Discussion:
Selecting hole positions for wind instruments
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c***@mail.ie
2005-12-06 21:26:20 UTC
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Hi all,

I'm having difficulty finding any online equation for calculating the
hole positions for a pvc clarinet. I have made the following instrument
and I now wish to make another in a different key -

http://www.geocities.com/danielbruner/instruments/clarA3.html

I presume the pitch at a hole is related to 3 parameters - the length
and diameter of the pipe, and the diameter of the first open hole from
the mouth piece. By adjusting the diameters of the holes in my last
instrument I was able to tune it. Can anyone supply me with the
equation? (I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone) I have the instrument
built and now I simply need to drill the holes.

Thanks very much for your help,

Charley.
Nick Odell
2005-12-06 22:07:19 UTC
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On 6 Dec 2005 13:26:20 -0800, ***@mail.ie wrote:
<snip>
...(I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone)...
I'm intrigued by this. What sort of things do you think should be freely
available to everyone?

Nick
--
real e-mail is themusicworkshop at ntlworld dot com
Peter Schug
2005-12-06 22:54:12 UTC
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Post by Nick Odell
<snip>
...(I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone)...
I'm intrigued by this. What sort of things do you think should be freely
available to everyone?
Nick
It's really not much different than fret spacing, or tuning various
temperments and all that stuff has been common knowledge among instrument
makers since the ancient Greeks started writing about it.

See Pythagoras

Pete
Nick Odell
2005-12-06 23:16:05 UTC
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Post by Peter Schug
Post by Nick Odell
<snip>
...(I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone)...
I'm intrigued by this. What sort of things do you think should be freely
available to everyone?
It's really not much different than fret spacing, or tuning various
temperments and all that stuff has been common knowledge among instrument
makers since the ancient Greeks started writing about it.
See Pythagoras
Oh, I agree. It's nice when the things you want to find out don't cost you
anything, made nicer by finding out that the people who have put the effort into
providing the information are giving out of their own generosity the knowledge,
the typing time, the webspace etc. In ye olde dayes (a few years ago) almost
everything was in books and we automatically expected to pay for the books or
use the "free" library services paid for out of our taxes. I'm not quite sure
when the idea that "things should be freely available" transliterated into
"things should be available, free" and I'm intrigued about where others see the
boundaries.

Nick
--
real e-mail is themusicworkshop at ntlworld dot com
Jim McGill
2005-12-07 16:48:09 UTC
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Peter

Actually it's a lot tougher than string spacing. Go look at one of
Benade's books. String spacing is simple 1 dimensional geometry problem.
Hole spacing on wind instruments calls for partial differential
equations. Part of the problem is that the air itself is vibrating and
the air in the wind instrument is attached to the outside air that the
listener is breathing (otherwise you couldn't hear it, sound not
traveling through a vacuum). The coupling between the constrained
dimensionality inside the instrument and the unconstrained air on the
outside is pretty tough to calculate, particularly if you have a conical
bore (speaker cabinets have the same problems). Rule of thumb is the
bottom note (all keys closed) extends roughly half the diameter of the
bottom opening outside the end of the bore. A lot of traditional wind
instruments (kavals and zurnas for example) get around this by being
longer than required and having a "devil hole" below the lowest closed
note which defines the actual acoustic end of the instrument. That way
the maker can tune the bottom note and not have to worry about the
coupling problems. But modern winds don't have that so you have to do
the math (or make a prototype and drill/fill a lot of holes, which is
the usual process :-).

Jim
b***@yahoo.com
2005-12-07 21:34:36 UTC
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I'm hoping I don't have to buy a book in order to obtain what should be freely available to everyone
You're dead right!

This should help you a lot -

http://homepages.bw.edu/~phoekje/acoustics/Flutexl4.xls
http://www.rogo.com/folkstuff/fluteinstruct.html

BTW, I have my music online for free; nothing special...

http://www.soundclick.com/bands/pagemusic.cfm?bandID=7731
c***@mail.ie
2005-12-07 23:07:15 UTC
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Thanks everyone for your help,

I have one pressing question. in the excel spreadsheet provided by the
last poster -

http://homepages.bw.edu/~phoekje/acoustics/Flutexl4.xls

the correct length of the pipe (1st iteration) is calculated as the
nominal_length - bore_diameter * 0.6133 /2. The design I'm using is the
same as this example -

http://www.geocities.com/danielbruner/instruments/clarA3.html

I'm just wondering if the angle at the mouthpiece will have much of an
effect on the value of 0.6133? I presume the length of this instrument
is defined as the length from the bore end to small hole (at the very
tip) that the player blows into.

