Re: "well-tempered"?

[BarMusProd <BarMusProd...>]

Dear Peter,

In a message dated 3/21/02 3:02:01 PM, klezbanjo (at) yahoo(dot)com writes:

>Yeah us string players who play chords know all about this.  Because of
>subtleties in ratios between harmonics, an "evenly tempered" instrument--
>e.g., tune each note exactly to what a metronone says it should be-- might
>not sound great when you're playing chords.  Why banjos can sound great
>in one key but may sound out of tune in another.  Especially effects plucky
>sounding instruments like banjos, tsimbls and especially harpsichords,
>where there have been many treatises written on the issue.  THere are a
>bunch of different tuning systems that optimize particular keys.

Wait a minute here--it depends on what you mean by "sounding great." (And I 
trust you mean a "tuner" rather than a metronome, unless you have a real 
fancy one that gives pitches as well as beats per minute.) If you are talking 
about maximizing just intonation, where everything is based on the overtone 
series and is acoustically pure, it basically cannot be done to work in all 
keys at the same time unless you are playing an instrument (or singing, of 
course) that is infinitely adjustable--like unfretted strings (violins and 
the string family) or a slide trombone. But if you would constantly play or 
sing in just intonation, you'd better do it solo because you're not going to 
be in unison with most any other instrument, and you will subtlely change 
pitch center as you go along because just intervals don't divide the octave 
equally (for example, if you ascended by justly tuned perfects fifths until 
you reached the starting note again [a number of octaves higher] you would be 
about 24 cents [about a quarter-tone] too high--the famous "Pythagorean 
Comma"--equal tempered fifths are tuned about 2 cents flat to compensate for 
this). Equal temperament (and all other temperaments) are compromises with 
just intonation to allow us to play equally (or unequally) slightly out of 
tune in all keys. But our ears over the centuries have also gotten used to 
the slightly out-of-tuneness of equal temperament, and it allows us to play 
together reasonably in tune with most other instruments. Whew--I haven't 
waxed on like that for many years--my apologies.

But fixed fretted instruments like the banjo, unless the frets are not placed 
properly, should be in equal temperament (in fact the presence of fretted 
instruments--although in the early days of lutes and viols, etc., the frets 
were adjustable--was one of the early impetuses for the acceptance of equal 
temperament. These fretted instruments could play in more keys and sound more 
or less in tune in all of them, unlike the harpsichord or organ, which was 
still tuned (in the earlier times) in an attempt to stay closer to just 
intonation, using "mean-tone temperaments" or a number of others as you 
mentioned. I don't understand why a modern fixed-fretted instrument like 
banjo or guitar should sound better or worse in one key or another, unless 
you are talking about the acoustical phenomenon of keys using more of the 
open strings (which are tuned in just fifths rather than tempered fifths, I 
would assume) than the keys that use more finger-stopped notes to play the 
chords, which would then be in the slightly out of tune equal temperament.

Have I just (no pun intended) answer my own question? Is this what you were 
referring to?

Best wishes,
Steve

Steve Barnett
Composer/Arranger/Producer
Barnett Music Productions
BarMusProd (at) aol(dot)com 

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