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entries are really the only thing that make a fugue a fugue. There are fugal devices, |
such as retrograde motion, inversion, augmentation, stretto, and so on, but one can |
write a fugue without them. Do you use any of those? |
Author: to be sure. My Crab Canon employs verbal retrogression, and my Sloth Canon |
employs verbal versions of both inversion and augmentation. |
Crab: Indeed-quite interesting. I haven't thought about canonical Dialogues, but I have |
thought quite a bit about canons in music. Not all canons are equally comprehensible |
to the ear. Of course, that is because some canons are poorly constructed. The choice |
of devices makes a difference, in any case. Regarding Artistic Canons, Retrogression's |
Elusive; Contrariwise, Inversion's Recognizable. |
Achilles: I find that comment a little elusive, frankly. |
Author: Don't worry, Achilles-one day you'll understand it. |
Crab: Do you use letterplay or wordplay at all, the way Old Bach occasionally did? |
Author: Certainly. Like Bach, I enjoy acronyms. Recursive AcronvmsCrablike |
"RACRECIR" Especially-Create Infinite Regress. |
Crab: Oh, really? Let's see ... Reading Initials Clearly Exhibits "RACRECIR'"s |
Concealed Auto-Reference. Yes, I guess so ... ( Peers at the manuscript, flipping |
arbitrarily now and then.) I notice here in your Ant Fugue that you have a stretto, and |
then the Tortoise makes a comment about it. |
Author: No, not quite. He's not talking about the stretto in the Dialogue-he's talking about |
a stretto in a Bach fugue which the foursome is listening to as they talk together. You |
see, the self-reference of the Dialogue is indirect, depending on the reader to connect |
the form and content of what he's reading. |
Crab: Why did you do it that way? Why not just have the characters talk directly about |
the dialogues they're in? |
Author: Oh, no! That would wreck the beauty of the scheme. The idea is to imitate |
Godel’s self-referential construction, which as you know is INDIRECT, and depends |
on the isomorphism set up by Godel numbering. |
Crab: Oh. Well, in the programming language LISP, you can talk about your own |
programs directly, instead of indirectly, because programs and data have exactly the |
same form. Godel should have just thought up LISP, and then |
Author: But- |
Crab: I mean, he should have formalized quotation. With a language able to talk about |
itself, the proof of his Theorem would have been so much simpler! |
Author: I see what you mean, but I don't agree with the spirit of your remarks. The whole |
point of Godel-numbering is that it shows how even WITHOUT formalizing |
quotation, one can get self-reference: through a code. Whereas from hearing YOU |
talk, one might get the impression that by formalizing quotation, you'd get something |
NEW, something that wasn't feasible through the code-which is not the case. |
In any event, I find indirect self-reference a more general concept, and far more |
stimulating, than direct self-reference. Moreover, no reference is truly direct-every |
reference depends on SOME kind of coding scheme. It's just a question of how |
implicit it is. Therefore, no self reference is direct, not even in LISP. |
Achilles: How come you talk so much about indirect self-reference? |
Author: Quite simple-indirect self-reference is my favorite topic. |
Crab: Is there any counterpart in your Dialogues to modulation between keys? |
Author: Definitely. The topic of conversation may appear to change, though on a more |
abstract level, the Theme remains invariant. This happens repeatedly in the Prelude, |
Ant Fugue and other Dialogues. One can have a whole series of "modulations" which |
lead you from topic to topic and in the end come full circle, so that you end back in the |
"tonic"-that is to say, the original topic. |
Crab: I see. Your book looks quite amusing. I'd like to read it sometime. |
(Flips through the manuscript, halting at the last Dialogue.) |
Author: I think you'd be interested in that Dialogue particularly, for it contains some |
intriguing comments on improvisation made by a certain exceedingly droll character- |
in fact, yourself! |
Crab: It does? What kinds of things do you have me say? |
Author: Wait a moment, and you'll see. It's all part of the Dialogue. Achilles: Do you |
mean to say that we're all NOW in a dialogue? Author: Certainly. Did you suspect |
otherwise? |
Achilles: Rather! I Can't Escape Reciting Canned Achilles-Remarks? Author: No, you |
can't. But you have the feeling of doing it freely, don't |
you? So what's the harm? |
Achilles: There's something unsatisfying about this whole situation ... Crab: Is the last |
Dialogue in your book also a fugue? |
Author: Yes-a six-part ricercar, to be precise. I was inspired by the one from the Musical |
Offering- and also by the story of the Musical Offering. |
Crab: That's a delightful tale, with "Old Bach" improvising on the king's Theme. He |
improvised an entire three-part ricercar on the spot, as I recall. |
Author: That's right-although he didn't improvise the six-part one. He crafted it later with |
great care. |