Klarinet Archive - Posting 000003.txt from 1997/06

From: Jonathan Cohler <cohler@-----.net>
Subj: Re: Pitch of tuning notes
Date: Sun, 1 Jun 1997 11:59:06 -0400

Stephen Froehlich wrote:

>On Sat, 31 May 1997, Jonathan Cohler wrote:
>
>> So for example, if one plays a high concert E (frequency 1320 Hz) and a
>> high concert C# (frequency 1100 Hz), one will also hear the note:
>>
>> 1320 - 1100 = 220 Hz
>>
>> or the A an octave below A 440.
>>
>> If the ear were perfectly linear, this would not be the case.
>
> Linear in what sense? I thought interference was a perfectly
>linear process.
>

A linear system is (by definition) one which when driven by a sinusoidal
wave of frequency f produces only more sinusoidal waves of frequency f
(possibly of different amplitude and phase).

If a system produces any other frequencies than f, it is called "non-linear".

Therefore, when the ear is driven by sinusoids f1 and f2 it should only
produce f1 and f2. The fact that it produces f1-f2 (and f1+f2 for that
matter), is a result of it's non-linearities. For those interested in the
math involved, the f1-f2 and f1+f2 come out of the multiple angle
trigonometric (sines and cosines) equations which I won't go into here.

That's the simple explanation.

-------------------
Jonathan Cohler
cohler@-----.net