Geometric Visions:
The Rough Draft

Compositions for the piano by Michael David Crawford,
available for free download in MP3, Ogg Vorbis, FLAC and AAC formats
and as sheet music.

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The sheet music is temporarily unavailable; I need to revise their LilyPond source files to work with the latest version of the LilyPond music engraver.

loosely speaking means "repetition". More precisely, it means a repeated enfolding-within, such as the play within a play in Hamlet, or the play within a play within a play in Rosencrantz and Guildenstern are Dead, itself a play derived from Hamlet.

Recursion is a technique used by mathematicians and computer scientists in which inward repetition, with simple variation, is used to create images of great beauty and complexity, such as the recursive structure of fractals, or fractal images of clouds, mountains, ferns and trees.

Recursion is a technique used by nature in which repetition, with simple variation, is used to create structures of great beauty and complexity, such as the construction of real clouds, real mountains, real ferns and trees from atoms and from the forces that bind them.

Recursion is a technique used by people in which repetition, with simple variation, is used to create beings of great complexity and beauty, such as the growth of human beings from the repeated division of single cells, themselves created by the joining of cells that were once themselves divided.

Download The Album in MP3 and Ogg Vorbis -
and Now Sheet Music!

I am making my recordings of my piano compositions available in MP3 and the new, higher quality Ogg Vorbis format so more people can get to know my music. I place the following license on Geometric Visions because I love my music so, that I know that I must set it Free. Please share my music over the Internet.

Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 2.5 License.

Title Time MP3 Ogg Vorbis MIDI Score
Emergence 2:25 MP3 2.2 MB Ogg 2.1 MB MIDI
Recursion 10:09 MP3 9.3 MB Ogg 9.2 MB MIDI
Sahara 7:23 MP3 6.8 MB Ogg 6.6 MB
As Yet Untitled 2:55 MP3 2.7 MB Ogg - 3 MB

The US Letter links are for printing the score on North American paper. The A4 is for metric paper. The LilyPond files are for typesetting my music with the LilyPond music engraving program.

Do You Like My Music?

Please encourage others to download my songs and help me fulfill my dream of going to music school by linking to this page.

FLAC files are compact disc quality audio that has been compressed with the Free Lossless Audio Codec. If you want to burn your own CD of Geometric Visions, download the FLACs. Your CD burning software might already support FLAC, but if it doesn't, you can find Free Software to convert the FLACs to WAV format by following.

Note: Both the Ogg Vorbis and the MP3 files of Recursion that used to be here had a clicking artifact partway through. This has since been fixed. If you downloaded Recursion before December 18, 2005, please download it again.

About Ogg Vorbis

Ogg Vorbis is a new music format that is free of MP3's patent restrictions. Please try the Oggs first because they're smaller and sound better than MP3. They were encoded at quality level 4.

You may already possess an Ogg Vorbis player. If not, you can download one. You can even get vorbis hardware including portable players.

About the Recordings

I'd like to give grateful acknowledgement to Pete Burnight for providing the recording equipment and producing the album for me.

These recordings were digitized from analog tape with Audacity 1.0 on Mac OS 9, then encoded to MP3 with lame and to Ogg Vorbis with oggenc on Mac OS X.

You can help me to compose and record more music, and to fulfill my dream of going to music school. It won't cost you anything but a few minutes of your time. Here's how:

Please link to this page from your website, your weblog, or from message boards.

That's it.

"But wouldn't you prefer a tip?" you quite reasonably protest.

Yes, I'm grateful for tips, but you would be helping me even more by giving me a link. If you had to do just one or the other, I'd actually rather you linked me than left a tip.

The reason is that I would do better in the long run if more people got to know and love my music. Presently this page only gets about two thousand hits per month, with about three thousand downloads of all my mp3s and oggs put together.

If you were to link this page, your link would not only bring the visitors who clicked it, but it would improve this page's position in the search engines a little. If a lot of people were to link this page, ten times as many people would download my music, maybe even more. Such links would help me more than if everyone who linked me had tipped me instead.

Your tips help, and I'm grateful for them, but they only help until I've spent them. Your link would help me forever. On the web, links are the gifts that keep on giving.

Thank you for your support. I really do appeciate it.

-- Michael David Crawford