new page of polynomial set root plots and sound

I added a new page to my website.

On it are plots of the roots of all the polynomials in certain sets arising from a given polynomial, P, by taking each coefficient of P and multiplying it by 1 or -1 to create a new polynomial. The plots are all roots of all polynomials generated in this was from a given P. The first is where all of the coefficients of P are 1, so the set of polynomials generated are Littlewood polynomials.

In addition to the plots, I generated sound for each one by treating each root as a sound event. Time runs "right to left" (so the real part of the root determines when its sound event occurs) and the pitch (frequency) is determined (linearly) by the imaginary part of the root. The result is a sound whose spectrogram looks like the plot of the roots.

The range of real parts varies, so the duration of the sounds varies. The extreme case is where the coefficients of P are the factorials of the degree; with such huge coefficients, the roots are quite small, and the result is that the sound is quite short.

trombonscalator

A new track. I've been posting something every day on Soundcloud, but I really like this one I made today. I used a piece of a field recording I did that includes a trombone and an escalator. This track is entirely in the spirit of tape music: though done digitally, it could, theoretically be done entirely with tape (with many, many, many splices). I hope you enjoy it! https://soundcloud.com/matthew-m-conroy/trombonscalator

Disquiet Junto 0607

A piece for Disquiet Junto 0607 .

My thoughts went like this.

We cannot be 40% silent at a single point in time, so we have to define the amount of silence at a point in terms of the sound that is happening around that point. I chose to define the percentage of silence at a point in time as the percentage of silence (time with zero amplitude) in a 14 second interval centered at that point in time.

Also, it seems to me that we do not actually hear silence unless it is of sufficient length (e.g., we do not hear “silence” when there is a 0.001 second gap in a sound). For this piece, I defined silence to be an interval of at least 0.5 seconds of zero amplitude. I could see an argument for requiring longer gaps than this, though, since with short “silences”, I feel that we are still hearing the sound that came before it, and not actually hearing the silence.

So then I randomly threw 25000 sound events onto a 5 minute span of silence, checking before each one that the percentage of sound at that point would not go above that required by the instructions (i.e., a linear increase from 0 to 40% sound at the midpoint and linearly back to zero for the second half).

The sound events are guitar samples I’ve made, pitched and filtered in various ways. There are many points where the samples “pile up” and make a noticeably louder occurrence; this happens because once a sound has been placed, another sound can be placed “on top” of it, with no reduction in the amount of silence.

It was fun coding this, and I’ve grown to like the result after numerous tweeks and re-listens.

Disquiet Junto 0605

The assignment was a track that is half sound, half silence. I reasoned like this. A piece with 50% sound and 50% silence will have periods of sound (with durations of, say, a1,a2,…,an) alternating with periods of silence (with durations of, say, b1,b2,…,bn), with a1+a2+…+an=b1+b2+…+bn. We can view these in pairs: (a1,b1),(a2,b2),…,(an,bn). Given a set of durations (say {6,7,8,9,10} seconds), we might want every pair from this set to appear among (a1,b1),…,(an,bn). (In other words, we might want {(a1,b1),(a2,b2),…,(an,bn)} = {6,7,8,9,10} x {6,7,8,9,10}=S, say.) So we essentially want to enumerate S; one way to do that is to use a knight’s tour of S. This has the advantage of not changing the durations too drastically (since the knight is limited in its movement) while guaranteeing that the durations both change from pair to pair (e.g., we would not go from (6,7) to (6,9)). So that’s what I did to generate the lengths of the sound bits and the lengths of the silence bits. The sounds themselves were made with Csound using a few recordings of metal objects I’ve made, with a bunch of filtering, ring modulation, and intentional clipping to get some variety. I made the sound bits decay quadratically; when I listen, it is not clear to me when the silence starts, which keeps things fun.

About Disquiet Junto: disquiet.com/2013/04/25/disquiet-junto-faq/

Disquiet Junto 0604

New track for Disquiet Junto 0604. On Sunday, I walked 5 km to a ballot drop-off location to vote for what I hope is improved representation on the city council, and I took a bunch of pictures of clouds on the way. I then rewrote from scratch my very old image-to-sound code that generates a Csound score with thousands of sine wave oscillators: the oscillators are gated depending on the content of the image, so the resulting sound has a spectrogram that looks like the original image. I used two different scales: one that creates comparatively short (time-wise) and low bandwidth sounds, and another that makes longer, wider bandwidth sounds. I used a bunch of images and made a bunch of sounds this way, and then mixed them “by hand” in Audacity.

Disquiet Junto 0601

For Disquiet Junto 601, I threw a die in my bathtub and recorded the throws with an AT822 stereo microphone (through a Zoom H5) that I bought (used) years ago but had never used (I’m not really much of a microphone person). Then, using Csound, I placed copies of each recording across about 3.5 minutes, with various densities, filtering, playback speeds and amplitudes. The rolls determined for how much of the piece each recording appears: the rolls were 3,5,6,5,6,3, so the 6 rolls appear throughout, the 5’s appear up to 5/6 of the piece and the 3’s cut off at the half-way point.

More info on Disquiet Junto 601: Disquiet Junto 0601