Othoundsto: rotating musical houndstooth

05.24.2015 § 1 Comment



Othoundsto is a musical work, and an illustrative example of the power of one of my Fun Musical Ideas: musical yaw.

You can experience a demo of othoundsto on my personal site here: douglasblumeyer.com/othoundsto

The basic idea is that the red bar is the play cursor. Just like the play cursor of any other music sequencing program, it combs across the music, playing notes as it crosses them. Notes the cursor strikes toward its top are higher in pitch, and notes it strikes towards its bottom are lower in pitch. The bar is the “now”; notes to the right are to be played in the future, and notes to the left have already been played. Since it is useful for “now” to stay on the screen, typically sheet music is split into segments which the play cursor reads left to read in rows (like you read words on this page), but another common implementation is for the cursor to hold in place and the music to comb under it, somewhat like a player piano’s reader is fixed in place and the roll winds through it; othoundsto works more like the latter. And of course while othoundsto doesn’t look much like sheet music or piano roll, the same type of information is encoded in it: borders between black area and white area are the notes, with vertices getting the stress and the line segments connecting them treated like glissando ties.

Musical yaw is when the sheet music fluxing across the cursor membrane rotates as it does so. Once it has rotated 90 degrees, all distances which used to affect note durations now affect pitch durations instead, and vice versa. In between 0 and 90 degrees you get some funky effects.



In othoundsto, I chose to link the composition to moments of vertical and/or horizontal alignment. It “teeters”, I call it, rocking back and forth, counter-clockwise and clockwise, with each turn swinging a little further that direction than it did last time, each time stopping at the next furthest angle of alignment. At these alignments, at least two notes either share the same pitch or occur sameltimeously, and there tend accordingly to be a minimum of interval sizes (both pitch and duration).

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Since pitch and duration are not actually related (well, of course they are, but at a scale too distant for this effect) the choice of 300 cents as the equivalent pitch unit to the 1 durational unit (the length of one horizontal line segment) was arbitrary. I could have picked any amount to get a different sound (and you are welcome to experiment). I chose 300 cents because that results in the octave (1200 cents, or the simplest 2:1 frequency ratio) repeating with the 2×2 supertile that houndstooth uses to tile the plane. You can really see how in musical yaw there are two types of duration: the micro-duration, the material of the pattern that can become another property in rotation, and actual time in which such rotation may occur.

An important note is that the play cursor is not a line but just a line segment. If it extended infinitely up and down, there would simply be too much crossing it at a time (even if we account for pitches going out of human hearing range); except at the moments of alignment, every pitch class would get heard. But it also would sound weird if pitches sliding off the top or bottom of the bar just disappeared. Thus, pitch circularity is applied. The pitches that strike in the center of the bar are loudest, and fall off in volume at a rate shaped like a bell curve toward the extreme top and bottom. This way, I can simply infinitely tile the plane with houndsteeth in all directions, and rotate the entire world about a pivot centered on the middle of the play cursor.



Now the thing is that when you’ve rotated this thing 45 degrees one way or the other, the former diagonal lines take precedence as your verticals and horizontals, and they are the square root of 2 the length of the original horizontal and vertical lines. While the square root of two is a beautiful transcendent number, unfortunately as a frequency ratio is not particularly impressive (as aren’t many important transcendent numbers like e and pi).

I admit that I am somewhat disappointed by the harmonic variety one gets out of othoundsto. The moments of alignment do not sound significantly less chromatic to me than the stretches of chaos in between them, even with the ratio between the stress of the vertices upped (de-emphasizing the glissandoing segments joining them).

What I think would make othoundsto more interesting would be a greater variety of timbres (than the one square wave, yes, I know). But seriously, this is a big part of what made houndstooth appeal to me for the purpose of illustrating yaw in the first place: it has just the right amounts of simplicity and complexity when dealing with rotations of itself. In particular, if you set a rule where a voice/timbre may be continuous whenever the line it’s following does not move backwards, you already begin to see a lot of interesting effects:




Here is the repo for othoundsto: http://github.com/DougBlumeyer/othoundsto

The implementation is unfortunately extremely specific to houndstooth at this point. I would love to generalize the yaw tool so that any midi file could be given to it, with instructions for rotations at given times. I would also love for it to be able to generate sheet music that could be used by live performers.

In terms of the existing repo, it would be great if I could have a stronger visual indication of the connection between the collision of the play cursor and lines in the houndstooth pattern – perhaps some glowing yellow points of contact – to help parse the sound. Though ideally I imagined the power of yaw would be being able to perceive the rotation between pitch and duration without needing it to be visualized – I’ll have to keep hacking on that.


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