Inharmonicity in strings

[Jim Coleman, Sr.]

HI Bill:

Answers interspersed below:

On Sat, 13 Jun 1998 Billbrpt@aol.com wrote:

> In a message dated 6/13/98 10:47:09 AM Central Daylight Time,
> pianotoo@IMAP2.ASU.EDU writes:
> 
> << Thanks for triggering me on this subject. I haven't written about this
>  since I wrote about it to Virgil Smith several years ago. this incidentally
>  forms some of the basis for his theory about listening to the fundamentals
>  only when tuning, or more correctly, listening to the whole tone.
>  
>  Jim Coleman, Sr. >>
> 
> Thank you for these remarks.  However, I don't think we are talking about the
> same thing.  In order to hear beats, you have to hear them between coincident
> partials which are mismatched.  If you had 2 pure tones (with no
> harmonics/partials) and one was slightly sharper than the other, you would
> hear a beat between them.  However, if one were at a pitch which would form a
> tempered 3rd, 4th or 5th or a stretched octave, I don't think you could hear a
> beat in that case.  Am I right or wrong about that?

You are right about that in that you would not hear beats between coincident
partials because there are none, however, in a pure M3rd there would be a
difference tone which is a beat. This would be two octaves below the 
lower note.

> 
> The example I think of is how you can clearly hear a beat in a tempered Octave
> and 5th (12th). The 3rd partial of the lower note is coincident with the
> fundamental of the upper one.  You cannot however hear a beat in an octave and
> a 4th because there are no coincident partials.  You could mistune the upper
> note flat or sharp all you want and there will be no beat.

YDou are correct about that.

> 
> Bill Bremmer RPT
> Madison, Wisconsin
> 

Jim Coleman, Sr.