May the 4ths be with you

[Richard Brekne]

Richard Moody wrote:

> > > What is the formula?
> >
> > 2^(((N-1+(I/100))/12)*27.5 * n
> >
> > where N is the note number, I is the inharmonicity constant
> > and n is the partial you want to find the frequency for.
> >
> > RicB

Yes.... as to what you write below. The  << I >> you get from the
formula below is plugged into the above formula to yeild frequency in
Hz for any given partial of any given note.  << I >> can also be
measured directly with an ETD instead of calculated using wire
parameters.

>
> This   one is from McFerrin which was developed by Robert W Young
> in the 1940's. I think you may have it or it was posted before.
>
> I = B*n^2
>

snip.......... thanks tho for reposting that formula for the list.

> If you need to know how much the frequency of the actual partial
> is increased by I then you need to compute how far sharp the cents
> value make the partial above its theoretical frequency.

Thats what the formula I first posted does.  ref Dr. Sanderson.

> It might
> be interesting to compute the actual frequencies of partials of an
> octave and compare the 2:1, the 4:2, the 6:3  and the 10:5 even.
>
> I suppose some brave soul might attempt this on a spread sheet ?

Thats what those two graphs I posted did Ric. Again... they were taken
from data Dr Sanderson himself collected.  The first graph shows the
basic curve development for the first 8 partials

http://home.broadpark.no/~rbrekne/images/actualharmonicseries.gif

The second shows how these actaully work out over this two octave
range in terms of Octave type beat rates.

http://home.broadpark.no/~rbrekne/images/octpartsdgm1.gif


Cheers !

--
Richard Brekne
RPT, N.P.T.F.
UiB, Bergen, Norway
mailto:rbrekne@broadpark.no
http://home.broadpark.no/~rbrekne/ricmain.html