Re: [Harp-L] more on temperament and such

"Vern Smith" <jevern@xxxxxxx> · Sat, 22 Oct 2005 10:48:25 -0700

----- Original Message ----- 
From: "Jonathan R. Ross" <jross38@xxxxxxxxxxx>

To: <harp-l@xxxxxxxxxx>

Sent: Friday, October 21, 2005 8:20 PM

Subject: [Harp-L] more on temperament and such
What other instruments are of necessity 12-TET (ie.
impractical to stock one for each key)?

None.  12TET is one solution to the problem, but not the only one by any
means..............

>>Where the instruments have a built-in chromatic scale (e.g. keyboard

and fretted instruments) AND they are played in various keys, only
equal temperament will work.

Not true.  Any temperament will work, but some have different
compromises than 12TET.  Playing an instrument tuned to 1/4 comma
meantone centered around C in C# may be a rather dissonant experience,
but it can be done and is actually correct for some periods of
music--and might be useful for the strangeness it imparts to new pieces.
But that is an extreme example, as the various well-temperaments can
work in all keys as well, but emphasize some over others.  12TET simply
emphasizes none and some would argue that it hurts them all equally
because of that.  It is _A_ solution, but by no means the only one which
is workable or musically acceptable........................

I suppose it depends on how you define "work."
Hermann Helmholtz in his Book: "On the Sensations of Tone" had this figured 
out 128 years ago. He devoted a 61 page chapter to the subject of keys and 
tuning.  He pointed out that 12TET was a compromise but the only practical 
tuning scheme for keyboard and other fixed-interval instruments:
"Hence as long as it is necessary practically to limit the number of 
separate tones within the octave to 12, there can be no question at all to 
the superiority of the equal temperament..................."
However he did not deny that within a particular key, just tuning made 
better sounding triads.
"But it must not be imagined that the difference between just and equal 
temperament is a mere mathematical subtlety without any practical value. 
That this difference is really very striking even to unmusical ears is shown 
immediately by actual experiments with properly tuned instruments."
Helmholtz's 1877 pronouncements have been echoed by Backus "The Acoustical 
Foundations of Music" in 1969 and by Fletcher and Rossing "The Physics of 
Musical Instruments" in 1998.
Once one strays from the historical consensus of what sounds consonant and 
out into the infinite universe of avant-garde personal taste, then it is 
possible to declare ANYTHING  pleasing to the ear.
Vern
Visit my harmonica website: http://www.Hands-Free-Chromatic.7p.com