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RE: tuning etc

To: brass-band@xxxxxxxxxxxxxxxxxx
Subject: RE: tuning etc
From: Philip Anderton <P.Anderton@xxxxxxxxxxx>
Date: Tue, 10 Mar 1998 01:34:58 +1000
In-reply-to: <199803061037.KAA06861@cav.logica.co.uk>
Priority: low
Reply-to: brass-band@xxxxxxxxxxxxxxxxxx

At 10:31 6/03/98 -0000, John Goodwin wrote:
>However so far no one has been able to explain which temperament brass
>instruments are designed to.

Just some thoughts about this question... I have always assumed that an
"open" brass instrument (i.e. column of air) would have to produce
geometric harmonics. These approximate the harmonic series of notes we play
on our open instrument ({Pedal C}, C', G', C'', E'', G'', Bb'', C''', D''',
E''', F#''' etc...

Assuming that  "Pedal C" was a frequency of 120 Hz, then the harmonics
produced by an open brass instrument of this equivalent tube length would be:

Pedal C - 120 Hz * 1 = 120 Hz
C'	-  120 Hz * 2 = 240 Hz
G'	-  120 Hz * 3 = 360 Hz
C''	-  120 Hz * 4 = 480 Hz
E''	- 120 Hz * 5 =  600 Hz
G''	- 120 Hz * 6 =  720 Hz
Bb''	- 120Hz * 7 =  840 Hz
C'''	- 120 Hz * 8 = 960 Hz etc...
D''', E''', F#'''

These harmonics are simple multiples of the fundamental frequency and do
not all line up with their counterparts in the  "well-tempered" scale.
Hence a good player must "lip" notes to get the right intonation, some more
than others. I was taught that the open Bb'' (minor 7th) is never used
intentionally as it is very, very flat.

Of course, parallel harmonics on different fundamental tube lengths are
available with one or more valves depressed, and their tuning depends on
the extra tube length added by the valves. 

Do I have the Physics right, or does the conical bore of a saxhorn
introduce a lot more complexity?

Philip

Philip Anderton			Phone: +61 2 9316 8301
Warringah Concert Brass
Sydney, Australia

Web: http://www.optom.unsw.edu.au/public/other/wcb.htm
Email: P.Anderton@xxxxxxxxxxx

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