A Different Temperament / Tuning Approach

[Richard Brekne]

 Bradley M. Snook wrote:

>> Let me see if I understand this graph correctly tho.. its built on
>actually sampled frequencies ? Or how did you arrive at them ? 
>Yes . . . and no: I sampled a few notes (A2, A3, A4, A5, and A6) to
>calculate "inharmonicity constants," and then filled in the rest of the
>unsampled tones with a [linear] progression. If I understand correctly,
>this is similar to what TuneLab uses when constructing a tuning curve.
>While a 'real' piano might not be as steady with the inharmonicity
>progressions, I think it accurately takes in to account some of the
>complexities of dealing with inharmonicity.
>

Ok... so these are by and large theoretical values... and I aggree they work
quite well for most situations and for most ears.

>I should make one point about calculating an "inharmonicity constant" [for
>one string]: there is really no standard way of making a calculation like
>this. The "constant" is an amount by which the partials increase
>exponentially. The problem with this is that strings do not exactly
>increase at a constant exponential rate. In general, the first few
>partials are unsteady; the predictability increases with the higher
>partials. One way to do this is to average the results together, but you
>could also do a weighed average, or even develop a more complex means of
>distributing the "inharmonicity constant" between the partials.
>
>This is an excellent method of predicting the location of each partial, so
>it is extremly useful when dealing with theoretical situations; I also
>think it is a very efficient means of doing normal everyday kind of
>tunings. But for concert level tunings, it is much more important to know
>the actual location of each partial, not the theoretical location of where
>the partial should be.
>
>
This is exactly why I like to use direct referencing of partials instead of
relying on calculated curves. The ETD has a degree of advantage over the ear in
that it can precisely identify exact frequencies more consistantly and quickly,
but the fact that the piano doesnt sooooo closely conform to theoretical curves
has kept me scratching my big toe since I started useing them. Yet  much has
been learned since (and because of)  the advent of SAT, RCT and the calculated
tuning curves. What I would like to see is a way of combining the best aspects
of what we have come to know are important tuning priorities Sanderson,
Reyburn, and others... with an ETD that directly compares an instruments real
partials on every note.

Verituner is the first step in this direction, tho its basic tuning algorithm
remains hidden from me. My experimenting with the pure 12ths approach is an
attempt to find a way of using a single partial display etd to both give
information about several partials simultaneously and develope a useable (read
"very good") method of tuning that directly references real partials note for
note.... and of course to in general see what I can find out, what I can learn
on the way :)

>
>In general, what do you do with bass strings? Like I said before, I still
>have a problem with doing bass strings for a very fine, concert level
>tuning. I really dislike that the "fundamental" is missing. Do you do
>anything to try and counteract this phenomenon, or do you just do it the
>normal way?
>
>
>Bradley

I have never quite been able to resist attempting to make the lower bass "sound
consistant"... and from a very wholistic perspective. So I end up trying to
adjust notes that the ETD tells me should be this way or another to suit my
ear. Tuning Curves or Direct Partial referencing... makes no difference here.
They get you close to where you want to be, (I think direct referencing has the
edge here tho) but no closer. I am not sure whether this is because of the lack
of the fundemental or whether its more because of the general variability of
the wash going on down there.

More later this week

Cheers !
RicB


Richard Brekne
RPT NPTF
Griegakadamiet UiB