interval class entropy?

Hello, all,

I'm crossposting something from the practical micro list that struck
me as having very interesting parallel ideas to harmonic entropy. My
purpose is not to say that this has anything directly to do with it
currently, but in hopes of inspiring a vision of a direction in which
it might one day be refined.

Where H. E., as I understand it, asks something like, "What
low-limit rational interval is the ear most likely to interpret a
given dyad as, when heard in isolation?", Dan asked himself something
like, "What interval class is a given melodic interval likely to be
heard as, given a certain musical and cultural context." The cultural
part my be pushing things too far for harmonic entropy, but the
musical context part might not be, and the addition of interval
classes and melodic intervals to the equation, while complicating it a
whole lot, might make the idea more appealing to composerly types.

Maybe too far out, but just a suggestion, and who knows?

Dan refers to a specific piece of music. It's not necessary to hear
it to follow what he says, though.

--BEGIN QUOTE--

One of the interesting things I was able to do with "At a Day Job" was
play with (and off of) the many expectations that are set up with such
familiar melodies and tune fragments.

As an example of this I'd point to the truncated reworking of the
"America the Beautiful" melody that the trumpet takes at the opening.
This is a very familiar, almost archetypal "tattoo". And it has been
pretty thoroughly branded into many folks mind.

The tuning that I used combines two overtone series, 10-20 and 14-28,
and I used these as a two octave keyboard mapping. For the opening
"America the Beautiful" tattoo I used a descending 13/10 in the role
of the expected minor third (and a 7/5 in place of the expected fourth
that follows) because this established a workable recasting of the
expected minor third proportion wise.

What do I mean by "workable"?

Well it's no surprise however that this is entirely context specific,
and my reactions to an isolated 13/10 and to the "O Beautiful" 13/10
tattoo in "At a Day Job" are very different indeed. Actual music sets
in motion many things that simple tuning examples and microtonal ear
training can never predict.

Along the lines of common expectations the 13/10 sort of sits on a
fence between two separate interval classes (unlike an 11/9, or
neutral third for instance, where it's guaranteed to strike most ears
as some kind of third). And I'd guess that the 13/10 is most often
heard as either an out-of-tune fourth (usually when presented as an
isolated, naked dyad), or as an extremely sharp third (usually when
presented as an isolated melodic interval).

However, the little "O Beautiful" descending minor third motif is so
familiar, the pull of its expectations so strong, that anything in its
place resembling a major third (to my ears anyway) sounds 100%
obstinately WRONG!

So what does the 13/10 sound most like in this context?

To my ears it sounds like an interval unto itself... definitely not a
major third in the traditional or comparative sense, but not quite a
fourth either.

Anyway, there's a lot of this business going on in that piece. (And
even some "math" too...)

thanks for listening,

--Yankee Doodle Danny

--END QUOTE--

David Finnamore

Hi there. I believe that the categorical perception of (especially melodic)
interval classes is a very important psychoacoustical phenomenon. But I
believe it has nothing to do with harmonic entropy, despite Monz' claim to
the contrary.