[haberman]

I don't mean to be rude, but I'm not sure you understand the comma. It has nothing to do with combining types of instruments. It's a problem that exists even with a single instrument.

The problem is that, even on a single instrument (say a piano), if you start on some note (say C0), going up seven octaves should land you on exactly the same note as going up twelve perfect fifths (C7). The problem is that the precise tuning of that C7 is different depending on if you followed the perfect octaves or perfect fifths.

If you followed perfect octaves, which have a ratio of 2/1 (or just 2), C7 should have a tuning of precisely (2^7)·C0 = 128·C0. If you followed perfect fifths, which have a ratio of 3/2, C7 should have a tuning of precisely ((3/2)^12)·C0 = ~129.74·C0. The difference between these two is the Pythagorean comma.

Equal temperament solves this problem by keeping the octaves perfect (2:1), but compromising on everything else. It defines a half-step as the 12th power of 2, so a fifth ends up being a little narrower than a perfect 3:2 perfect fifth.

[dcsommer]

I'd recommend "How Equal Temperament Ruined Harmony" if you are interested in the nuances and trade offs of the imperfections of tuning.

[BurningFrog]

I understand that pianos have to pick a frequency for each key.

I wonder if there is any effort in electronic instruments to produce "better" frequencies on the fly? I'll explain:

On a piano hitting C+G plays something close to a perfect fifth.

An electronic instrument could move the G slightly to produce a perfect fifth when that key combination is played.

[mhax]

It's not just a matter of 'better' frequencies. It's trivial to have a softsynth or something similar set up to use just intonation (and many modern composers have experimented with this), but that has practical problems of it's own. Problems which were the very reason that equal temperement took over in the first place. This page has some wonderful examples http://www.nesssoftware.com/home/asn/homepage/teaching/exp-l...

[jpitz]

You cant do that, without a large effort in music education or ensembles of all electronic instruments implementing this feature. Everyone else will be out of tune.

Edit: you could do it, but you'd better implement it on a feedback system that can re-tune in a hundred milliseconds or so.

[BurningFrog]

I'm just talking about an individual keyboard, though if all instruments are digital, which is pretty common these days, you could have a whole orchestra dynamically adjusting pitch to make "perfect" harmonies.

What I wonder is mostly if that would sound any better.

[graycat]

Nice. I'd go with the 2^7 and not the (3/2)^(12).

> It defines a half-step as the 12th power of 2

Uh, instead, "12th root of 2".