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Post by fuguestate on Sept 13, 2017 18:46:18 GMT
This board has been quiet thus far, and I almost( ) feel bad for starting the first topic with more fugue talk. Over the past while I've been grappling with Kristofer Emerig's idea of a fractal fugue. Basically, you take the subject, and recursively substitute each note with a copy of the subject, transposed to the pitch of the note. The idea itself is pretty straightforward, of course. But the challenge comes from making the result make sense harmonically, and, more importantly, sound convincing as a piece of music. Furthermore, being the "rule bender" that I am, I'm not satisfied with merely mechanically applying the algorithm and posting the result as-is. I want, and need, to be able to turn it, twist it, warp it, and mold it to my tastes before I'll let it bear my name as a composition of mine. Anyway, so far I have worked out two possible ideas. The first is to pre-plan the subject such that its various parts correspond with the overall plan of the fugue. For example, the opening notes will correspond with the subject entries in the exposition, the middle notes will correspond with entries in the ensuing episodes, and the ending notes will correspond with the final entries. Note length will correspond with passage length, so if the exposition had a bridge after the answer, for example, the 2nd note of the subject would be lengthened accordingly. A series of fast notes in the subject would correspond with stretto entries (if their corresponding passage length is shorter than the length of the subject). This scheme yields a 2-level fractal fugue. A second idea is to use a short subject, the notes of which spell out the subject entries in the exposition, and then the episodes will reintroduce the exposition, transposed according to the notes of the subject. Free counterpoint in the episodes will link these expositions to each other. This yields a 3-level fractal fugue. Initially, this seemed like a more attractive idea than the first, but on further thought, it poses significant challenges: since the notes of the subject must now correspond with the entries in the exposition, the number of notes it has will also dictate the number of voices in the fugue, which limits it to be about 3-5 notes long. I have a hard time writing a convincing fugue subject with only 3-5 notes! This was as far as I got until yesterday, when it occurred to me that there's another possibility: I can start with, say, a 4 quarter-note seed as the basis for the fractal, and write, say, 4-part harmony for it. I could write an exposition using this 4-note seed, but that will not be its final form: after sorting out the 4-part harmony, alter individual notes by inserting passing notes, ornamentations, etc., so that a convincing, interesting fugue subject is obtained. The rest of the fugue will expand the fractal according to the 4-note seed, so we could still have a 3-level fractal, but the fractal structure now serves as the underlying harmonic basis for the fugue, rather than its final, external form. So there will be more freedom in manipulating the melodic lines, adding "extraneous" notes for flavor and character. And of course, room for episodic material will still be allowed for.
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Post by Bob Porter on Sept 13, 2017 21:40:25 GMT
"and, more importantly, sound convincing as a piece of music."
I guess this will be the deal breaker for me, also. Good luck!
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Post by Mike Hewer on Sept 14, 2017 7:13:27 GMT
I'm still debating this technique in my head. It seems clear to me that the more expanded your harmonic language, the more option you will have. Of course this also runs into your problems too Teoh, but in my case I have to be a little more careful to not let the machine run without responsibility, because given a more dissonant language, it'd be all too easy to accept the print out after the number crunching.
Let's hope Kris joins us here.
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Post by fuguestate on Sept 14, 2017 19:55:38 GMT
My rule of thumb as far as harmony goes is that I can't hear something in my head, I won't write it. (Well, I might, if only to learn what it sounds like, but you know what I mean -- I won't use it in a composition until I've learned what it sounds like and how to use it.) And if something sounds "wrong" (and my definition of "wrong" is not necessarily traditional harmony, mind you), I'll rewrite it.
Still, harmony aside, the ultimate criterion is whether the result sounds convincing as a piece of music. This is highly subjective, of course, but in one way or another, it has to "work". Can't just be some random splotches of notes produced by an algorithm. At the very least, there has to be some kind of progression of motifs, some kind of build-up and climactic point, and usually a denouement. IOW, some kind of dramatic arc. As you said, it's too tempting to just accept the printout from the number crunching. That may well be fine and good as a piece of mathematics, but not necessarily as a piece of music, IMO.
Anyway, apart from a strict fractal fugue, I think Kristofer's idea of equating notes with entries is far more widely applicable than may first appear. Going back to his initial observation that the traditional I-V-I-... exposition key scheme can be thought of as a fractal expansion of the subject against a motif of scale degrees 1, 5, 1, ..., we don't necessarily need to require that the subject be expanded against itself (which yields the strict fractal fugue). We could, example, treat the series of entry keys in the exposition as a secondary motif, and independently introduce and develop it over the course of the fugue. We could make it coincide with a countersubject. We could make the fugue's episodes revolve around its permutations. Kris has already mentioned at some point that he has come to use such secondary motifs as the basis for writing episodic material, in place of the traditional sequence. There is much to explore here, IMO, apart from the strict application of fractal fugues.
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Post by Bob Porter on Sept 14, 2017 23:59:53 GMT
I know I don't really belong in this discussion. But what the heck. I'm reading your words but my brain is kind of rolling up in my head. I love a good fugue. But then you aren't distracted by a graphical interface.
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Post by fuguestate on Sept 15, 2017 21:27:07 GMT
Bob Porter: I think people get far too worked up about the term "fugue" -- it probably triggers unconscious negative associations or repressed memories or something, or at the very least the idea of something obscure, abstract, and just plain hard. I hope to dispel this notion in the future by writing more "fun" fugues. You certainly do belong here, Bob.
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luis
New Member
Posts: 22
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Post by luis on Sept 27, 2017 8:43:25 GMT
I've listened to some examples of fractal music and it's amazing. using it in a fugue can be great. Surely it's worth trying.
