piano timbre and tuning (was: McLaren, Math and Music)

> From: <carl@...>
> To: <crazy_music@yahoogroups.com>
> Sent: Friday, July 27, 2001 12:41 PM
> Subject: [cm] Re: McLaren, Math and Music
>
>
> I'd make a small wager that you're right, John (that modern pianos
> are less harmonic than fortepianos); I happened to get invited to
> a private concert of historical pianos in San Francisco the other
> day, and I was reminded how "nasal"/"vocal" their timbre is, when
> compared to a modern piano.

Hmmm... has anyone written about this idea before?...

This single aspect of piano development may go a long
way towards explaining the wide acceptance of 12-EDO.

The piano became a very popular instrument thruout
the 1800s, and as its timbre tended to get more inharmonic,
stretched in opposite directions toward either end,
Setharean theory would (as far as I know) say that it
would sound best in a stretched 12-EDO-type tuning... right?
... Thus ensuring the widespread use of that kind of tuning.

love / peace / harmony ...

-monz
http://www.monz.org
"All roads lead to n^0"

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> Hmmm... has anyone written about this idea before?...

You bet.

> This single aspect of piano development may go a long
> way towards explaining the wide acceptance of 12-EDO.

I doubt it.

> The piano became a very popular instrument thruout
> the 1800s, and as its timbre tended to get more inharmonic,
> stretched in opposite directions toward either end,
> Setharean theory would (as far as I know) say that it
> would sound best in a stretched 12-EDO-type tuning... right?

Not unless the timbres became closer to stretched 12-tET.

-Carl

--- In crazy_music@y..., carl@l... wrote:
> > Hmmm... has anyone written about this idea before?...
>
> You bet.
>
> > This single aspect of piano development may go a long
> > way towards explaining the wide acceptance of 12-EDO.
>
> I doubt it.
>
> > The piano became a very popular instrument thruout
> > the 1800s, and as its timbre tended to get more inharmonic,
> > stretched in opposite directions toward either end,
> > Setharean theory would (as far as I know) say that it
> > would sound best in a stretched 12-EDO-type tuning... right?
>
> Not unless the timbres became closer to stretched 12-tET.

Forget about 12-tET. The octaves (relationships between Nth partials
and 2Nth partials) are the strongest spectral determinant of
stretched tuning matching stretched timbre. Piano tuners learn to
tune 2:1 octaves in the high register, 4:2 octaves lower, 6:3 octaves
lower still . . . where the numbers indicate the partials being
matched.