source file: mills3.txt Date: Tue, 25 Nov 1997 10:36:45 +0100 Subject: valves 12tet? From: jon wild 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 SendTo: CN=coul1358/OU=AT/O=EZH ReplyTo: tuning@eartha.mills.edu $MessageStorage: 0 $UpdatedBy: CN=notesrv2/OU=Server/O=EZH,CN=coul1358/OU=AT/O=EZH,CN=Manuel op de Coul/OU=AT/O=EZH RouteServers: CN=notesrv2/OU=Server/O=EZH,CN=notesrv1/OU=Server/O=EZH RouteTimes: 25-11-97 10:38:36-25-11-97 10:38:37,25-11-97 10:38:38-25-11-97 10:38:38 DeliveredDate: 25-11-97 10:38:38 Categories: $Revisions: Received: from ns.ezh.nl ([137.174.112.59]) by notesrv2.ezh.nl (Lotus SMTP MTA SMTP v4.6 (462.2 9-3-1997)) with SMTP id C125655A.0034F6CD; Tue, 25 Nov 1997 10:38:30 +0100 Received: by ns.ezh.nl; (5.65v3.2/1.3/10May95) id AA00511; Tue, 25 Nov 1997 10:40:09 +0100 Date: Tue, 25 Nov 1997 10:40:09 +0100 Received: from ella.mills.edu by ns (smtpxd); id XA00509 Received: (qmail 17376 invoked from network); 24 Nov 1997 12:13:24 -0800 Received: from localhost (HELO ella.mills.edu) (127.0.0.1) by localhost with SMTP; 24 Nov 1997 12:13:24 -0800 Message-Id: <01bcf914$612afa80$LocalHost@a1a05977> Errors-To: madole@mills.edu Reply-To: tuning@eartha.mills.edu Originator: tuning@eartha.mills.edu Sender: tuning@eartha.mills.edu