Clarinet acoustrics

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Olivia.McElwee@gmail.com - 13 Dec 2005 23:15 GMT

Hi all,

I have a few questions about the clarinet I'm hoping you can help me
with.

This website shows how to simulate a clarinet -

http://www.phy.mtu.edu/~suits/clarinet.html
as -

s(t) = sin(w1t) + 0.75*sin(3*w1t) + 0.5*sin(5*w1t) + 0.14*sin(7*w1t) +
0.5*sin(9*w1t) + 0.12*sin(11*w1t) + 0.17*sin(13*w1t)

But I'm wondering what dictates the applitude of the odd harmonics. In
otherwords, why does the third harmonic have an amplitude which is
0.75% of the 1st?

This webiste -

http://hyperphysics.phy-astr.gsu.edu/hbase/music/clarw.html

states -

"This higher note of the clarinet has much less upper harmonic content
than notes in the lower range of the instrument. It also departs from
the rule of odd harmonics only. This implies that the column no longer
acoustically approximates a closed cylinder."

Can anyone explain to me how the harmonics are formed for higher notes.
Any links which might help me.

Thanks,

olivia

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salmonegg@sbcglobal.net - 14 Dec 2005 02:57 GMT

On 12/13/05 3:15 PM, in article
1134515737.081793.102050@o13g2000cwo.googlegroups.com,

> Hi all,
>
[quoted text clipped - 30 lines]
>
> olivia

The musician has much control of the timbre a clarinet has. There is not
strict relationship defining the amplitudes of the harmonics. The reed
excites vibrations in the air while the body of the clarinet is a filter
that lets only odd harmonics through. As the diameter becomes large compared
to the length, the clarinet resonance are no longer those of a small bore
pipe.

Bill

-- Ferme le Bush

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Tim Roberts - 14 Dec 2005 08:04 GMT

>I have a few questions about the clarinet I'm hoping you can help me
>with.
[quoted text clipped - 10 lines]
>otherwords, why does the third harmonic have an amplitude which is
>0.75% of the 1st?

This topic is worthy of a graduate course in acoustics. The canonical book
on the subject of musical instrument acoustics is Arthur Benade's
"Fundamentals of Musical Acoustics". It is dense going, but fascinating.

A clarinet behaves acoustically as if it were a cylindrical pipe, closed at
one end. The reflections in such a pipe cause the resulting sound to have
its even harmonics attenuated. That attenuation is lessened in the upper
registers.

>Can anyone explain to me how the harmonics are formed for higher notes.

I strongly suggest you invent in Benade's book. I doubt that any newsgroup
posting could do the subject justice.

Signature

- Tim Roberts, timr@probo.com
Providenza & Boekelheide, Inc.

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Natural Science Forum / Physics / Acoustics / December 2005

Clarinet acoustrics