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