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	<title>Fourier transform &#8211; Tremblings and Warblings</title>
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	<link>https://www.tremblingsandwarblings.com</link>
	<description>A Blog on the Science of Music and Speech</description>
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		<title>The Kinkiness of a Vibrating String</title>
		<link>https://www.tremblingsandwarblings.com/2017/10/kinkiness-vibrating-string/</link>
		<comments>https://www.tremblingsandwarblings.com/2017/10/kinkiness-vibrating-string/#respond</comments>
		<pubDate>Tue, 31 Oct 2017 10:07:41 +0000</pubDate>
		<dc:creator><![CDATA[tremblingsandwarblings]]></dc:creator>
				<category><![CDATA[Instruments]]></category>
		<category><![CDATA[Fourier transform]]></category>
		<category><![CDATA[Sine waves]]></category>
		<category><![CDATA[Spectrum]]></category>
		<category><![CDATA[String]]></category>
		<category><![CDATA[Violin]]></category>

		<guid isPermaLink="false">http://www.tremblingsandwarblings.com/?p=776</guid>
		<description><![CDATA[<img width="150" height="150" src="https://www.tremblingsandwarblings.com/wp-content/uploads/2017/10/violin_strings-150x150.jpg" class="webfeedsFeaturedVisual wp-post-image" alt="Violin closeup" style="display: block; margin-bottom: 5px; clear:both;max-width: 100%;" /><p class="p1"><span class="s1">Here’s a super-slow-motion video of a vibrating violin string:</span></p>
<div class="youtube-player" data-id="FEyND1GvdxI" data-tags="FEyND1GvdxI?start=100&#38;end=160&#38;rel=0&#38;theme=light"></div>
<p><span style="color: #808080; line-height: 0px; display: block;"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;"><em>Video by <a href="https://www.youtube.com/channel/UCTTafL52cfiJCL5_jK2UxNA" target="_blank" rel="noopener noreferrer">Jost Fischer</a>.</em></span></span></span></p>
<p class="p1"><span class="s1">I think this is pretty cool — there’s this <i>kink</i> that’s travelling up and down the length of the string.<span class="Apple-converted-space">  </span>What’s going on here, and why don’t we see this with the naked eye?<span class="Apple-converted-space">  </span>In this post I’ll explain how a bowed string vibrates, and how, unintuitive as it seems, the odd kinky motion of the </span>&#8230; <a href="https://www.tremblingsandwarblings.com/2017/10/kinkiness-vibrating-string/" class="read-more">Read the rest</a></p>
<p>The post <a rel="nofollow" href="https://www.tremblingsandwarblings.com/2017/10/kinkiness-vibrating-string/">The Kinkiness of a Vibrating String</a> appeared first on <a rel="nofollow" href="https://www.tremblingsandwarblings.com">Tremblings and Warblings</a>.</p>
]]></description>
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		<slash:comments>0</slash:comments>
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		<item>
		<title>Digitally Transforming a Female Voice to a Male Voice</title>
		<link>https://www.tremblingsandwarblings.com/2017/07/digitally-transforming-a-female-voice-to-a-male-voice/</link>
		<comments>https://www.tremblingsandwarblings.com/2017/07/digitally-transforming-a-female-voice-to-a-male-voice/#comments</comments>
		<pubDate>Sun, 23 Jul 2017 20:18:08 +0000</pubDate>
		<dc:creator><![CDATA[tremblingsandwarblings]]></dc:creator>
				<category><![CDATA[Human Voice]]></category>
		<category><![CDATA[Digital audio technology]]></category>
		<category><![CDATA[Formants]]></category>
		<category><![CDATA[Fourier transform]]></category>
		<category><![CDATA[Spectrum]]></category>
		<category><![CDATA[Timbre]]></category>

		<guid isPermaLink="false">http://www.tremblingsandwarblings.com/?p=575</guid>
		<description><![CDATA[<img width="150" height="150" src="https://www.tremblingsandwarblings.com/wp-content/uploads/2017/07/original-spectrum-with-arrows-150x150.jpg" class="webfeedsFeaturedVisual wp-post-image" alt="Formants" style="display: block; margin-bottom: 5px; clear:both;max-width: 100%;" /><p class="p1"><span class="s1">Here’s a recording of a woman reciting a line from the Catalan poem <i>La Vaca Cega</i>:</span></p>
