valves 12tet?

On Sun, 23 Nov 1997 tuning@eartha.mills.edu wrote:
> This is not quite right. Three-valved brass instruments are
> actually seven natural horns sharing a bell and a mouthpiece. The valves
> are usually tuned to lower the open horn by multiples of
> equal-tempered semitones (1st valve by 2 semitones, 2nd by 1, third by 3;
> actually it might have been more flexible if the third valve lowered by 4
> but this seems to place horns below the optimal diameter to length ratio
> - the more valves added, the weaker the sound). So the fundmentals of the
> tones produced by all combinations of valves are set to 12tet.

Not quite true either ... it's impossible for all combinations of valves
to be tuned exactly to 12tet, because when they are used together they
have to add tubing to different horn lengths. Thus if the semitone valve
added a length exactly equal to 2^(1/12) of that of the open horn, then
when added to the horn *plus* the second or third valve it would no longer
lengthen the tube by as large a ratio, since the tube would be longer to
begin with (not a very good sentence but hopefully you get the point). The
third valve by itself lengthens the tube by more than the combination of
the first and second, because it's designed to be used only in tandem with
the other valves. That's why you use valves 1 + 2 to go down a minor
third, instead of valve 3. Seven independently tunable natural horns would
be a great thing in one instrument, but it can't be done with three
valves.

One exaggerated example to show why instrument makers have to compromise
on tube-lengths for the various valves: say your horn is 5 feet long, and
you want valve #1 to lower the pitch by a just minor third (5:6), then you
need one extra foot of tubing, right? If you want valve #2 to lower the
pitch of the open horn by a just minor sixth (5:8), then that valve should
have 3 feet of tubing... Problem is, if valve #2 is depressed, your "minor
third" valve now adds its foot of tubing to an 8-foot horn, so only lowers
the pitch by an 8:9 tone. Same sort of problems (but with messier, albeit
smaller numbers) apply to real-world "12tet" valves. So if you want to be
able to combine valves, you have to compromise on accuracy so they can be
used across the board. (Of course, players can and do correct for the
inaccuracy - it doesn't mean valved instruments can't play in 12tet, just
that the fundamentals of each valve combination aren't in *exact* 12tet
relationships.)


SMTPOriginator: tuning@eartha.mills.edu
From: "Fred Kohler"
Subject: Re: TUNING digest 1246
PostedDate: 25-11-97 10:40:09
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