</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>13</mn> <mn>4</mn> </mfrac> </mrow> <mo>)</mo> </mrow> <mo>=</mo> <mn>1.7</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {13}{4}}\right)=1.7}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d747ccfdc78ad56bf58a47239d38b164bac33584" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -2.505ex; width:38.008ex; height:6.176ex;" alt="{\displaystyle {\text{number of octaves}}=\log _{2}\left({\frac {13}{4}}\right)=1.7}"></span></dd></dl> <dl><dd><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 {\text{Mag}}_{13{\text{ kHz}}}=52{\text{ dB}}+(1.7{\text{ oct}}\times -2{\text{ dB/oct}})=48.6{\text{ dB}}.\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msub> <mrow class="MJX-TeXAtom-ORD"> <mtext>Mag</mtext> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mn>13</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> kHz</mtext> </mrow> </mrow> </msub> <mo>=</mo> <mn>52</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> dB</mtext> </mrow> <mo>+</mo> <mo stretchy="false">(</mo> <mn>1.7</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> oct</mtext> </mrow> <mo>×</mo> <mo>−</mo> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> dB/oct</mtext> </mrow> <mo stretchy="false">)</mo> <mo>=</mo> <mn>48.6</mn> <mrow class="MJX-TeXAtom-ORD"> <mtext> dB</mtext> </mrow> <mo>.</mo> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\text{Mag}}_{13{\text{ kHz}}}=52{\text{ dB}}+(1.7{\text{ oct}}\times -2{\text{ dB/oct}})=48.6{\text{ dB}}.\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/175b0fb512f0d5d770c073b6b0103eb9bc678174" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:55.364ex; height:2.843ex;" alt="{\displaystyle {\text{Mag}}_{13{\text{ kHz}}}=52{\text{ dB}}+(1.7{\text{ oct}}\times -2{\text{ dB/oct}})=48.6{\text{ dB}}.\,}"></span></dd></dl> <div class="mw-heading mw-heading2"><h2 id="See_also">See also</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Octave_(electronics)&action=edit&section=3" title="Edit section: See also"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/Octave" title="Octave">Octave</a></li> <li><a href="/wiki/Octave_band" title="Octave band">Octave band</a></li> <li><a href="/wiki/One-third_octave" title="One-third octave">One-third octave</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="Notes">Notes</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Octave_(electronics)&action=edit&section=4" title="Edit section: Notes"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.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">The prefix <a href="/wiki/Octa-" class="mw-redirect" title="Octa-">octa-</a>, denoting eight, refers to the eight notes of a <a href="/wiki/Diatonic_and_chromatic" title="Diatonic and chromatic">diatonic scale</a>; the association of the word with doubling is solely a matter of customary usage.</span> </li> </ol></div></div> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Octave_(electronics)&action=edit&section=5" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1239543626"><div class="reflist"> <div class="mw-references-wrap"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">Levine, William S. (2010). <i>The Control Handbook: Control System Fundamentals</i>, p. 9–29. <style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background: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.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781420073621" title="Special:BookSources/9781420073621">9781420073621</a>/<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9781420073669" title="Special:BookSources/9781420073669">9781420073669</a>.</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">Perdikaris, G. (1991). <i>Computer Controlled Systems: Theory and Applications</i>, p. 117. <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a> <a href="/wiki/Special:BookSources/9780792314226" title="Special:BookSources/9780792314226">9780792314226</a>.</span> </li> </ol></div></div>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">Retrieved from "<a dir="ltr" href="https://en.wikipedia.org/w/index.php?title=Octave_(electronics)&oldid=1148544407">https://en.wikipedia.org/w/index.php?title=Octave_(electronics)&oldid=1148544407</a>"</div></div> <div id="catlinks" class="catlinks" data-mw="interface"><div id="mw-normal-catlinks" class="mw-normal-catlinks"><a href="/wiki/Help:Category" title="Help:Category">Categories</a>: <ul><li><a href="/wiki/Category:Acoustics" title="Category:Acoustics">Acoustics</a></li><li><a href="/wiki/Category:Audio_electronics" title="Category:Audio electronics">Audio electronics</a></li></ul></div><div id="mw-hidden-catlinks" class="mw-hidden-catlinks mw-hidden-cats-hidden">Hidden categories: <ul><li><a href="/wiki/Category:Articles_with_short_description" title="Category:Articles with short description">Articles with short description</a></li><li><a href="/wiki/Category:Short_description_is_different_from_Wikidata" title="Category:Short description is different from Wikidata">Short description is different from Wikidata</a></li></ul></div></div> </div> </main> </div> <div class="mw-footer-container"> <footer id="footer" class="mw-footer" > <ul id="footer-info"> <li id="footer-info-lastmod"> This page was last edited on 6 April 2023, at 20:28<span class="anonymous-show"> (UTC)</span>.</li> <li id="footer-info-copyright">Text is available under the <a href="/wiki/Wikipedia:Text_of_the_Creative_Commons_Attribution-ShareAlike_4.0_International_License" title="Wikipedia:Text of the Creative Commons Attribution-ShareAlike 4.0 International License">Creative Commons Attribution-ShareAlike 4.0 License</a>; additional terms may apply. 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