I tried pluging in the values for the hole diameters that are supplied
with the A3 clarinet into the excel spreadsheet and got the follow hole
spacings for the 4th iteration -

0.28
2.68
2.60
2.31
3.05
2.85
6.22

and these for the 5th -

0.16
2.67
2.63
2.28
3.07
2.85
6.22

The builder of the A3 clarinet used -

0.64
2.54
2.54
2.54
2.54
2.54
5.56


Are the calculated values much different from the actual values in your
opinion? I could always drill very small holes and open them wider with
a reemer...

thanks for your help,

Charles.
Peter Schug
2005-12-08 01:05:00 UTC
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Post by Jim McGill
Peter
Actually it's a lot tougher than string spacing. Go look at one of
Benade's books. String spacing is simple 1 dimensional geometry problem.
Hole spacing on wind instruments calls for partial differential
equations. Part of the problem is that the air itself is vibrating and
the air in the wind instrument is attached to the outside air that the
listener is breathing (otherwise you couldn't hear it, sound not
traveling through a vacuum). The coupling between the constrained
dimensionality inside the instrument and the unconstrained air on the
outside is pretty tough to calculate, particularly if you have a conical
bore (speaker cabinets have the same problems). Rule of thumb is the
bottom note (all keys closed) extends roughly half the diameter of the
bottom opening outside the end of the bore. A lot of traditional wind
instruments (kavals and zurnas for example) get around this by being
longer than required and having a "devil hole" below the lowest closed
note which defines the actual acoustic end of the instrument. That way
the maker can tune the bottom note and not have to worry about the
coupling problems. But modern winds don't have that so you have to do
the math (or make a prototype and drill/fill a lot of holes, which is
the usual process :-).
Jim
For the third time I said, "Rough Guide."

I read "Horns, Strings and Harmony in High School and I am sixty-eight now.

Again, ROUGH GUIDE.

FILL THE HOLES WITH WAX AND TRY AGAIN. (I said that in reply to Tho)

I ALSO SAID THAT BY THE THIRD INSTRUMENT YOU SHOULD BEGIN TO KNOW WHAT YOU
ARE TRYING TO DO.

O K A Y ???

Pete, Who knows it isn't quite as easy as placing frets
(and who makes fiddles so he doesn't even have to do that!)

Peter Schug
2005-12-06 23:10:14 UTC
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Post by c***@mail.ie
Hi all,
I'm having difficulty finding any online equation for calculating the
hole positions for a pvc clarinet. I have made the following instrument
and I now wish to make another in a different key -
http://www.geocities.com/danielbruner/instruments/clarA3.html
I presume the pitch at a hole is related to 3 parameters - the length
and diameter of the pipe, and the diameter of the first open hole from
the mouth piece. By adjusting the diameters of the holes in my last
instrument I was able to tune it. Can anyone supply me with the
equation? (I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone) I have the instrument
built and now I simply need to drill the holes.
Thanks very much for your help,
Charley.
A rough answer is that the hole shortens the pipe to the position of the
hole.

In other words if you put a hole in the middle of the pipe you should get an
octave change. This may be different for a clarinet since it also has the
peculiarity of breaking to the 19th semitone rather than the twelfth. Hmm...

In actuality I think a hole at the mid-point will give a bit less than an
octave, and the exact pitch is size dependant.

To some degree you will have to experiment. Boehm (sp??) wrote about it in
his book on the development of his flute. He opted for very large holes and
used pads instead of fingertips.

I really don't think there is an "equation," just approximate positions and
tuning until you have a working model.

The main thing is length. Small diameter long pipes tend to break to their
harmonics more easily. The tabor pipe has a very small diameter compared to
it's length.

Flutes are considered open at both ends and the clarinet acts as if it is
closed at one end, which leads to it sounding an octave lower than a flute
of the same length. Tapered bores sound at the same pitch as a flute would
even if they are closed at one end, like an oboe or bassoon.

I would try tuning a simple flute for practice since it is the easiest
instrument to make, or maybe a kena, which is a knotched flute.

