<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></parent_chain><comment><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></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></parent_chain><comment><author>sopooneo</author><text>I have never yet found anyone who agrees with me, but I believe the terminology around music theory is horrible. I mean that it is unnecessarily confusing. Most people that use it have no problem, but I believe they developed their overall understanding almost independent of the terminology, so now just use it as descriptive in its context, and do not at all notice how bad it is if you are trying to use the language as your first point in &lt;i&gt;comprehending&lt;/i&gt; the underlying notions.</text></comment>