May the 4ths be with you

[Richard Brekne]

Richard Moody wrote:

> ----- Original Message -----
> From: Richard Brekne <Richard.Brekne@grieg.uib.no>
>
> >
> >Dr Sanderson did say right out that inharmonicity changes the
> > theoretical picture relative to 5ths and 4ths... which should
> also
> > have their contiguous relationships.
>
> I think inharmonicity facilitatates the tuning of ET on modern
> pianos.
> It seems at least in theory to give a 'natural" stretch to the
> octaves. That is if the upper partials of the lower notes are
> sharper than the lower upper partials of the upper note in all the
> intervals being tuned.

Hmmm.. I'd like to hear more on your thoughts here. Why does this
facilitate ET ? I think (now anyways) that maybe I would agree at
least soundwise, except for the fact that tho the upper partials of
lower notes by and large stay sharper then their coincidents from
notes above, they tend to do so less and less the higher up you go.
This results in the need for to vary progressively beat rates in
different octave types. And I cant see that that particular phenomenon
is in the spirit of ET theory... or what ?.

>
> I would say in spite of inharmonicity it can be demonstrated the
> beat rates follow closely the theoretical.   In fact so closely
> that an anomaly usually indicates a mistake on the part of the
> tuner rather than the piano maker.
> Aural tuning is much like live performance, mistakes will be made,
> no two will be exactly alike and but for a rare magical few most
> can be improved on.  But I bet if performers knew the checks we
> have to prevent error they would be envious.     ---ricm

How does this jive with whats been said about 4ths having rather
steady beat rates, 3rds not actually having a true contiguous
relationship, and 5ths actually moving from narrow to wide as one
moves up into the treble ?

Certainly we are able to create an ET that by and large fits the
bill.  That we eliminate HT key colour variance is evidence enough of
that.

Maybe I misunderstand the formal definitions of ET, but it seems like
to me that inharmonicity forces us to come in conflict with some of
these rules.

Cheers

RicB

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