Pete
Tho X. Bui
2005-12-06 23:34:35 UTC
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Post by Peter Schug
Post by c***@mail.ie
I'm having difficulty finding any online equation for calculating the
hole positions for a pvc clarinet. I have made the following instrument
and I now wish to make another in a different key -
...
A rough answer is that the hole shortens the pipe to the position of the
hole.
In other words if you put a hole in the middle of the pipe you should get an
octave change. This may be different for a clarinet since it also has the
peculiarity of breaking to the 19th semitone rather than the twelfth. Hmm...
In actuality I think a hole at the mid-point will give a bit less than an
octave, and the exact pitch is size dependant.
I wish it were that simple...When I was doing this (trying to create an
experimental wind instrument), I found that not only the hole size and
location affect the pitch, the wall thickness and sharpness of edges
also affect the pitch.

The biggest obstable? Other holes. Every time you add a hole, the
original hole(s) changes pitch. Good luck making a hole smaller in size
or moving it after it's drilled.

Tho
Peter Schug
2005-12-07 01:58:00 UTC
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Post by Tho X. Bui
Post by Peter Schug
Post by c***@mail.ie
I'm having difficulty finding any online equation for calculating the
hole positions for a pvc clarinet. I have made the following instrument
and I now wish to make another in a different key -
...
A rough answer is that the hole shortens the pipe to the position of the
hole.
In other words if you put a hole in the middle of the pipe you should get an
octave change. This may be different for a clarinet since it also has the
peculiarity of breaking to the 19th semitone rather than the twelfth. Hmm...
In actuality I think a hole at the mid-point will give a bit less than an
octave, and the exact pitch is size dependant.
I wish it were that simple...When I was doing this (trying to create an
experimental wind instrument), I found that not only the hole size and
location affect the pitch, the wall thickness and sharpness of edges
also affect the pitch.
The biggest obstable? Other holes. Every time you add a hole, the
original hole(s) changes pitch. Good luck making a hole smaller in size
or moving it after it's drilled.
Tho
The standard for making a hole smaller is wax. I've got a book on tuning
recorders and that has been the solution for hundreds of years. I suppose
that if I were experimenting I could plug _all_ the holes and start on a new
set with better placement and sizing, and then make a new instrument when I
felt I had a handle on what was needed.

Benade had an article in the Scientific American a long time ago outlining
the problems of tuning winds and describing the them as analogs of
electronic circuits.

I called my advice a rough guide. You really have to make a model first,
then make a second with the knowledge you gained on the first. By the time
you get to the third you should be pretty good.

The Dixie slide whistle has none of those problems and sounds an octave
deeper than it's length would normally allow for, but it isn't a great
instrument unless you really want to devolop your ear, or can't afford a
trombone.

My own disaster in wind instrument making involved the belated discovery of
a major allergy to rosewood after getting a pretty good start at making my
first recorder. Nothing by half steps, I used very good wood, and had
several fine recorders to use as models, but I never got that far.

Always wash your hands BEFORE going to the bathroom when working with
unfamiliar materials!

I love spruce and maple. No problems there.

Pete
a***@invalid.co.uk.invalid
2005-12-07 00:48:00 UTC
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Post by c***@mail.ie
Hi all,
I'm having difficulty finding any online equation for calculating the
hole positions for a pvc clarinet. I have made the following instrument
and I now wish to make another in a different key -
http://www.geocities.com/danielbruner/instruments/clarA3.html
I presume the pitch at a hole is related to 3 parameters - the length
and diameter of the pipe, and the diameter of the first open hole from
the mouth piece. By adjusting the diameters of the holes in my last
instrument I was able to tune it. Can anyone supply me with the
equation? (I'm hoping I don't have to buy a book in order to obtain
what should be freely available to everyone) I have the instrument
built and now I simply need to drill the holes.
Thanks very much for your help,
Charley.
Its not as simple as an equation and involves transmission line
theory. It seems that exact tuning is impossible. What can be done is
to bring the errors within the range that the player can easily
adjust.

Introductory book
Arthur H Benade - Horns Strings & Harmony

or:

http://ccrma.stanford.edu/marl/Benade/documents/Benade-Physics323-1977.pdf

http://www.chrysalis-foundation.org/flute_tone_holes.htm

It seems to be knowledge that has required masses of hard work to
acquire. We should be grateful that some people are willing to share
it so freely.


Arthur
--
Arthur Quinn
real-email arthur at bellacat dot com
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