Pitch, Tuning, and Temperance[Originally posted in Xanada, May 07, 2004] Yesterday a music programmer on CBC’s Radio Two spoke of mean-tone tuning in relation to a piece of organ music. I’ve been intrigued by musical tunings for a while: I could never get my guitar to sound exactly right for all purposes, back in the far-gone days before electrical tuners; and when I sang, my own pitch was okay, but not great, and I envied those with perfect pitch. So I took a look to see what the web threw up about mean-tone tuning and the whole matter of making things sound right. The thing is at once far more complex and at its core more understandable than I had known. In my ignorance, I had assumed that once we’d discovered frequencies and how to measure them, tuning was simply the business getting things to vibrate at the correct Hz (Hertz: cycles per second): A is 440 and B is… Well, it turns out that this is the problem: there are a lot of Hz to choose from, and it’s a matter of taste, I suppose one might say, as to which to pick. What I’ve learned comes principally from an extraordinary web site, Dolmetsch Online, the work of Dr. Brian Blood, now the CEO of the famous recorder making company. The site is a huge venture in expounding musical theory, offering recorder lessons on line with sheet music and midi files, and presenting essays on many aspects of music and recorders in particular. In a nutshell, I think I learned that three things drive (or vex) tuning. One is the current desire to transpose music from one key to any other, whether to accommodate fractious instruments or simply as a matter of preference. A second is the human ear’s love for a perfect fifth, and, perhaps to a slightly lesser extent, a perfect third. These are the simple harmonies that can be found the world over, and that lots of folks can sing with relative ease. The third thing is the octave, which seems to be recognized everywhere as a span of fundamental importance in music, the problem being how best to carve it up. It seems that if you just go ahead and indulge the love for fifths, climbing up perfect fifth-sized steps until you’ve charted a whole bunch of notes that might be used within an octave, you’ll get a great sound in one key, for example, but you’ll wind up seriously off track, such that a high C, for instance, will be “off” when compared to the C from which you might have started. Equally bad, some combinations of notes sound absolutely wretched. But this could be lived with, provided that you avoided these combos and the band could agree on a key that was good for their instruments. When it came to the point that a lot of instruments needed to coordinate and composers wanted to use all the combinations possible, a compromise had to be struck. There have been a great many attempts to “temper” the scale of notes within an octave. We in the West have chosen an equal temperament that says there are 12 tones within an octave, each of which is the same distance apart (in terms of frequency). The result is a decent but not perfect sound in some respects. The fifth, for example, that critical touchstone, is not the 660Hz it “should” be if we start with the 440Hz A, but rather 659.25Hz; indeed, no other note then is a whole integer. The ear — the Western ear — became used to this, and it now sounds “right” to us. But there are other tunings, other modes, of which meantone is one, and just intonation is another, both of which can be heard today in specialized musical settings. Indeed, as I said at the outset, the topic is deep and complex, worth exploration by anyone who enjoys music and wants to get a bit beyond humming along. What continues to fascinate me is the tension and interplay between the innate (pleasure in fifths, octaves etc.) and the social (the need to to play together). Others might want to look into the mathematics, or, perhaps, the physics that underpin the theory and the practice. Those who are interested might want to start with the following sites, in addition to the music theory pages on the Dolmetsch site I cited at the beginning:
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