Klarinet Archive - Posting 000464.txt from 2000/08

From: Roger Shilcock <roger.shilcock@-----.uk>
Subj: Re: [kl] Unloading.....
Date: Thu, 17 Aug 2000 07:27:01 -0400

But this looks just like a fancy way of restating Fourier's theorem!
Sorry - but how is it helpful?
ROger S.

On Thu, 17 Aug 2000, Tony Pay wrote:

> Date: Thu, 17 Aug 2000 10:59:27 +0100
> From: Tony Pay <Tony@-----.uk>
> Reply-To: klarinet@-----.org
> To: klarinet@-----.org
> Subject: Re: [kl] Unloading.....
>
> On Thu, 17 Aug 2000 09:20:21 +0100 (BST),
> roger.shilcock@-----.uk said:
>
> > Tony P.,
> > In that case, I think you should explain what you mean by "overtones",
> > given that all wind instruments don't sound the same.
> > Roger S.
>
> This has been gone over before, but it's worth while saying again,
> because clearly it's your moment to 'get' it, and perhaps some other
> people's moment to 'get' it, too.
>
> Any periodic oscillation can be thought of as a superposition of a
> collection of sine waves: a lowest one, called the 'fundamental' (which
> has the frequency of the repetition rate of the oscillation, f say) and
> different proportions of higher frequency sine waves that are integral
> multiples of the fundamental, called 'overtones'. Thus the frequencies
> of the sine waves called overtones are 2f, 3f, 4f, 5f, etc.
>
> This is a fundamental mathematical theorem called Fourier's theorem.
>
> Different musical instruments have different waveforms, and not
> surprisingly, their overtone structure is different.
>
> But what is different is just the *proportion of ingredients* in the
> recipe for the mix; the recipe is the same, and the ingredients
> themselves are the same.
>
> Consider two instruments, both playing the same note, frequency f. When
> we look at the sine wave recipe, we find that what determines the
> difference between the sustained sounds of the different instruments is
> just the *proportions* of 2f, 3f, 4f, etc. in the mix. A clarinet, for
> example, has particularly strong 'odd' overtones, namely 3f, 5f, 7f,
> etc., whilst an oboe has more equal proportions of odd and even.
>
> But for *any* instrument, the *ingredients*, 2f, 3f, 4f, 5f, etc are the
> same, and the recipe is the same, that is, just add them.
>
> By the way, some people are confused by the recipe 'just add them'. But
> it's just like waves on the sea: if I make a little wave with my hand on
> top of a big, slowly moving swell, the height of the water above the
> seabed is greater at the crest of my little wave than at a trough of my
> little wave. You get the height of the water above the seabed at any
> point by just 'adding up' the effects of the two waves.
>
> The sequence, f, 2f, 3f, 4f, 5f, etc is called the 'harmonic series',
> and sounds that can be analysed in this way -- periodic sounds -- are
> called 'harmonic'.
>
> This applies just to *sustained* sounds. Any *sustained* sound is
> periodic.
>
> What we've been talking about here in this thread is the difference
> between sustained sounds, like oboes, clarinets and organs, and
> *un*sustained sounds, like pianos and bells. Because pianos and bells
> are just struck and left to ring on by themselves, their waveforms
> *aren't* completely periodic.
>
> (See http://www.sneezy.org/Databases/Logs/1999/01/000080.txt)
>
> Therefore they aren't susceptible to the analysis above. Their sounds
> aren't harmonic, and so they are said to be 'anharmonic', or to 'exhibit
> anharmonicity'.
>
> They do have overtones in another sense, though: they can be thought of
> as being the sum of different modes of vibration of the thing struck.
> Our ears sometimes perceive a bell as just one note, but you can also
> hear other notes if you listen carefully. And these other notes don't
> in general have a whole number frequency relationship with the lowest
> one. When our ear/brain system has to assign a pitch to such a bell, in
> general it delivers the best approximation it can to fitting all the
> notes into a whole-number template, and therefore delivers a pitch that
> is usually sharper or flatter than the frequency of the lowest note.
>
> Doubtless, this bias on our part for hearing harmonically related
> components as a single sound (and therefore incidentally for trying to
> squash anharmonic sounds into the same mould) has evolved for survival
> purposes: humans and other animals make sounds that are sustained, and
> therefore harmonic, and the advantages of being able to process them
> efficiently is important both for avoidance and for communication.
>
> Going back to clarinets and oboes, it turns out that how individual
> instruments begin notes is very characteristic of them, too; there was
> an experiment where recordings of different instruments had the
> 'attacks' chopped out. Listeners found it much more difficult to
> distinguish between different instruments on the modified recordings.
>
> Also how different instruments negotiate the transitions from one note
> to another is important, I believe.
>
> Tony
> --
> _________ Tony Pay
> |ony:-) 79 Southmoor Rd Tony@-----.uk
> | |ay Oxford OX2 6RE GMN family artist: www.gmn.com
> tel/fax 01865 553339
>
> ... Error 216: Tagline out of paper
>
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