Monday, July 2, 2012

Thoughts on music

When I was in Vancouver, living in its notorious East Side, I spent a lot of time hanging out with an aspiring musician.  He said he was going to teach me to play base and wanted me to manage his band.  He even restrung his guitar left-handed for me.  At the time I didn't take this too seriously as I'd hardly picked up an instrument and didn't think I had any talent to speak of.  A couple of years later my sister and her husband gave me a guitar for my birthday and I've been playing ever since.

One of the things I remember about my time with Adam was a silly argument we got into.  I was willing to go along with his plans as long as he was willing to go along with mine--being at loose ends with no prior commitments, I wanted to go travelling.

"We can take it to the road," I would tell him.  "Bring guitars and advertise our open air concerts on the internet."

"Will we bring amps?" he would ask.  "We've gotta have amps..."

I thought this was silly.  Like Tony Hawks fridge, I figured it would be difficult to hitch with a pair of 25-pound amplifiers.

"C'mon," I would reply, "Musicians have been playing instruments for thousands of years and they didn't need amps..."

Later on I realized there was more to this argument than meets the eye.  What is it that makes good music?  A fundamental idea in classical music theory is that of consonant versus dissonant intervals.  That is, to produce a pleasant-sounding chord, the ratio between the fundamental frequencies of the notes must be simple, rational-fraction intervals, say 3:2.

To understand what I mean by this, we must go back to our basic physics: the mechanics of standing wave.  If we have a vibrating string (such as on a guitar) that is fixed at both ends, the fundamental frequency will be a wave twice the length of the string.  Of course the string won't just vibrate at this frequency, there will also be standing waves with wavelengths the length of the string, 2/3 the length of the string, 1/2 the length of the string and so on.  Thus all the frequencies (or harmonics) can be predicted to first order by a simple arithmetic sequence.

If two strings are vibrating at a rational-fraction interval, say 3:2, then every second harmonic of the first string will constructively interfere with every third harmonic of the second string.  To demonstrate this effect, try taking a guitar and fretting the low 'E'  string (topmost, thickest string) on the fifth fret.  It is now at the simplest rational fraction interval with the 'A' string (the one below it), 1:1.  If you pluck one of the two strings, the other will start to vibrate in sympathy, assuming your guitar is well tuned.

The question this leads me to, is simply, is good music simply louder than bad music?  This makes a certain brutal and obvious sense: louder music will shout down quieter music.  Hence Adam's desire for amplification.

Ever since the sixties, rock'n rollers have been on a quest for ever more volume.  This has led to some interesting developments.  First, when you try to amplify a standard guitar, you frequently get feedback, that squealing noise often heard from microphone PA systems, as the sound from the amplifiers gets picked up again by the guitar and re-amplified.  This led to the development of solid-body electric guitars which don't suffer from this problem as much.  Also, when you try to drive an amplifier too hard, it goes outside of its linear range, resulting in a distortion of the signal as the wave-forms get clipped.  Rock'n rollers decided that they liked this sound, resulting in the development of devices, such as this effects pedal, to produce the effect artificially at much lower volumes.

With the development of equally-tempered tunings, much of the preceding discusion about consonance and dissonance is fairly moot.  In the past, it was common to use a just tuning, that is, every note in a scale is a rational fraction interval from every other note, with consonant intervals being simple fractions while dissonant intervals are more complex fractions.  Older music is based on a 7-note scale which defines the key of the piece--music is still written in this way.  When we switch keys, a consonance in one key may become a dissonance in another.  This led to the development of equal-temperament.  That is, we take the number of notes in the scale and divide the octave into that number of equal intervals.  Modern Western music uses a chromatic, or twelve-note scale, meaning that the next-higher note is the twelfth root of two times the frequency of the previous one.  If we now go back to our basic maths, the twelfth root of two is not a rational fraction.  The older, diatonic, or seven-note scale, is now picked out from the chromatic scale.  All keys sound the same, just sharpened or flattened by a certain interval.

A fretted, stringed instrument such as a guitar is almost by necessity tuned in equal temperament.  Most pianos are tuned somewhere between a just and equal temperament.  The implication being, except for perfect octave intervals and their multiples, no two notes are ever perfectly consonant as they only ever approximate a rational fraction interval.  

All chords on a guitar are somewhat dissonant.  Hence modern musicians' reliance on electronic amplifiers and the feedback they produce for generating volume.  Heavy metal musicians in particular are fond of what was traditionally considered the most dissonant interval: the tri-tone or one-half octave.

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