Stretch tuning a resistor string... why NOT to!

[Harry Bissell]

Well (the snipped comments were mine so I'll take this one...)

If you are making a monosynth (or polysynth)... don't bother. The reason for the
sharp and flat (atretch) tuning of the piano is beacuse the harmonics of the
strings are not correct... the piano strings are "real" not ideal.

An example... (numbers might not be quite right, but close)

Take A = 440Hz on a piano. if we play the octave we expect it to be 880Hz.

Now the real piano string second harmonic is 882Hz (because of stiffenss) so
there is a 2Hz beat at the octave (which should be zero beat). So we retune the
octave a little sharp, until we zero beat the A440 2nd harmonic (882Hz) with the
A880 (now A = 882).

The same thing now for the upper octaves... each one gets a little sharper
still... and the lower octaves get flatter.  We tune the midrange of the piano
(the most used or useful range) as close to correct as we can (including that
equal temperment is a bastard anyway...) and then sharp and flat the upper and
lower keys of the piano.  Try playing any one octave span and we are not too far
out of tune. Play the same notes four octaves apart... and you are off by a long
shot !!!  The best pianos (grand) have careful design to make their strings more
"ideal" so they require less "stretch" in the tuning. That's why they are
favored over the spinet piano for everything except living room furniture !!!

The Synth overtones are a PURE harmonic series... A440Hz second harmonic is
exactly 880Hz.... and this relation holds true throughout the audio spectrum. So
if you stretch tune a synth it will sound like Sh!t.  If you use a sample of a
real piano string... it will have the sharp overtones and then you will need to
stretch tune. Or your samples will be chosen so that you have already recorded
the "proper" tuning (without caring that the micro is playing back the correct
pitches, and that the samples are "wrong"

The best thing to do with the resistors is to try to match them to better than
1% by using an accurate meter.  Digi-Key sells 1% 1/4 watt resistors with a
50ppm tempco for $8.
(make sure to get the 50ppm... the price is the same as the 100ppm so why not
get the more stable ones...) Then sort them into little bins (use the wife's
china cups if she'd not looking...) of 0.1% values... when you have 50 or so
that are close enough for rock and roll you are ready to start soldering....

Or scan the keyboard, and feed a DAC. I'm not going there again. Read the last
week's posts and choose your poison !!!

:^) Harry

Tim Daugard wrote:

> > The Resistor Divider method may be better than you think... even 1%
> resistors
> > from the same manufacturing lot are usually closer than 1%... and the
> errors
> > do not add.. .they usually (statistically) subtract... One that is a
> little
> > high is often compensated by one that is a little low...  Depends on how
> fussy
> > you are...
>
> So, should I put the low resistors on the bottom and the high resistors on
> the top to create the same spread tuning effect as a piano? A regulated
> current source makes sense, but doesn't the loading by the output buffer
> affect the tuning?
>
> I've been using a bass or guitar as my oscillator source so far and using
> the synth circuits to modify the signals but I have to build the VCO and
> keyboard soon. I'm just waiting on an inexpensive organ to turn up to tear
> apart for a keyboard. There's a two manual lowery for $79 eventually it will
> come down further.
>
> Tim Daugard