dan131m

tenorman, I believe you're thinking of the book that Euler wrote about music, not a piece of music. As far as I know Euler never composed any music. * * * I've gone home for the summer, and I won't be back at Caltech until the beginning of next year. I hear the Page lab has an awesome color laser now, though, so I'll be able to print some up in full color.

I've just posted the first in a series of music-theory related posts on my math blog. For one thing, I'd like to know how much sense it makes to non-mathematicians. For another, I want to be sure that I'm not saying anything that's misleading. In order to keep the article under book-length I've had to make some simplifications and gloss a few things over. Finally, I know there are some microtonalists around here, and as the article briefly mentions 19tET and 34tET systems and their relative benefits and downsides, I thought it might spark some interesting discussion (read: internet food fight!) http://mclaury.blogspot.com/2006/06/why-ar...per-octave.html

Okay, here's a (tweaked) automatically-generated MIDI of the progression.

I'm not a pianist, so it's hard for me to work with chord progressions, i.e. the fact that I'm ending on B9. What do you think of the progressions? Edit: Lead Sheet

Bach championed the well tempering system, hence the title "Wohltemperierte Klavier," meaning "Well-tempered Klavier." He indeed lived more than a hundred years ago -- much more than a hundred years ago. Pythagoras lived even more hundreds of years ago -- about two thousand years ago, in fact -- and did not work with tempered scales at all but instead with perfect intervals on stringed instruments. The system we use today, that of equal tempering, has been around for somewhere in the vicinity of 150 years. That piece with heterodyning oscillators sounds exactly like the coil heater in my bathroom heating up. I'm not sure I'd call that music. On a trumpet, you can get at least fifty or sixty distinct, named sounds out of the same note. On a piano, much of the timbre has to do with chords and the relations of different notes. Composing for the instruments is a completely different process, and a composer trained only in the piano and/or strings generally writes very dull wind/brass parts.

Argg. I *knew* I shouldn't have mentioned the hyperinstruments. I've been working on some of the problems people have mentioned off and on; the pieces are supposed to modulate keys but for the most part they don't and I don't understand why; I guess I need to do some more work with the code. I could post the csound intermediary files, but the only thing that would let you do would be to produce the exact same sounds from your computer, since there's no graphical editor that loads them nor anything at present that converts them to MIDI. All I meant by bringing up the hyperinstruments was that my score specified not only the pitch and duration of each note but also included notatation of the timbre. This was both to simulate the effect of multiple instruments and to kill some of the dullness that comes from listening to MIDI simulations with each note articulated exactly like every other note. Beyond that, I'm not up on anything having anything to do with research at the MIT media lab. I've been busier this summer than I expected, so it'll take a while to get the next generation of music out. Eventually I hope to have a computer-aided composition environment that will take as input a melody / harmonic structure and produce sucessive generations of orchestral scores that can be interactively refined by the composer until a close-enough approximation is produced, at which point the parts can be hand-tweaked. Writing 80 different parts moving at the same time is simply too difficult for a single composer. On the other hand, perhaps what would be computer input can simply be put onto a page and the performers can come up with their own parts. In either case I'm going to have to work a bit more to figure out some rules that make sense.

I don't know much about hyperinstruments, really. That wasn't the point of the music anyway; I just wanted something that sounded better than MIDI in terms of expressiveness. If you want to know more I guess just poke around on Google.

The idiomatic vocabulary may be narrower, but it's considerably wider than that of the blues, which is an exceptionally emotional form. I would, however, agree that everything from the baroque to the ninteenth century is often played in an emotionless style nowadays because much of the market for orchestral, chamber, and piano music is for background noise.

It is a standard violin, at least to the extent that a Stradivarius is standard. It's the bow that's special.

Eww.

Umm, classical music certainly has emotion to it...

I was listening to Copland's "Variations on a Shaker Melody" and thinking about all the various ways of presenting the same material, and then I sort of imagined another way of presenting a chord, one in which everyone in the orchestra would have a different part and there would always be something moving. I can kind of hear what I want it to sound like, but it's very difficult to just write it down since I'm thinking of going from one sound in my head to ninety moving lines on paper. I sort of think about it like this: start with a chord and then replace it with the Alberti bass form; the change means that there is more movement. Now sort of do the same thing to the alberti bass to get even more movement, and then continue several more iterations until you can't pick out the individual notes but only a sense of movement, both melodically and in terms of left-right, front-back throughout the orchestra. (There's an excellent sense of the latter in Tchaikovsky's Trepak). Anyway, these recordings are sort of intermediate drafts of what I'm trying to go for, but I'm beginning to believe that I could be headed in the wrong direction; I'm not sure that this sort of thing can be notated traditionally. If anyone is familiar with the jazz composer Charles Mingus and how his pieces are always played with the instruments slightly out of sync with each other, that's part of what I'm going for. He didn't notate that, though, he just taught his band how to play that way, and I think that may be the answer here, if there even is an answer. As to the instrumentation, the pieces are written for what people have (rather unsucesfully) tried to term a hyperinstrument, one for which the pitch, frequency, and exact articulation for each note are notated. Not having such an instrument available. Such instruments do exist; here's a recording of Paganini's 24th caprice played on one. Not having one available myself I simulated one using the Karplus-Strong algorithm in csound. I don't have scores in a format that your computer could read since I wrote most of my own software for this (which only runs on Linux), but if there's really interest in reading them I can probably write some stuff to convert them to PDF files once I can figure out a better way to write out the articulations.

If you want the best printed output you have to use Lilypond. It doesn't have an editor; it's just a typesetter, but you can export to MusicXML from Finale or Sibelius, convert the file to a lilypond input file, and run lilypond on it (although this doesn't take advantage of all the features of lilypond).

Hmm.. apparently I can't get an mp3 down small enough to fit on here, so I put some links up instead. 82bNLB.mp3 1DW2Hu.mp3 gbAm6n.mp3 sUUKyr.mp3 What do you guys think? Any suggestions?