temperaments:clear as mud?

A440A@AOL.COM A440A@AOL.COM
Wed, 31 Oct 2001 18:21:27 EST


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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