Re: Science Fair, syntonic comma, and "unfamiliar" musics

Hello, there, and thanks to Paul Erlich and David Finnamore for their
responses to my suggestion for a possible Science Fair project
comparing the approach of different musical styels and tunings to the
syntonic comma.

As both Paul and David pointed out, many musical styles such as those
of Gothic Europe during the 13th and 14th centuries might be quite
unfamiliar to many participants at a Science Fair, making it difficult
for these participants to form any ready opinion on a preferred
tuning.

More generally, any _alternate_ tuning or musical style must face a
this kind of barrier to one degree or another: people need to hear it
and get acquainted with it in order to have an opportunity to
appreciate its aesthetics and beauty. In order to get acquainted with
it, however, they have to encounter it.

Please let me emphasize that while it's not so surprising that I would
propose Gothic European music as an example of a music where the
syntonic comma is _not_ a "universal problem," various world musics
using or approximating Pythagorean tunings could equally well have
been selected.

In fact, I regard the view sometimes expressed here that "Gothic music
is very hard to comprehend" as a positive opportunity, since it places
me in a position somewhat comparable to those of musicians following
many other world traditions. How misguided I would be to miss the
benefits of such a situation by seeking a privileged position for
Gothic music simply because it happens to be composed European music!

If one takes the view that a Science Fair project can and should be an
opportunity for people to discover "unfamiliar" musics around the
world, then the remarks of Paul and David suggest the wisdom of
creating a welcoming and exploratory atmosphere for participants.

The message would be that it's not "wrong" if something sounds "weird"
or totally unfamiliar. If there are surveys as to which tuning a
participant suspects might be associated with which piece, or which
tuning the participant prefers, including choices such as "I don't
know," or "The music is too unfamiliar for me to judge" might be a
wise policy.

Having said this, I might add that while inaccurate statements of
facts about music can often be easily corrected, style-specific
judgments about intervals and tunings (often implicit) are often more
difficult to have recognized as indeed style-specific.

For example, it is easy to show that 53 pure 3:2 fifths very closely
approximate 31 pure octaves, and that by tempering the last fifth in
the cycle to obtain a pure 2:1 octave, we can obtain a "virtually
closed" system. (The last fifth is narrowed by ~3.62 cents.) In
contrast, 72 pure fifths will be much further from any pure octave.
While Chinese musicians seem to have recognized the close affinity of
the first and 54th notes in such a cycle, we can confirm these
conclusions using logarithms simply by taking the size of a pure
fifth, ~701.955 cents, multiplying the requisite number of times, and
seeing how closely the result approximates an integer multiple of 1200
cents (a pure 2:1 octave).

Demonstrating that the syntonic comma is a "problem" in some musics --
but not all -- may be a more difficult process, because ideally it
involves exposure to musics illustrating how this comma may or may not
be a problem.

The more I consider this process, the more I am inclined to conclude
that a Science Fair project exploring this issue should _not_ include
Gothic European music as the _one_ example of a 3-limit music where
the syntonic comma is not a problem. Chinese or Japanese music based
on a tuning in pure fifths, for example, would give listeners a wider
cultural view and also show, when compared to Gothic music, that not
all 3-limit or Pythagorean musics are alike.

Further, it seems to me that Gothic music offer suffers from a quite
"non-splended isolation" -- people compare it _only_ to later styles
of European music, in isolation from other world musics which either
use Pythagorean tunings or prefer fifths and fourths as the main
vertical intervals in polyphony. This leads to the idea that Gothic
music is somehow "unnatural" or a mere intellectual abstraction, as
opposed to one of many great world musics.

Most respectfully,

Margo Schulter
mschulter@value.net