May the 4ths be with you

[Richard Moody]

> > 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


I the Ih graphs look wonderful.   The beat rate graphs, I would
rather see in spread sheets.   I suppose one wonders what is the
point of such data and its graphical representation.  To prove
there can not be beatless 4:2 and 2:1 and 6: 3  all in the same
piano?  Well that is exactly the task of the piano tuner.   To
produce all the intervals as close as possible to theoretical.
So do you trust your ears or be swayed by a graph ?
    For me the 2:1, 3:1, 4:1, 5:1, 6:1 should all conform as close
as possible to theoretical.  That the 2:1, 4:2, 6:3 should be
beatless. For those who say it is not possible, that is true for
them.  But for those who say, "I can offer for your ears a good
illusion of beatless", then we have a lot of notes to compare and
really need to get together from time to time to keep our skills
intact and keep improving.    ---ric