<div class="track"><span class="songtitle">La Vaca Cega</span><span class="audiobutton"></span></p>
<div class="albumtrack" style="visibility:hidden;"><!--[if lt IE 9]><script>document.createElement('audio');</script>< ![endif]--><br />
<audio class="wp-audio-shortcode" id="audio-575-1" preload="metadata" style="width: 100%;" controls="controls"><source type="audio/mpeg" src="http://www.tremblingsandwarblings.com/wp-content/uploads/2017/07/speech-female.mp3?_=1" /><a href="http://www.tremblingsandwarblings.com/wp-content/uploads/2017/07/speech-female.mp3">http://www.tremblingsandwarblings.com/wp-content/uploads/2017/07/speech-female.mp3</a></audio></div>
</div>
<p><span style="color: #000000;"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;"><em><a href="http://freesound.org/people/xserra/sounds/317745/" target="_blank" rel="noopener">Speech-female.wav</a> by <a href="http://freesound.org/people/xserra/" target="_blank" rel="noopener">xserra</a> / <a href="https://creativecommons.org/licenses/by/3.0/" target="_blank" rel="noopener">CC BY</a>.</em></span></span></span></p>
<p class="p1"><span class="s1">Suppose that you wanted to take the recording and change the quality of the voice — change it into a male-sounding voice, for instance.<span class="Apple-converted-space">  </span>How would you go about it?<span class="Apple-converted-space">  </span>I did this recently for an online audio processing course I </span>&#8230; <a href="https://www.tremblingsandwarblings.com/2017/07/digitally-transforming-a-female-voice-to-a-male-voice/" class="read-more">Read the rest</a></p>
<p>The post <a rel="nofollow" href="https://www.tremblingsandwarblings.com/2017/07/digitally-transforming-a-female-voice-to-a-male-voice/">Digitally Transforming a Female Voice to a Male Voice</a> appeared first on <a rel="nofollow" href="https://www.tremblingsandwarblings.com">Tremblings and Warblings</a>.</p>
]]></description>
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		<slash:comments>4</slash:comments>
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		<item>
		<title>The Fourier Transform and the Spectrum</title>
		<link>https://www.tremblingsandwarblings.com/2017/05/fourier-transform-spectrum/</link>
		<comments>https://www.tremblingsandwarblings.com/2017/05/fourier-transform-spectrum/#respond</comments>
		<pubDate>Mon, 08 May 2017 10:24:56 +0000</pubDate>
		<dc:creator><![CDATA[tremblingsandwarblings]]></dc:creator>
				<category><![CDATA[Physics of Musical Sound]]></category>
		<category><![CDATA[Digital audio technology]]></category>
		<category><![CDATA[Fourier transform]]></category>
		<category><![CDATA[Sine waves]]></category>
		<category><![CDATA[Spectrum]]></category>
		<category><![CDATA[Timbre]]></category>

		<guid isPermaLink="false">http://www.tremblingsandwarblings.com/?p=322</guid>
		<description><![CDATA[<img width="150" height="150" src="https://www.tremblingsandwarblings.com/wp-content/uploads/2017/05/violin_fourier-150x150.gif" class="webfeedsFeaturedVisual wp-post-image" alt="Sine waves combining to form a violin waveform" style="display: block; margin-bottom: 5px; clear:both;max-width: 100%;" /><figure id="attachment_756" style="width: 600px" class="wp-caption aligncenter"><img class="wp-image-756" src="http://www.tremblingsandwarblings.com/wp-content/uploads/2017/05/violin_fourier-1024x512.gif" alt="" width="600" height="300" /><figcaption class="wp-caption-text">Sine waves combining to form a violin waveform.</figcaption></figure>
<p>In <a href="http://www.tremblingsandwarblings.com/2017/04/what-makes-a-musical-sound-part-2-tone-quality-and-spectra/" target="_blank" rel="noopener noreferrer">What Makes a Musical Sound Part 2</a>, I talked about the <a href="http://www.tremblingsandwarblings.com/2017/04/what-makes-a-musical-sound-part-2-tone-quality-and-spectra#spectrum" target="_blank" rel="noopener noreferrer">spectrum</a>, which shows what frequencies are present in a sound.  In this explicative post, I’ll go into more detail about how we obtain the spectrum, and about what it means when we say a sound is made up of different frequencies.</p>
