Brews you can use

A tangent-laden conversation at work the other day led to a discussion of musical pitch, tuning, and temperament (in the sense of “well-tempered clavier”). As a result, I think I’ve added music theory to the list of subjects I wish I could learn in reverse order. There appears to be some interesting stuff going on at the advanced level, but only after the boring or unrewardingly difficult fundamentals that any course or book will cover first. In short I’d like to know it without actually learning it, just jump in at the deep end of and learn the basics as needed, rather than the way things are usually taught.

I played music for a large part of my life, but was never interested in music theory. I could play notes and rhythms, and with a little work read them off sheet music, but I never really knew why the key of Bb had two sharps, while F had one, why the flats in the key signature appeared in the order B-E-A-D-G-C-F and sharps in the opposite order. It all seemed rather arbitrary. Notes are notes, right? Just take the octave and divide it up equally into 12 steps (on a logarithmic scale), give some of them letters, call others sharps and flats, and start noodling away, right?

Not quite.

The current approach to defining notes is called “equal temperament” tuning, and is a relatively recent invention (late 1700s/early 1800s), and was somewhat controversial in its early years of adoption. It’s not ideal for any key, but plays equally well (or equally poorly) in most keys. It was preceded by multiple competing tunings, all of which tried to make certain chords and intervals ideally consonant, at the expense of others. With this new (to me) information, it finally occurred to me that all of what we take for granted in western music, key signatures, the 12-tone chromatic scale, etc. wasn’t arbitrarily chosen to torture piano students, but arose from simpler mathematical relationships between sets of frequencies that make good chords. At this point, I needed to do some reading, lest I follow this path to Pythagorean mysticism….

A little web searching took me to the invaluable Wikipedia, where I found a wealth of information on the different tuning schemes. Many of the terms were unfamiliar to me, and I have little to no undertstandings of the basics of music theory, but the advanced articles had links to the more basic stuff, where I found answers to questions like “what’s a ‘perfect fifth’?” and “what does it mean for an instrument to be ‘keyed’ in a certain key?” Yes, I had been playing in ensembles, taking lessons, and talking shop with music majors without learning any of this stuff, even by osmosis.

The key for me was Pythagorean tuning (I knew Pythagoras would be involved sooner or later…) This explained a lot. Pythagorean tuning takes 2 intervals: the octave, a 2:1 frequency ratio that the ear hears as a single pitch, and the perfect fifth, a 3:2 frequency ratio that sounds pleasant. Starting from the root of your octave, you generate a new tone by stepping up a perfect fifth. Whenever it goes more than an octave above your starting point, take it down an octave. We get 12 tones because (3/2)¹² is very close to a power of 2. It’s not exact, and managing this discrepancy while still maintaining decent-sounding perfect fifths has led to multiple different competing tunings. In any case, it’s the intervals that are fundamental, and the notes exist to make good intervals. Just that shift of my frame of reference was enough to make my head hurt.

This could get interesting…

This entry was posted on Saturday, January 21st, 2006 at 10:54 pm and is filed under Computers & Internet, Farts & Seizure.