<story><title>The Saddest Thing I Know about the Integers</title><url>http://blogs.scientificamerican.com/roots-of-unity/2014/11/30/the-saddest-thing-i-know-about-the-integers/</url></story><parent_chain><item><author>dandelany</author><text>I went looking for examples of what you were talking about and discovered that, amazingly enough, a &lt;i&gt;single&lt;/i&gt; human voice can even reliably produce overtones! I&amp;#x27;m guessing these are very different, though, than what you&amp;#x27;re talking about &lt;a href=&quot;https://www.youtube.com/watch?v=2i61_JNc_Nc&amp;amp;t=1m25s&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;watch?v=2i61_JNc_Nc&amp;amp;t=1m25s&lt;/a&gt;&lt;p&gt;I&amp;#x27;d love to hear some examples of a barbershop n-tet doing it too, I&amp;#x27;m sure it&amp;#x27;s even better. But when I search for &amp;#x27;barbershop overtones&amp;#x27; it&amp;#x27;s all music by groups &lt;i&gt;called&lt;/i&gt; The Overtones :)</text></item><item><author>depoll</author><text>Welcome to the world of Barbershop music (one of my primary hobbies) ;)  Unlike a piano, which must be tuned and which has a temperament that is fixed from chord to chord in a piece, the human voice can make minute adjustments to come as close as possible to those nice integer ratios (both in the fundamental and in the upper partials produced by their voices).  When we do, we are rewarded with (sometimes screaming loud) overtones caused by the constructive interference between the sounds being produced by each of the four parts.&lt;p&gt;As this article points out, it&amp;#x27;s mathematically impossible to perfectly tune some of these intervals, but depending on the relationships between the notes being sung, you can tune to one singer or the other.  It takes a lot of practice and a good ear, but the resulting effect is pretty darned cool.</text></item></parent_chain><comment><author>depoll</author><text>If you&amp;#x27;re curious about overtone singing, listen to this -- it&amp;#x27;s insane: &lt;a href=&quot;https://www.youtube.com/watch?v=vC9Qh709gas&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;watch?v=vC9Qh709gas&lt;/a&gt;&lt;p&gt;The principle is actually the same -- she is modifying her singing apparatus to emphasize different upper partials that are already in her voice.  Barbershoppers do this as well, though less explicitly (we do vowel matching, which helps emphasize upper partials to produce greater ring).&lt;p&gt;Here&amp;#x27;s a video from a perennial favorite quartet (the Gas House Gang): &lt;a href=&quot;https://www.youtube.com/watch?v=pvYT_yWiLqU&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;watch?v=pvYT_yWiLqU&lt;/a&gt;  The top&amp;#x2F;tenor note is often the same note as the primary overtone produced by the other 3 parts (adding further emphasis to the overtone), but this effect is what gives barbershop the quality of sounding like more than 4 voices, and produces the &amp;quot;ring&amp;quot; in the sound.</text></comment>
<story><title>The Saddest Thing I Know about the Integers</title><url>http://blogs.scientificamerican.com/roots-of-unity/2014/11/30/the-saddest-thing-i-know-about-the-integers/</url></story><parent_chain><item><author>dandelany</author><text>I went looking for examples of what you were talking about and discovered that, amazingly enough, a &lt;i&gt;single&lt;/i&gt; human voice can even reliably produce overtones! I&amp;#x27;m guessing these are very different, though, than what you&amp;#x27;re talking about &lt;a href=&quot;https://www.youtube.com/watch?v=2i61_JNc_Nc&amp;amp;t=1m25s&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;watch?v=2i61_JNc_Nc&amp;amp;t=1m25s&lt;/a&gt;&lt;p&gt;I&amp;#x27;d love to hear some examples of a barbershop n-tet doing it too, I&amp;#x27;m sure it&amp;#x27;s even better. But when I search for &amp;#x27;barbershop overtones&amp;#x27; it&amp;#x27;s all music by groups &lt;i&gt;called&lt;/i&gt; The Overtones :)</text></item><item><author>depoll</author><text>Welcome to the world of Barbershop music (one of my primary hobbies) ;)  Unlike a piano, which must be tuned and which has a temperament that is fixed from chord to chord in a piece, the human voice can make minute adjustments to come as close as possible to those nice integer ratios (both in the fundamental and in the upper partials produced by their voices).  When we do, we are rewarded with (sometimes screaming loud) overtones caused by the constructive interference between the sounds being produced by each of the four parts.&lt;p&gt;As this article points out, it&amp;#x27;s mathematically impossible to perfectly tune some of these intervals, but depending on the relationships between the notes being sung, you can tune to one singer or the other.  It takes a lot of practice and a good ear, but the resulting effect is pretty darned cool.</text></item></parent_chain><comment><author>baddox</author><text>Overtone singing itself isn&amp;#x27;t very common in barbershop music, but their harmonies certainly make use of overtones. Here&amp;#x27;s a performance of a song called Play That Barbershop Chord (a stable in the genre). It&amp;#x27;s not instructive, but it&amp;#x27;s got some great harmonies: &lt;a href=&quot;https://www.youtube.com/watch?v=F5bYnRkwpco&quot; rel=&quot;nofollow&quot;&gt;https:&amp;#x2F;&amp;#x2F;www.youtube.com&amp;#x2F;watch?v=F5bYnRkwpco&lt;/a&gt;&lt;p&gt;Here&amp;#x27;s a fairly technical article about three different seventh chords, one (the harmonic seventh) being the so-called barbershop seventh chord. There are embedded YouTube videos with computer-generated audio samples. &lt;a href=&quot;http://www.garygarrett.me/?p=1575&quot; rel=&quot;nofollow&quot;&gt;http:&amp;#x2F;&amp;#x2F;www.garygarrett.me&amp;#x2F;?p=1575&lt;/a&gt;</text></comment>