A different temperament / tuning approach

[Richard Brekne]

 Mike and Jane Spalding wrote:

>Ric,
>
>I just finished entering your offsets into Excel, and graphed the results.
> Very interesting to compare the shape of the two curves.  RCT is a gentle
>continuous curve.  TuneLab is two straight lines, making an abrupt change
>of direction at E6.  Seems to say that your tuning made an abrupt change
>of direction an octave-fifth below, say at A4.  ??

The Tunelab two point curve is linear. The 3rd partials of notes D3 to A4 are
calculated with that. Since the fundementals of the next 19 semitones A#4 - E6
are equvilant to the coincedent 3rd partials from the first 19 then they should
also show the exact same curve. The resulting 3rd partials of these notes then
are then used as the fundementals for notes F6 to B7. So really only these last
should show any real divergence from the origional curve detemined for D3 to A4
(because of whatever inharmonicity is present in these resulting 3rd partials)
.

In the bass tho the tuning starts right off dealing with inharmonicity issues
as it is the resulting fundementals (as opposed to the calculated 3rd partials)
of D3 to A4 that are used as the 3rd partial frequencies for the first 19
semitones going downwards. 

>I'll e-mail the excel file off-list to anyone that wants it.
>
>Mike Spalding, RPT
>

Count me in for sure. 

I will have more and in better resolution as the next months go by. Perhaps I
will end up in the same place that Dean and Sanderson ended in the end.... but
something has always bothered me about the curves generated by them, and the
apparent (to me)  lack of ability to directly match partials. This perception
may change as I get more into this. Still, this tuning of the piano so that all
twelths are perfect results in a really nice sounding piano.

Thanks for the interest and for taking the time to plot out the graphs in
Excell

RicB

Richard Brekne
RPT NPTF
Griegakadamiet UiB