temperaments:clear as mud?

[Joe & Penny Goss]

Hi Ron,
Answer this question,
If there is no key color in ET why do composers change key at all during a
composition ie the trio in a march or a step or half step at the end of a
composition or section?
Joe Goss
imatunr@srvinet.com
www.mothergoosetools.com
----- Original Message -----
From: "Ron Koval" <drwoodwind@hotmail.com>
To: <pianotech@ptg.org>
Sent: Wednesday, October 31, 2001 4:21 PM
Subject: temperaments:clear as mud?


> OK everyone,
>
> Here's a new angle I haven't heard before.  In my spreadsheed meanderings,
> I've come across a simple fact that might possibly add a whole new
dimension
> to the ET/HT discussion.
>
> It is said that ET has no key color, that all the thirds are the same,
while
> optomizing temperaments have key color because there are differing widths
to
> the thirds.  There are a few people out there that claim to hear key color
> in ET.  This can't be possible if all the thirds are the same, can it?
>
> I've spent a fair amount of time graphing many different temperaments, and
> then setting them on pianos and comparing what the graphs predict, verses
> what I hear.  The graphs are a very seductive tool, with their nice bell
> shaped, inverted V's, all seeming to fit in a circle of fifths order.
> However, most temperaments don't 'play' quite as predicted.  Take the
Thomas
> Moore temperament, which I use as an introduction quite often.  It has a
few
> keys that are closer than pure and then most keys are predicted to be
evenly
> less pure. When tuned, however, the third Ab-C SOUNDS less pure than the
> thirds that are supposed to match, according to the graphs.
>
> Soooo..... What is it that we hear?  Oh yeah, those beat thingys!  Think
for
> a moment about ET.  Does it sound equal?  Not likely.  Take our 'landmark'
> F-A third of around 7 beats/second.  What's the beat rate an octave
higher?
> Yup, around 14 beats/second.  So the thirds in the keys are NOT the same,
> they progress in a chromatic fashon from really slow in the bass to really
> fast in the high treble, doubling every octave.  Go up, the energy
> increases, go down the energy decreases.
>
> An optomizing temperament changes this equation.  Remember Bill Bremmers
> directions for EBVT?  In one octave the F, G, and C major thirds all beat
> THE SAME.  Bb and A thirds beat THE SAME. Gb and Ab beat THE SAME.
>
> Only by using an optomizing temperament can you get equality, sameness, or
> chords that match.  ET only gives us varying thirds.  There is NO equality
> to beats (sound, tension, etc) in equal temperament, only equal
differences
> between beat rates of equal steps.
>
> (picture the end of Soylent Green: "THERE IS NO EQUALITY IN EQUAL
> TEMPERAMENT!")
>
> Hmmmmmmmm......
>
> more to chew on.
>
> Ron Koval
> Chicagoland
> (Yes, I've been graphing predicted beat rates, yes, it's confusing and
> interesting at the same time!)
>
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