RE: [tuning] Re: Tuning-related Science Fair Question

All good ideas, Rick,

>the fundamental tuning problem with commas -- i.e., the seven octaves isn't
really equal to 12 perfect fifths...

While that is the Pythagorean comma "problem", I would be tempted to say
that if there is one "fundamental tuning problem with commas" it is the one
concerning the syntonic comma, i.e., that 3 fifths isn't really equal to a
major sixth plus an octave, or that 4 fifths isn't really equal to a major
third plus two octaves. Most pieces of music don't need 12 perfect fifths,
but since the diatonic scale has 6 consecutive perfect fifths, even a simple
piece encounters these syntonic comma problems in spades.

Paul H. Erlich wrote:

> While that is the Pythagorean comma "problem", I would be
> tempted to say that if there is one "fundamental tuning
> problem with commas" it is the one concerning the syntonic comma,

Yes, Paul is right; this one isn't encountered all the time in real music, while the syntonic comma is encountered very easily in real harmonic situations.

I picked out the Pythagorean comma because (in my experience) it's the first one that students of tuning encounter, and explains why the "circle of fifths", which western music theory students are taught early on, is more of a spiral...

Whichever comma you pick for starters opens the door to understanding that standard western music theory, as children are taught (and as even experienced musicians believe), is really quite a simplification.

Rick