Post by Larry Deack"Aryeh Eller"
Post by Aryeh EllerI suggest an excellent book on this subject, Douglas Hofstadter's
Pulitzer Prize-winning
Gödel, Escher, Bach: An Eternal Golden Braid
I read it long ago and it has led me to some of the ideas I posted here.
Really? And where exactly in the book are you basing these ideas on?
Post by Larry DeackEvidently we came away from that book with very different ideas about Bach
and what Hofstadter was saying since it seems to me I should be suggesting
the same book to you if you wish to understand my post better.
I understood your post, I've quoted the relevant text from Hofstadter's
book below so that other readers can judge for themselves if there are
indeed multiple ways of understanding his words - I don't think there
are, Hofstadter is very clearly saying what I'm saying - see below.
Post by Larry DeackBach's structure is recursive.
What's your point here? I don't disagree with you, here's what
Hofstadter says what recursive means:
Figure and Ground in Music
(Godel, Escher Bach - An Eternal Golden Braid pg. 70)
"One may look for figures and grounds in music. One analogue is the
distinction between melody and accompaniment - for the melody is always
in the forefront of our attention, and the accompaniment is subsidiary,
in some sense. Therefore it is surprising when we find, in the lower
lines of a piece of music, recognizable melodies. This does not happen
too often in post-baroque music. Usually the harmonies are not thought
of as foreground. But in baroque music---in Bach above all---the
distinct lines, whether high or low or in between, all act as "figures".
In this sense, pieces by Bach can be called "recursive"
Post by Larry DeackPost by Aryeh EllerBach's music sounds like you're able to hear multiple
independent lines at once but you can only really follow
one fully and completely at any given time
I can follow more than one line and in fact that is what I was advocating
others try. It feels like holding your focus between the lines but I
certainly agree one must first learn to follow the lines easily.
I don't think Hofstadter says you can follow more than one line fully
and completely without shutting out or taking away from your full
perception of another independent line - There are two modes of
listening, one can follow one line completely or one can take in the
whole thing - but once you take in the whole thing you've lost the
following of the complete independence of each line. The brain does not
allow for both.
Here's the relevant text about that from Hofstadter, a dialogue between
Achilles, the Tortoise, the Crab and the Anteater. (pgs. 281-84)
Achilles: I have a question about fugues which I feel a little
embarrassed about asking, but as I am just a novice at fugue-listening,
I was wondering if perhaps one of you seasoned fugue-listeners might
help me in learning....?
Tortoise: I'd certainly like to offer my own meager knowledge, if I
might prove of some assistance.
Achilles: Oh thank you. Let me come at the question from an angle. Are
you familiar with the print called "Cube with Magic Ribbons" by M.C.
Escher?
(Here's a picture of the print, follow this URL)
http://www.edu-negev.gov.il/oded/mc24.htm
Tortoise: In which there are circular bands having bubble-like
distortions which, as soon as you've decided that they are bumps, seem
to turn in dents--and vice versa?
Achilles: Exactly.
Crab: I remember that picture. Those little bubbles always seem to flip
back and forth between being concave and convex, depending on the
direction you approach them from. There's no way to see them as concave
AND convex----somehow one's brain doesn't allow that. There are two
mutually exclusive "modes" in which one can perceive the bubbles.
Achilles: Just so. Well, I seem to have discovered two somewhat
analogous modes in which I can listen to a fugue. The modes are these:
either to follow one individual voice at a time, or to listen to the
total effect of all of them together, without trying to disentangle one
from another. I have tried out both of these modes, and, much to my
frustration, each of them shuts the other. It's simply not in my power
to follow the paths of individual voices and at the same time to hear
the whole effect. I find that I flip back and forth between one mode and
the other, more or less spontaneously and involuntarily.
Anteater: Just as when you look at the magic bands, eh?
Achilles: Yes. I was just wondering...does my description of these two
modes of fugue-listening brand me unmistakably as a naive, inexperienced
listener, who couldn't even begin to grasp the deeper modes of
perception which exist beyond his ken?
