----- 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. > > This goes back to what I tried to say to David Andersen about the > whole definition of ET being really quite impossible to implement on > the piano. Inharmonicity precludes that, and we are left with an ET > adjusted for inharmonicity which essentially breaks some of the rules > for what an ET is. 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
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