Yet my aural imagination wasn't developed enough to generate novel music, except when I was in certain moods or about to fall asleep. And most of what I could hear in my head I found impossible to transcribe.

I can't speak with certainty about your particular situation, but there's a decent chance you would find these tasks easier if you had a more powerful theory of music at your disposal. Such things exist, and are known to experts; unfortunately, despite the fact that they have been around for a while now, one is still unlikely to be exposed to them without doing graduate work in music, preferably at an elite university. (The linked blog is one of very few places on the internet where I have ever seen such things discussed.)

But let me stop lamenting and instead try to improve the situation, such as can be done within the confines of a blog comment.

One thing I noticed right away about your compositional process, as you described it, was that it was almost entirely local. As you said, you only composed 2-4 measures at a time. (You did mention recaptiulating things, something which requires a bit of global planning, hence the "almost".) This is roughly like trying to paint a picture one detail at a time without knowing what it is you're painting a picture of. Maybe some painters work like this, but I doubt most do. (By the way, this has nothing to do with how abstract the painting is. I suspect that even the most abstract painters have some overall idea of what they want their painting to look like well before they finish it.)

Unfortunately, "traditional" music theory (by which I mean that which the layman can easily find online, or in bookstores, as opposed to what specialists have in their university libraries) does a very poor job of allowing one to think precisely about global phenomena. At its worst, it trains one to ask questions like "what chord should come next?", which is totally the wrong way to think about music.

In the early 20th century, an Austrian named Heinrich Schenker came up with a theory of the right sort: one that explicitly dealt with musical works on all levels of structure, from the most global and far-reaching down to the minutiae of individual notes. Schenker's own intellectual context for his achievement was of course quite different from the modern one in which his work is usually placed, but in any event his ideas were picked up and run with by anglophone music theorists, and now "Schenkerian theory" is a standard, literature-rich academic discipline that most readers probably didn't know about.

This comment is getting too long, so I'll close with a specific recommendation: musically-inclined LWers will definitely want to take a look at Peter Westergaard's book An Introduction to Tonal Theory. It's a favorite at the site I linked to above, and indeed, although it was originally written for college freshmen* I almost think its title could have been: "Music Theory For Smart People Who Care About Occam's Razor 'n Stuff".

*While, I hasten to add, Westergaard was teaching at Columbia and Princeton in the 1960s and 70s.

I get the impression you didn't keep up with this? I wonder whether, if you had, you would have gradually picked up the ability to compose without needing to resort to brute force. After all, what you did sounds like a lot like ordinary practice - do something, see if it works, if not correct, repeat until your brain starts to pick up on the correct pattern.

Can't speak with authority as a composer here, but I found your piece harmonically okay and spoiled only by lack of logic and form, not lack of melody.

Here's how you may get form: take a few measures of your piece that form a cohesive block, maybe from the beginning to the notes d c#, and play them repeatedly until your ears bleed and you desperately want the music to go somewhere else. Then go somewhere else - do something outrageous on the piano, and then return to your first few measures. Voila, instant verse-chorus form :-) The music should shift when you want it to shift, not just because a new measure has started and demands new chords. There's nothing wrong with repeating a lot and rephrasing a lot.

Here's something born from this kind of methodology. I lack your hearing and harmonic sense, so I just make the music as stupidly obvious and self-similar as possible.

When I was 11, I wanted to write a game in which two players raced to get to the finish of a randomly generated maze. So I thought: How can I make a random maze?

My solution was to use two perpendicular walls to split the game area into four quadrants, and cut a 1-unit opening in a fixed location along each of the four wall sections separating pairs of quadrants.

Then I manually created 20 maze tiles -- 5 for each of the four quadrants, with pathways leading out of the block at the places where there were holes in the center divider. So for every new game, the program randomly drew one of a possible 625 mazes. It seemed random enough to me and others who played.

Rather than a brute force algorithm, this is an example of another "null heuristic": hard coding the solution space into the program.

In a sense, I think that all creative pursuits are served well by the type of "brute force" you're talking about. You write/play/draw something, decide if you like it, and then work from there. However, narrowing down the search space, as you described, can be easier if you leave it to the unconscious. If you've been listening to the style of music you're composing in, or reading the style you're writing in, etc., it should have at least a few heuristics already loaded up. In the case of your melodies, what happens if you just "hum something?"

I generated a segment by pianistic experimentation (rather than from my aural imagination)

This is how I write most of my music. Every once in a while, a melody or chord progression will just show up fully formed, usually on the subway or in the shower, but it's rare. Most of the other songwriters/composers I know work similarly. You say you don't hear new music in your head; a lot of the time, I don't either. I hear it as it comes out of my mouth or speakers in real-time.

I can hear chords. I can hear two-part harmony. Yet my aural imagination wasn't developed enough to generate novel music, except when I was in certain moods or about to fall asleep. And most of what I could hear in my head I found impossible to transcribe.

I had exactly the same problem - and with the same strange exception: Music sometimes start to flow through my head just before I fall asleep, in multipart harmony.

I'd be interested in any ideas as to what makes this mental state different, and how to cultivate it.

I find it's easier to imagine novel music if I restrict myself to a particular genre+style. Just settling on the instruments helps a lot.

What is a problem that you have attempted to solve using brute force, and how well did it work? What kinds of problems seem amenable to brute force, and what kinds don't?