Tortoise: No, not at all, Achilles. I can only speak for myself, but I
too find myself shifting back and forth from one mode to another without
exerting any conscious control over which should be dominant. I don't
know if our other companions here have also experienced anything similar.
Crab: Most definitely, It's quite a tantalizing phenomenon, since you
feel that the eesence of the fugue is flitting about you, and you can't
quite make yourself function both ways at once.
Anteater: Fugues have that interesting property, that each of their
voices is a piece of music in itself; and thus a fugue might be thought
of as a collection of several distinct pieces of music, all based on one
single theme, all played simultaneously. And it is up to the listener
(or his subconscious) to decide whether it should be perceived as a
unit, or as a collection of independent parts, all of which harmonize.
Achilles: You say that the parts are "independent", yet that can't be
literally true. There has to be some coordination between them,
otherwise when they were put together one would just have an
unsystematic clashing of tones---and that is as far from the truth as
could be.
Anteater: A better way to state it might be this: if you listened to
each voice on its own, you would find that it seemed to make sense all
by itself. It could stand alone, and that is the sense in which I meant
that it is independent. But you are quite right in pointing out that
each of these individually meaningful lines fuses with the others in a
highly nonrandom way, to make a graceful totality. The art of writing a
beautiful fugue lies precisely in this ability, to manufacture several
different lines, each one of which gives the illusion of having been
written for its own beauty, and yet which when taken together form a
whole, which does not feel forced in any way. Now this dichotomy between
hearing the fugue as a whole, and hearing its component voices, is a
particular example of a very general dichotomy, which applies to many
kinds of structures built up from lower levels.
Achilles: Oh really? You mean that my two "modes" may have some more
general type of applicability, in situations other than
fugue--listening?
Anteater: Absolutely.
Achilles: I wonder how this could be. I guess it has to do with
alternating between perceiving something as a whole, and perceiving it
as a collection of parts. But the only place I ever run into that
dichotomy is in listening to fugues.
Tortoise: Oh my, look at this! I just turned the page while following
the music, and came across this magnificent illustration facing the
first page of the fugue.
Crab: I have never seen that illustration before, Why don't you pass it
'round?
(The Tortoise passes the book around. Each of the foursome looks at it
in a characteristic way--this one from afar, that one from close up,
everyone tipping his head this way and that way in puzzlement. Finally
it has made the rounds, and returns to the Tortoise, who peers at it
rather intently.)
Achilles: Well I guess the prelude is just about over. I wonder if, as
I listen to this fugue, I will gain any more insight into the question,
"What is the right way to listen to a fugue: as a whole, or as the sum
of its parts?"
Tortoise: Listen carefully, and you will!
Post by Larry DeackI can follow more than one line and in fact that is what I was
advocating others try. It feels like holding your focus between the
lines but I certainly agree one must first learn to follow the lines
easily.
What you're describing here is moving between the two modes of
perception that Hofstadter talks about -- one can move extremely quickly
like a strobe light between the two but it is still an aural illusion
that makes you feel as if you're following and taking in multiple
independent lines in their completeness at once.
Post by Larry DeackPost by Aryeh EllerWhen you look at a painting you can literally take
in every piece of information about that painting
immediately
I think you are incorrect on this point. Visual perception is much more
complicated and so is how we hear music.
I'm not talking about complexity, they both can be very complex in their
own way, I'm talking about the time factor, music unfolds through time,
the structure and form is not immediately apparent. I use the difference
between the visual and music when I teach the concept of Form in music
to my HS students. Basic shapes are immediately recognized by the eye
because we have been taught what they are before hand - If one listens
to music one can also assess its form but you have to wait as it unfolds
through time to do so - You can then compare what you've heard to a
pre-established and explained form like Binary, Ternary, Rondo,
Sonata-Form, Theme and Variations, etc.