Cyber ears

[Richard Brekne]

"Jim Coleman, Sr." wrote:

> Hi Richard:
>
> Not only is this doable, but it has been done, way back in the late '70s.
> Francis Mehaffey used such a machine to listen to specific coincidental
> partials and then provided a digital readout. I believe his son is the
> one who designed the machine following the ideas of his father. Incidentally
> Francis is now in a rest home somewhere in or near Claremont, CA.
>
>
> Now, to get off of the negatives for such a machine. It would indeed be
> possible to develop such a machine that would compute a smooth curved
> tuning, but there might be some problems with the patents which Dr.
> Sanderson holds where he claims the right to any type of tuning which is
> derived from measured partials. Perhaps one who wishes to pursue this could
> get a license to use some of his patent ideas and apply them to a machine
> which listens to beats and gives digital readout of the same to be compared
> to a pre-calculated set of beat rates. I still think it is much simpler
> to do as the present state of the art machines do it.
>
> Jim Coleman, Sr.
>

Thanks again for the reply here Jim. The name Sanderson rang a bell, so I
started looking through my old PTG Journals today to see what I could find. In
the June 1978 issue an article on Dr. Sandersons work by Hiram T. Hunnicutt was
to be found. The list of partials and translation tables to bps are exactly what
I had in mind. Now this data and ensuing tables are quite incomplete for my
purposes being only measurements and translations  for 2 octaves (C3 to C5) and
only up and including the 8th partial.

Table B on page 16 is a rendering to bps of actual frequencies of a "well tuned
grand piano". At first glance things look normal enough yet if one looks a bit
closer at the intervals of a fourth (taken as a 6-8) and the Octave (as a 3-6)
some very interesting things happen.

According to the "theory" fourths and all coincidental partials they generate
should become increasingly faster as one progresses up the piano registers.
Further they should be "wide". Yet this is not the case. the 6-8 partials are
wide (starting at C3), and decrease in wideness until at C4 they are beatless,
afterwhich they become increasingly narrow.  This same applies to the octave
taken as a 3-6. Also of note is the radical divergence from the theoretical of
the octave taken as a 4-8. This coincidental beats (narrow) at 4.7 bps.

Now I suppose most tuners are aware of in some sense or another that there are
"discrepancies" that one is to be on guard for. Perhaps this is why my teacher
used to tell me to simply ignore anything but a few basic test intervals. But he
never told me why, and frankly I dont think he really knew himself. He wasnt
into alot of theory. He followed the recipie and was good at it. Good enough to
pass any test he took, and he took several. As for me however, I always got
disturbed by these overtones you are not supposed to listen to. Number one
because they often sound bad, and number two I have this curiosty about such
things that refuses to quit.

Now this is just one table, take over 20 years ago, and it only includes 8
partial for 2 octaves. In itself interesting enough, but what is going on with
the higher partials, especially in the bass and highest treble? And what about
the rest of the piano. And how if at all can this information be used ?

The answer to the last in anycase is that one never knows until one assembles
enough data and takes a look see..

Now all this is perhaps useless to most tuners who are interesting in other side
issues, have their hands full, etc. And besides if one sticks to the recipie its
not neccessary. Be that as it may I am fascinated, and I learn best by this kind
of understanding. I doubt that I am alone in this, at least one other individual
has persued this line.

If you know of more of Sandersons work, or any follow up I would like to hear
where I can get ahold of it. And if you know of a resource for such data
covering the entire piano, hopefully with a few more partials included, I would
love to get a hold of them.

As for the Tune Lab program, or Cyber Ear for that matter. It would be really
nice for them to include an option for recording this data up to at least the
12th if not the 16th partial. in table form for the entire piano. (I'd like to
take a look at the octave as an 8 16 and the double octave in all senses.) I
cant see that this would require so very much in terms of new code. (correct me
if I am wrong)

well well, lengthy again.. enough for now..

thanks again

Richard Brekne

PS the use of the lowest number first in nameing partial relationships is
Sandersons notation. This might be confusing to those accustomed to the custom
of using the lowest note (it's partial) in the interval first.