<h3 id="sinewaves">Sine Waves</h3>
<p class="p1"><span class="s1">But<span style="color: #000000;"> first – what</span> does </span>&#8230; <a href="https://www.tremblingsandwarblings.com/2017/05/fourier-transform-spectrum/" class="read-more">Read the rest</a></p>
<p>The post <a rel="nofollow" href="https://www.tremblingsandwarblings.com/2017/05/fourier-transform-spectrum/">The Fourier Transform and the Spectrum</a> appeared first on <a rel="nofollow" href="https://www.tremblingsandwarblings.com">Tremblings and Warblings</a>.</p>
]]></description>
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		<slash:comments>0</slash:comments>
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		<item>
		<title>What Makes a Musical Sound Part 2 &#8211; Tone Quality and Spectra</title>
		<link>https://www.tremblingsandwarblings.com/2017/04/musical-sound-tone-quality-spectra/</link>
		<comments>https://www.tremblingsandwarblings.com/2017/04/musical-sound-tone-quality-spectra/#comments</comments>
		<pubDate>Fri, 07 Apr 2017 20:45:03 +0000</pubDate>
		<dc:creator><![CDATA[tremblingsandwarblings]]></dc:creator>
				<category><![CDATA[Physics of Musical Sound]]></category>
		<category><![CDATA[Digital audio technology]]></category>
		<category><![CDATA[Formants]]></category>
		<category><![CDATA[Fourier transform]]></category>
		<category><![CDATA[Timbre]]></category>

		<guid isPermaLink="false">http://www.tremblingsandwarblings.com/?p=297</guid>
		<description><![CDATA[<img width="150" height="150" src="https://www.tremblingsandwarblings.com/wp-content/uploads/2017/04/Glock-combined-with-snapshots-150x150.png" class="webfeedsFeaturedVisual wp-post-image" alt="Glockenspiel Spectrogram, Waveform and Spectrum Snapshots" style="display: block; margin-bottom: 5px; clear:both;max-width: 100%;" /><p>Here&#8217;s a violin playing the note G (with frequency 784 <a href="http://www.tremblingsandwarblings.com/2017/03/what-makes-a-musical-sound-part1#pitch-frequency" target="_blank" rel="noopener noreferrer">Hz</a>), followed by a flute playing the same note:</p>
<div class="track"><span class="songtitle">Violin &#38; Flute Playing G5</span><span class="audiobutton"></span></p>
<div class="albumtrack" style="visibility:hidden;"><audio class="wp-audio-shortcode" id="audio-297-11" preload="metadata" style="width: 100%;" controls="controls"><source type="audio/mpeg" src="http://www.tremblingsandwarblings.com/wp-content/uploads/2017/04/Violin-Flute.mp3?_=11" /><a href="http://www.tremblingsandwarblings.com/wp-content/uploads/2017/04/Violin-Flute.mp3">http://www.tremblingsandwarblings.com/wp-content/uploads/2017/04/Violin-Flute.mp3</a></audio></div>
</div>
<p><span style="color: #000000;"><span style="font-family: Times New Roman,serif;"><span style="font-size: small;"><em>Sounds from the <a href="http://www.philharmonia.co.uk/explore/sound_samples" target="_blank" rel="noopener noreferrer">Philharmonia Orchestra&#8217;s free sound samples</a> / <a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en_GB" target="_blank" rel="noopener noreferrer">CC BY-SA 3.0</a>.</em></span></span></span></p>
<p><a id="timbre"></a>In <a href="http://www.tremblingsandwarblings.com/2017/03/what-makes-a-musical-sound-part1/" target="_blank" rel="noopener noreferrer">part 1</a> of this series on what makes a musical sound, we looked at two basic properties of a musical note – its pitch and loudness. Since these two notes &#8230; <a href="https://www.tremblingsandwarblings.com/2017/04/musical-sound-tone-quality-spectra/" class="read-more">Read the rest</a></p>
<p>The post <a rel="nofollow" href="https://www.tremblingsandwarblings.com/2017/04/musical-sound-tone-quality-spectra/">What Makes a Musical Sound Part 2 &#8211; Tone Quality and Spectra</a> appeared first on <a rel="nofollow" href="https://www.tremblingsandwarblings.com">Tremblings and Warblings</a>.</p>
]]></description>
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		<slash:comments>4</slash:comments>
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