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A H Benade, register hole formula

2853 Views 7 Replies 5 Participants Last post by  jbtsax
Would somebody please give me some assistance in the use of the Benade formula for tone hole size & placement for saxophone ( conical instruments )

From Benade's book "fundamentals of Musical Acoustics" 2nd revised edition
Page 458


Benade states "this formula is easy to use" but it is only EASY if you know how!. and at the moment I don't

I am not too good with understanding formula, so can someone give me a simple approach to using this formula. Am i right in asuming the following...

b is the register hole radius
a is the bore radius at the desired register hole location

L is the distance from the cone apex to the centre of the tonehole for which the register hole is being designed.

te is the wall thickness of the neck + 1.5 times the register hole radius.

assuming that my above assumptions are correct then how do I do the maths
to make this = 3.253 ???

Many thanks to anyone who can help shed some light - so that I can understand more and continue with my experiments with register holes.
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Not that this will completely answer your question, but go to this link
and download the pdf of "register hole design for woodwinds"

There is an excellent graph that he did for George Jameson in it.

thanks for that David,

I am still scratching my head trying to understand the maths?

help still needed!!!

Yes, the math, I know. I'm not big on the math thing either. I showed it to a high school math teacher and he said "Oh, that's easy. It's just a quadratic equation." And then he worked out an example problem for me on paper. I should have made more of an effort in school with the algebra. Just show it to a math teacher. They will probably be thrilled that someone has a math question that isn't part of a test paper.

Thankyou All For Your Interest.

I Will Let You Know How I Get On With The Equation.

And How It All Fits In With The Saxophones I Am Working On.

Best Wishes To You All
It would help if you would indicate the unknown you are trying to find. Is it the register hole radius? My understanding is that the size and placement of the two octave vents on the saxophone are a compromise to accommodate the several notes each needs to work for.

The last handwritten entry at the bottom of Benade's sketch given by the link in a previous post is quite interesting. After all the math and all of the calculations he writes:

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