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.

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 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