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Re: Why is the low F flat?

Author: Tony Pay ★2017
Date: 2006-12-11 23:36

sherman wrote:

>> The problem has been soved by more than one manufacturer, without an Oehler mechanism.>>

It's a question of what you mean by 'solved'. That the F/C twelfth is in tune doesn't mean that compromises haven't been made elsewhere -- on a single register key instrument, that is.

The sound of a clarinet note is always 'harmonic' -- meaning that the frequencies of the overtones are whole number multiples of the fundamental frequency. This is a consequence of the steady state repeating waveform that results from a 'driven' oscillation -- as opposed to a piano note, say, which is struck and thereafter vibrates freely.

The nonlinearity of the reed vibration at reasonably strong dynamics guarantees the presence of higher partials. Then, the normal modes of vibration of the tube for a given fingering (plus the open lattice fingerholes below the fingering) usually aren't so far away from the harmonic series appropriate to the length of tube for that fingering, so the resonances corresponding to these normal modes amplify the higher partials. The upshot is that the partials that 'sit' well in the peaks of these resonances are more amplified than the ones that don't. A 'good' clarinet sound has a rich, well-balanced harmonic spectrum, so this 'sitting well' is desirable.

But, you can hear that the sequence of normal modes of vibration of a 'well in tune' clarinet -- the sequence of notes you get if you 'overblow' a chalumeau note -- differ fairly appreciably from harmonicity. This is a result of the divergences of the bore from cylindricality that are essential to guarantee that when you open the register key, the twelfths are sufficiently well in tune. (Overblowing without the register key, corresponding to the normal modes, is flat at the bottom and the top of the instrument, and true only around B flat / F.)

So a 'well in tune' clarinet has its resonance peaks in the 'wrong' place for resonant sound in the lower register! There is a trade-off, and you can't 'have it all'.

Furthermore, because of the nonharmonicity of the modes of resonance of the instrument (not the nonharmonicity of the resultant *sound*), the perceived pitch in the steady state may be different from the fundamental corresponding to the length of tube. According to Benade (Physics of wind instrument tone and response, 1971) the fundamental frequency locks into position in such a way as to maximise the weighted average height of all resonance values R1, R2, R3,.... corresponding to the harmonics f1, 2f1, 3f1,....

This is a bit arcane, I know, but the message is that the pitch of a note on a clarinet that has been organised to be 'well in tune' by bore modification can depend on the dynamic -- which obviously you don't want to happen too much either.

Tony

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Why is the low F flat? new

skygardener

2006-12-10 17:39