Often if I'm trying to work out an algorithm to solve a problem that is possibly solvable by brute force, I'll start by writing a quick brute-force algorithm to perform the task. Then I'll leave it running in the background while I'm working on a better algorithm - that way, my time to implement the 'more efficient' algorithm is never more than the time it would have taken to brute force it.

But now that I think of it, I don't think I've actually used this solution since the days when computers were a lot slower.

It's better to see heuristic search as an order of enumeration, always exhaustive, but prioritizing specific elements, perhaps those representative of the elements in some simplified representation. When you need to choose from 100 options, it's better to let your intuition do the prioritization, to refine whatever heuristic you are following consciously, instead of starting from 1 up. And conversely, it's important to train intuition to implement good prioritization heuristics, even if you know an explicit algorithm guaranteed to lead to solution.

Knights and knaves puzzles are a perfect example of brute force working. Since every participant must be either a knight (truth-teller) or a knave (liar), and there is (presumably) only one working configuration, then you only have to enumerate two possibilities: that the first person who spoke was a knight, or that the first person who spoke was a knave. Here's one of my own design.

Five natives (call them A, B, C, D, and E) come up to you.

• A says: B is a knave.
• B says: D is a knave.
• C says: B and D are both knaves.
• D says: E is a knave.
• E says: There are even number of knights in this group.

Which are knights, and which are knaves?

Do you have more of this music to share? Perhaps in a format other than embedded flash video? MP3 maybe?

I'm a big fan of this comic on this subject.

excellent piece of music, to my ears. i consider myself a musician (amateur composer?) with an adequate knowledge of theory. even though the notion of a confined search-space was already priming me for a possibly less continuous melody, the melody still struck me, even emotionally. the brute-force method, to generalize from a single example, seems to be excellent (when well-constrained) for writing novel chord progressions. perhaps if you use the second chord of each sequence as the first chord of a new sequence, afterward piecing them together, you could increase continuity even further. i think this piece, however, might say more about the qualities that would satisfy your goals (IOW, a solution to the problem) than the search-space you covered, perhaps? to clean up this particular example, perhaps one might more clearly define what qualifies as a solution in the first place? for example, how "good" did one phrase need to sound before it was acceptable?

I'm unsure whether you were using brute force as a hack to spur your musical imagination and create a good song or whether it was intended to isolate parts of composition you wanted to become more proficient in. Was the goal to create individual good songs or create a better understanding of music to apply later to a non-brute force style? It seems the brute force style is clearly wrongheaded as far as creating fully developed music, but you probably knew that going in (and it does serve as a good example of the null heuristic).

If it was instead a method to better learn music theory, did it work?

I have largely the opposite problem. I am able to compose endless original music in my head on a whim, but all of my attempts to get it out in any form have met with failure. I have recently come up with a possible new approach, but have not yet tried it.

Yet my aural imagination wasn't developed enough to generate novel music, except when I was in certain moods or about to fall asleep. And most of what I could hear in my head I found impossible to transcribe.

I can't speak with certainty about your particular situation, but there's a decent chance you would find these tasks easier if you had a more powerful theory of music at your disposal. Such things exist, and are known to experts; unfortunately, despite the fact that they have been around for a while now, one is still unlikely to be exposed to them without doing graduate work in music, preferably at an elite university. (The linked blog is one of very few places on the internet where I have ever seen such things discussed.)

But let me stop lamenting and instead try to improve the situation, such as can be done within the confines of a blog comment.

One thing I noticed right away about your compositional process, as you described it, was that it was almost entirely local. As you said, you only composed 2-4 measures at a time. (You did mention recaptiulating things, something which requires a bit of global planning, hence the "almost".) This is roughly like trying to paint a picture one detail at a time without knowing what it is you're painting a picture of. Maybe some painters work like this, but I doubt most do. (By the way, this has nothing to do with how abstract the painting is. I suspect that even the most abstract painters have some overall idea of what they want their painting to look like well before they finish it.)

Unfortunately, "traditional" music theory (by which I mean that which the layman can easily find online, or in bookstores, as opposed to what specialists have in their university libraries) does a very poor job of allowing one to think precisely about global phenomena. At its worst, it trains one to ask questions like "what chord should come next?", which is totally the wrong way to think about music.

In the early 20th century, an Austrian named Heinrich Schenker came up with a theory of the right sort: one that explicitly dealt with musical works on all levels of structure, from the most global and far-reaching down to the minutiae of individual notes. Schenker's own intellectual context for his achievement was of course quite different from the modern one in which his work is usually placed, but in any event his ideas were picked up and run with by anglophone music theorists of the postwar era, and now "Schenkerian theory" is a standard, literature-rich academic discipline that most readers probably didn't know about.

This comment is getting too long, so I'll close with a specific recommendation: musically-inclined LWers will definitely want to take a look at Peter Westergaard's book An Introduction to Tonal Theory. It's a favorite at the site I linked to above, and indeed, although it was originally written for college freshmen* I almost think its title could have been: "Music Theory For Smart People Who Care About Occam's Razor 'n Stuff".

*While, I hasten to add, Westergaard was teaching at Columbia and Princeton in the 1960s and 70s.

intermediate durations such as quarter note

Should be "dotted quarter note", I assume.