para-inharmonicity and tuning curves

[Richard Brekne]

Robert Scott wrote:

> Unless you take inharmonicity readings of all 88 notes, there are
> going to be some notes that you do not measure, but you still have
> to tune them.  Somehow, the measurements that you do make are
> assumed to correlate with measurements that you did not make.
> Thus, a little predictive theory is built up whenever a tuning
> curve is generated.  Maybe it's not identical to the general theory,
> but it is a theory just the same.  But do the "deviant" measurements
> apply?  That is, if I measure one deviant inharmonicity on one string
> in one piano, what are the chances that all the other strings of that
> piano are also deviant in a similar manner?  Well, that depends on the
> deviation.  If it was caused by an accident of stringing, then I would
> not expect to gain much useful information about the rest of that
> piano from that one string.  In fact, I would be tempted to throw
> away that reading and measure a different, more representative string.
>
> Robert Scott
> Real-Time Specialties

Music to my ears... grin. I couple weeks back I called for just such
measurements of all 88 notes up and including the 12th wherever it was
possible. Tho I'll be the first to admit I had no real clear idea of what
I was looking for. But I have had a growing interest in el-tuning devices
and wondered exactly about just how reliable sampling 5 or 6 notes could
be, or rather how wrong (from time to time) that could be. Another thing
that struck me was the value of assembling the data for study. Just to see
what you could find out by presenting the resulting data in various
graphical ways. Since that discussion I have heard that no one has done
such a study. Is that true ?

As for the matter of para-inharmonicity. I am, in my learning phase, at
the moment most interested in gaining some more insight as to the side of
this which gives rise to negative inharmonicity, tho perhaps that will
change. Yet negative inharmonicity gives rise to a particular tuning
problem that I want to get a better handle on. It seems from comments I
have recieved so far that not much is really known for sure about its
causes. If that be true then there is little dependable knowledge about
why it behaves as it does.

A little side point.. As to measuring inharmonicity, and this gets back
into another side issue also discussed at lenght a couple weeks back. Now
this might be a ridiculous idea but I have to throw it out.. Seems like
much of the problem with measuring inharmonicity is the inherent weakness
of partials compaired to the fundemental, or to other partials. How about
(and here it comes) useing a bandpass filter set to around the frequency
of the partial you are trying to narrow in on in line between the pick-up
and an amplifier, then returning the resulting sound to the soundboard via
a contact transducer. Good old fashioned feedback, but a bit more
controlled ? Is is possible to "drive" a partial in this manner ??  Dont
laugh too loud now guys.. after all I am still just an egg in these
matters..

Richard Brekne