Friday, October 13, 2006

For musicians 
Interesting discussion on intonation here.

I remember as a teenage guitar player - and a pretty serious student at that time - being incredibly frustrated because no matter how careful I was, I couldn't tune the damn guitar to sound good in D/Bm and in C/Am. It was particularly apparent in upper positions.

It took me a long time to actually figure out that it wasn't me. It is mathematically impossible to tune a guitar. And what's worse is that if there is any flex to the neck at all (and there has to be a slight bow, or the lower notes will buzz against the frets), the very act of pressing the string down to the fret increases tension on the string, pulling it out of tune.

That's why I eventually became enamored with the violin -- you can play in just temperament in any key without having to retune the damn thing.

Not that I'm God's Gift to Intonation or anything. I'm not by a long shot. But when you're in tune, and in the zone...it's magic.

Splash, out


The guitar, like the piano, is an equal-tempered instrument. "Tune" and "temper" mean two slightly different things. You can certainly tune a piano for one key. La Monte Young did exactly that for his piece "The Well-Tuned Piano". (Search for it on Amazon for more info.) So the piano does not HAVE to be tempered, but just about every piano is. That allows every key to be equally "off", so that B major sounds no worse than C major, and no better. Guitar frets are tempered. If the frets are in the right places, you should be able to make the guitar sound no worse than the piano in all keys by tempering the open strings, matching each one to the corresponding piano note.
Well, except you can't, because the F# over a D is slightly flatter than the leading tone F# you would play in a Gmaj 7.

And any G chord has a D and a G, so you would probably lean towards the sharper F# (except in a blues/jazz context), but when the song comes around to the V chord, neither a guitar nor a just-temperament piano will have that F# available that is harmonically sympathetic to to the open D string.

Violinists, vocalists, fretless banjo players and -to an extent - dobro people don't usually have that problem.

Suck it, pianists!
If you actually do tune your piano to a specific key, you have to play a completely different kind of music (as La Monte Young did, and Harry Partch before him). You can't modulate, and chord progressions work in a different way. If you were tuned to G, the D chord could only work as a dominant, because of the F# that leads to G. As you point out, the tension of the F# clashing with D would make it unstable.
One solution for synthesizers is to dynamically update the frequency tables depending on the notes that are played. There is a product that does this: see http://hermode.de
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