[CAUT] Jim Ellis stretch article

[Fred Sturm]

Hi all,
    I was initially going to write on this subject privately to Jim Ellis,
then thought it might spark some discussion on the list. So this is a
reaction to Jim's article in the Jan PTJ.
    First of all, it is very nice to have documentation of this tendency "to
want octaves to be stretched." I've heard a lot of anecdotal evidence, and
have participated in informal demos myself, but this quantifies the
phenomenon and gives it more credibility.
    I, for one, would love to see more experimentation along these lines. A
couple things I'd like to see added:
1) Compare results of the experiment as set out in the article with an
experiment using inharmonic partials - in the general range of what pianos
produce. I have long wondered how much that plays a part in perception of
pitch of upper notes. (Actually, this should be done, not as separate
experiments, but as one combined experiment - with both harmonic and
inharmonic tones, comparing results of the same listeners to see if there is
any difference).
2) Do wider intervals as well as single octaves: double, triple and
quadruple octaves. I think this is perhaps even more important in deciding
how much to stretch a piano tuning, as it is in the perception of what both
hands are doing in performance that we really listen to the total sound.
Complaints of "not enough stretch" are likely to come when low bass is
played simultaneously with high treble.
    It also seems like the raw data of the original experiment could be
mined a bit more. For instance, I note that there are far more than 9
"correct" answers in each graph, meaning that each listener (or many) said
more than one octave size was in tune. It would be interesting to look at
"average correct pitch" for each individual, and also for how wide a range
each individual considered "correct." Perhaps those with the "widest
tolerance" might be eliminated, to keep them from skewing the overall
results. There are any number of more sophisticated manipulations, but they
make better sense with a larger sample.
    I'd love to have results for professional musicians, especially samples
from various instrument groups (vocal, unfretted strings, woodwinds, brass,
etc). All in all, though, thanks to Jim for doing this work, and
contributing to our knowledge base.
Regards,
Fred Sturm
University of New Mexico