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
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