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Post by fuguestate on Sept 29, 2017 6:57:02 GMT
Here's an update on my fractal fugue attempt. I finally managed to figure out a way to work a 9-note subject into an extended exposition of sorts by allowing much room for free counterpoint. Basically, the subject determines the pitches and location in time of the first 9 entries, and the rest of the space is used to make a believable passage out of the sometimes unlikely juxtapositions and strettos imposed by the subject. Of course, the subject itself must be carefully chosen, but even then, it was quite a challenge to make the resulting sequence of notes convincing as a piece of music.
Now I'm faced with the next challenge: how to continue. Since the subject dictated 9 entries, this is a pretty hefty exposition, much longer than a traditional fugue would employ. If I were to go with a strict application of the next level of fractal expansion, it would mean there would be a total of 81 entries. I'm not confident I have the skill to write an 81-entry fugue that doesn't put the audience to sleep! I'd run out of interesting ideas long before I get to 81 entries. So I must use some other method of continuing. The big question is, what method to use that will still qualify under the title of a fractal fugue.
Thoughts?
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Post by Mike Hewer on Sept 29, 2017 14:03:03 GMT
would diminution work? If the subject is written in say minims, you could perhaps reduce it to crotchets and keep going down to semis...just a thought.
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Post by fuguestate on Sept 29, 2017 14:26:19 GMT
Diminution would help, but not by much, because I'd still have to write counterpoint for another 72 entries. I'm not sure I can make up enough variety to keep things interesting for that many entries! With a 2-bar subject in 4/4 at 95bpm, this would still produce an incredibly long fugue, longer than I have the skill to make it interesting. Some possibilities I thought of (none are perfect): - Instead of fractally expanding the entire subject, expand only the first N notes, so either use truncated entries, or expand the next level corresponding only to the first half, say, of the subject, or both.
- Simplify the subject by picking out the key notes, and restrict the expansion only to that.
- Adapt your idea of using diminution by having the next set of entries in half the note values, then again in 1/4 of the note values, until it becomes just a blur of notes, then skip to the end. A kind of musical ellipsis, implying the rest of the entries but not actually writing all of them out. The catch here is how to convey this to the audience effectively.
- Write a short bridge and another 9 entries that mirrors somehow the first 9 entries, so producing a kind of bipartite form.
Have to mull over this a bit more!
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Post by Mike Hewer on Sept 29, 2017 14:32:28 GMT
You are definitely thinking in the right way though Teoh. Adaptation to suit is the way to go. I like the idea of cherry picking if you can work it. Whatever you do I don't think an audience would be aware of it and perhaps a deus ex machina is the only way----where is Emerig when you need him, come on Kris, sign up.
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Post by fuguestate on Sept 29, 2017 14:49:09 GMT
Another idea occurred to me: simplify the rhythm of the subject entries, so that I can squeeze more of them into a small space without getting inordinately short notes. Right now there's a mixture of quarter notes, half notes, and dotted quarters... if I reduce them to just a single note value, I could sneak in those 9 notes more easily in unexpected places. Better yet, if I allow the rhythm to freely vary, there may be more interesting ways to work the subject. Still, 72 more entries is a bit much. Gotta find some way of reducing that...
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Post by Mike Hewer on Sept 29, 2017 15:04:45 GMT
You are facing head on some of the problems I envisaged with fractal technique. My imagination runs quite wild though the minute you relax the idea and not be so strict. When I was contemplating one to include in my piano set, I kept wandering off at a tangent and having groupings sprouting off one another (in my imagination that is - not written down!). Of course Mr E would no doubt tell me I wasn't being a pure Fractalite, but just the idea of fractal technique instils fantastical derivations from the pure for me. Simplifying the rhythm (or actually changing it in diminution) seems like it could work, turning the theme into a short motivic cell perhaps, or even just a quick succession of notes. Imagine 10 of these cells sprouting off one another in a mad stretto - not unlike the multiverse in string theory....see what I mean about how creative you could get, the further away you get from the strict application. Anyway, just a brain dump to gee you along....
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Post by fuguestate on Sept 29, 2017 17:11:29 GMT
Yeah, I've already been accused by Mr. E of not being a pure fractalite. But personally I just can't crank a subject through the motions of some fixed algorithm and just leave it at that. I'm a control freak, I crave control over my creative output, I need control over it. I want to be able to bend the rules to my will, to sculpt it as I see fit, algorithms and rules be damned. I've already taken quite a few liberties in my current WIP, in the sense that each entry begins with the corresponding note in the subject, but for reasons of voicing, harmony, or just pure dramatic arc, I allowed the octave to freely vary. So the result is not readily discernible as a fractal structure to a casual listener, but upon analysis the correspondences should become quite clear. And reading your idea of motivic cells sprouting off each other in a mad stretto, that jives with one of my ideas, the one about subsequent entries becoming shorter and faster, until the whole thing becomes a mad flurry of notes, and then suddenly the notes of the subject re-emerge from the fractal structure. Y'know, the kind of feeling you get when zooming out from a fractal structure, and as the parts become smaller and smaller, suddenly a larger version of the part comes into view, revealing the self-similarity. Depending on how I do it, that could be the grand conclusion. Perhaps. If I can pull it off. (Which is a big if.)
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Post by Mike Hewer on Sept 29, 2017 17:37:35 GMT
Yes, that zooming out and re-emergence of the subject immediately put me in mind of one of the (for me) great moments in 20thC music - the end of the Young Person Guide. I find it spine tingling the way Purcells' theme crawls up from the brass in augmentation over the manic what is now, accompaniment, of the fugue theme - the ultimate triumphant culmination of the fugue and the work. If you can achieve an inevitability like that then wow.
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