Ron writes:
>>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. <<
This is something totally different than the distinctions between equal
and non-equal tuning. The ear doesn't hear beats in isolation, but rather,
they are plotted against pitch. 10 bps at 200/210 hz and 20 bps at 400/420
Hz are virtually similar in their effect. Equality is attainable.
The human brain hears ratios, and it hears them at the pitch-processing
level, not in the cochlea. This has been demonstrated by use of tests using
headphones, playing a pitch of 100 in one ear and 105 in the other will cause
the listener to hear 5 bps, even though there is no physical "mingling" of
the frequencies. Tempering at various levels of pitch still cause the same
psycho-emotive effects.
This is reinforced by another, slightly adjunct phenomenom, that the
human perception will synthesize a missing fundamental if we hear the
partials, ie, if we play a group of partials comprised of only of 200, 300,
400, 500, etc. we will also hear a 100 Hz signal, even though it is NOT
physically there. It is the way our pitch processing brain works. Our brains
extrapolate that for us. This indicates that pitch is not the same as
tempering, and I will try to look up the research that has been done here.
Even if this were true, a non-ET would be even more distinct at the various
pitch levels, due to the octave increase affecting the more highly tempered
thirds even more so.
ET is ET, and those that want to ascribe different "characters" to the
keys will have to explain why a piano tuned 1/2 step flat will make the key
of C sound just like the key of B. I have heard musicians recognize the
'character" of B on such a piano, even when I was playing in C!! I maintain
that it is purely pitch recognition that causes listeners to think that ET
has different characters in the keys.
Regards,
Ed
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