The following problem is considered by Bjorklund, in connection with the operation of certain components (such as high voltage power supplies) of spallation neutron source (SNS) accelerators used in nuclear physics.

Construct a binary sequence of n bits with k one’s, such that the k one’s are distributed as evenly as possible among the zero’s. For example, if n = 16 and k = 4, the solution is [1 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0]. The problem of primary interest is when k and n are relatively prime numbers, i.e., when k and n are evenly divisible only by 1.

This is an excerpt from the somewhat melodramatically titled paper, The Euclidean Algorithm Generates Traditional Musical Rhythms. In short, sequences generated by the equal spacing algorithm described resemble various traditional rhythms, or otherwise sound pretty good. Create Digital Music did a post on various musical applications of it recently, like this neat little sequencer in flash.

Being a SuperCollider chauvinist I was happy to see Fredrik Olofsson had already written a pattern class to generate these sequences. It didn’t support embedding of patterns within it (which is what I really wanted to play with) but after a quick email to the list he patched it. Thanks Fredrik.

Anyway, here is a quick demo, with code after the jump.

Last year I asked Metafilter where I could find more music like Doctor P’s Sweet Shop, a rave nostalgia track that seemed to be mandatory play during the months I’d been going to shows in England. Empath came through with this seemingly canonical but in any case brilliant playlist of early 90’s rave tunes with syncopated piano chords, though I only noticed last week. I recommend Rhythm Quest’s Closer to All Your Dreams (Piano Mix) and Jem 77’s Never Felt This Way in particular.

For more modern day imitators try Skream’s offering (gloriously shameless: TB303 and amen breaks) and the Where were you in ‘92? album by Zomby.

Reminds me of this KLF track. I’m impressed and confused by how evocative even prosaic spoken word recordings can sound with some music behind them.

Artist Golan Levin maintains “An Informal Catalogue of Slit-Scan Video Artworks and Research”.

Popular uses of the effect include the stargate sequence at the end of 2001: A Space Odyssey and (if you’re British) these Dr. Who titles. In many CMOS image sensors, the diachronic polling of pixels is considered a bug, leading smartphone owners to shoot unintentionally avant-garde images. What used to be a pretty involved in-camera effect can now be done in a few lines of code.

An implementation of an idea of Nam Jun Paik’s. If you’re in DC, you should really see the installations of his work at the American Art Museum. They’re intense.

He kept a written log of his life broken up into five minute intervals. He claimed his diary was complete, that every minute over the course of 20 years was carefully accounted for by thousands of words a day, a task that the interviewer characterized as having taken over his life. Buckminster Fuller’s Dymaxion Chronofile, the only similar effort I’m aware of, broke up the day into comparatively slipshod 15 minute chunks. I suppose you have to limit the temporal specificity of your log to avoid falling in to an recursive loop of logging one’s logging…

Reminds me of a very short story by Jorge Luis Borges: On Exactitude in Science.

Do not try and sit down and write a complete song. Songs that have been written in such a way and reached Number One can only be done by the true song writing genius and be delivered by artists with such forceful convincing passion that the world HAS TO listen. You know the sort of thing, “Sailing” by Rod Stewart, “Without You” by Nilsson What the Golden Rules can provide you with is a framework that you can slot the component parts into.

Firstly, it has to have a dance groove that will run all the way through the record and that the current 7″ buying generation will find irresistible. Secondly, it must be no longer than three minutes and thirty seconds (just under 3′20 is preferable). If they are any longer Radio One daytime DJs will start fading early or talking over the end, when the chorus is finally being hammered home – the most important part of any record. Thirdly, it must consist of an intro, a verse, a chorus, second verse, a second chorus, a breakdown section, back into a double length chorus and outro

It is going to be a construction job, fitting bits together. You will have to find the Frankenstein in you to make it work. Your magpie instincts must come to the fore. If you think this just sounds like a recipe for some horrific monster, be reassured by us, all music can only be the sum or part total of what has gone before. Every Number One song ever written is only made up from bits from other songs. There is no lost chord. No changes untried. No extra notes to the scale or hidden beats to the bar. There is no point in searching for originality. In the past, most writers of songs spent months in their lonely rooms strumming their guitars or bands in rehearsals have ground their way through endless riffs before arriving at the song that takes them to the very top. Of course, most of them would be mortally upset to be told that all they were doing was leaving it to chance before they stumbled across the tried and tested. They have to believe it is through this sojourn they arrive at the grail; the great and original song that the world will be unable to resist.

So why don’t all songs sound the same? Why are some artists great, write dozens of classics that move you to tears, say it like it’s never been said before, make you laugh, dance, blow your mind, fall in love, take to the streets and riot? Well, it’s because although the chords, notes, harmonies, beats and words have all been used before their own soul shines through; their personality demands attention. This doesn’t just come via the great vocalist or virtuoso instrumentalist. The Techno sound of Detroit, the most totally linear programmed music ever, lacking any human musicianship in its execution reeks of sweat, sex and desire. The creators of that music just press a few buttons and out comes – a million years of pain and lust.

We await the day with relish that somebody dares to make a dance record that consists of nothing more than an electronically programmed bass drum beat that continues playing the fours monotonously for eight minutes. Then, when somebody else brings one out using exactly the same bass drum sound and at the same beats per minute (B.P.M.), we will all be able to tell which is the best, which inspires the dance floor to fill the fastest, which has the most sex and the most soul.

Maybe we shouldn’t be so hard on them. As Spider Robinson points out…

There are eighty-eight notes. One hundred and seventy-six, if your ear is good enough to pick out quarter tones. Add in rests and so forth, different time signatures. Pick a figure for maximum number of notes a melody can contain. I do not know the figure for the maximum possible number of melodies–too many variables–but I am sure it is quite high.
…
For one thing, a great many of those possible arrays of eighty-eight notes will not be perceived as music, as melody, by the human ear. Perhaps more than half. They will not be hummable, whistleable, listenable–some will be actively unpleasant to hear. Another large fraction will be so similar to each other as to be effectively identical: if you change three notes of the Moonlight Sonata, you have not created something new.

To be fair, there are worse progressions to rip off.