A Different Temperament / Tuning Approach

[Richard Brekne]

 Bradley M. Snook wrote:

>Richard,
>What is a 3 point quadratic interpolation? This time I am not exactly sure
>what you did; I don't have RCT. Could you please explain a little more
>about
>how you set up the temperament "12th" to smooth out the bend?
>
>Bradley M. Snook

This is a feature in Tunelab 97. I dont know if Tune Lab Pro has it or not. In
TL97 useing the numerical editor you can either choose linear or this 3 point
quadratic depending on whether you use 2 or 3 notes to set the tuning for the
range of those notes.

Smoothing out the bend.. yes... if you saw Mikes graphing of the comparison
data between RCT's curve and the perfect 12th tuning I did with Tunelab, you
will see that the RCT has a slow even exponetial like curve whereas the Tunelab
P-12th tuning consisted of 2 straight lines with differeing gradients which
changed at A4. This basically reflects the steepness in the gradient at which
the change of frequencies for the 3rd partial happens, and of course the
gradient will be steeper in the the 12th range between A4 and E6 then it is
lower down between D3 and A4. But since the higher 12th was simply a direct
reflection of the lower 12th the curves are of course both linear.

Ok.... useing Tunelabs 3 point quadratic interpolation instead of its 2 point
linear (to figure the temperment 12th) you get an exponetial like curve instead
of a linear one. You just need to use one extra note in the dialogue box for
the numerical editor. This curve then also gets reflected in the 12th A4 - E6
but because the rate of change for 3rd partials frequencies is greater in this
area the curve gets steeper... just as with the linear. Only exception being
that now you get something a bit closer to a continuous curve the whole way....
from D3 to E6.

There still remains to seperate curves tho... this you can see by doing a 3
point quadratic on D3 to E6 and still use A3 at the same frequency as above and
look at what happens to the frequencies of other notes. A4 for example goes
about 2 cents sharper. 

You can also do more or less the same in the graphing editor by anchoring on
the end notes and then pulling down A3 to the disired frequency. Using the
graphing editor you can actually watch the change from the linear to the
exponetial happen. Doing that one time is enough to understand whats going on.
Tho the resolution of the frequencies is a bit less precise it seems.

I suggest you do this in Tunelab 97 as its really easy in that version due to
the presence of the numerical editor.

Hope this answers your question. I get to go play today with a nice instrument
at the U. I'll see what I can get done and post tonite.

RicB

Richard Brekne
RPT NPTF
Griegakadamiet UiB