Skip to the Main Content

Note:These pages make extensive use of the latest XHTML and CSS Standards. They ought to look great in any standards-compliant modern browser. Unfortunately, they will probably look horrible in older browsers, like Netscape 4.x and IE 4.x. Moreover, many posts use MathML, which is, currently only supported in Mozilla. My best suggestion (and you will thank me when surfing an ever-increasing number of sites on the web which have been crafted to use the new standards) is to upgrade to the latest version of your browser. If that's not possible, consider moving to the Standards-compliant and open-source Mozilla browser.

June 2, 2009

Treq Lila

Posted by John Baez

I should have been finishing a paper, but instead I finished an album.



I’ve been working on this for a couple of years now, on and off — mainly off. It just took a couple days to finish up.

The interesting thing about this album is that I didn’t write any of the melodies! Instead, I evolved them with the help of Wolframtones, a program that creates musical compositions using cellular automata. For example, the title track is based on the cellular automaton shown on the album cover.

You can read more and download individual tunes or the whole album here.

I’ll warn you right now that it’s nothing like pop music. You have to like weird stuff.

Posted at June 2, 2009 9:24 PM UTC

TrackBack URL for this Entry:   http://golem.ph.utexas.edu/cgi-bin/MT-3.0/dxy-tb.fcgi/1982

8 Comments & 0 Trackbacks

Re: Treq Lila

You can read more and download individual tunes or the whole album here.

Not working for me!

Posted by: Jamie Vicary on June 2, 2009 11:05 PM | Permalink | Reply to this

Re: Treq Lila

Posted by: Toby Bartels on June 2, 2009 11:22 PM | Permalink | Reply to this

Re: Treq Lila

Thanks for giving the right URL, Toby. I fixed my blog entry. But now the website has crashed, doubtless due to the extraordinary surge of people downloading Treq Lila.

(Yeah, right.)

So, right now you can’t even see the picture of the album cover on my blog entry. When it comes back, that means the website is back up.

Posted by: John Baez on June 3, 2009 6:16 AM | Permalink | Reply to this

Re: Treq Lila

Interesting stuff. You should have joined us at DIMACS, Algorithmic Mathematical Art. See especially the previews on this page . Note that Dmitri Tymozcko and John Kiehl were there. (I imagine that your cousin has had some interactions with John, particularly if she recorded in NYC).

In particular, look at the graphic for John’s talk.

My summer plans include reading Dmitri’s book and having further discussions with Alissa about harmonic structures.

Posted by: Scott Carter on June 4, 2009 4:13 PM | Permalink | Reply to this

Re: Treq Lila

Heck, why make people click a link? Our blog should be full of beautiful stuff. Here’s the graphic for Dmitri Tymoczko’s talk:


and here’s the one for John Kiehl’s:

I got an email from Kiehl after he listened to Treq Lila; I hope it’s the beginning of a conversation.

My summer plans include reading Dmitri’s book and having further discussions with Alissa about harmonic structures.

Cool. Is she visiting you after her stay in Bonn? What sort of harmony theory stuff are you talking about with her?

Posted by: John Baez on June 6, 2009 9:21 PM | Permalink | Reply to this

Re: Treq Lila

Alissa and I don’t have anything specific music theory planned yet. To be honest I haven’t read her paper, and only skimmed your associated TWF. I haven’t had correspondence with her since my going to Trieste.

There is a nice quandle that covers the dihedral quandle, though, and it might be interesting to relate that to dihedral actions in chord space.

So far Dmitri’s book has been very interesting. For the hard core theorists, there is an article on his home page. The book is much more gentle both to the mathematician with an interest in music and the musician who is trying to learn the math beyond the theory.

Dmitri describes 5 items that he thinks are necessary for good music. (1) Conjunct melodic motion: melodies take small steps within the associated scales, (2) Acoustic Consonance: Consonant harmonies are preferred to dissonant ones and form stable points, (3) Harmonic Consistency: harmonies within a passage tend to be similar, (4) Limited Macroharmony: Over moderate time spans a relatively small number of tones are used, (5) Centricity: Over moderate spans of music one or more notes is more prominent than others.

A corollary is, I think, that there will be repeated patterns, motifs, or phrases, but that repetition without change leads to tedium.

His central thesis, however, seems to be that one can analyze and compose using the quotient of the n-torus by symmetries. The n-torus is the space of all ordered n-chords, and the quotient considers inversions as equivalent. Chords are connected by one step paths, where (using Dmitri’s example) CEG (C major) is one step away from BEG (e minor).

Posted by: Scott Carter on June 7, 2009 7:18 PM | Permalink | Reply to this

Re: Treq Lila

These tracks are actually pretty enjoyable (more so than I would have expected). But do I detect a trace of neo-Riemannian harmonic structure here? (just kidding)

Posted by: Charles G Waldman on June 5, 2009 4:58 PM | Permalink | Reply to this

Re: Treq Lila

Charles wrote:

These tracks are actually pretty enjoyable (more so than I would have expected).

Thanks! But I don’t think this is the review I’ll use as a blurb on the album cover.

To me music is no use if not enjoyable — I’ve no use for music as a dry intellectual exercise. However, I enjoy many kinds of music, from Bach’s Art of Fugue to Billie Holiday’s These Foolish Things to Led Zeppelin’s Achilles Last Stand to Gnawa trance drumming to Thomas Köner’s Permafrost and Alvin Lucier’s Music on a Long Thin Wire. Indeed, one thing I love about music is how it can mean so many things.

Posted by: John Baez on June 6, 2009 6:28 PM | Permalink | Reply to this

Post a New Comment