# Interstate Hydra - Nocturnes

Exactly three years ago I made an ambient EP under the name "Interstate Hydra" and put it up on Bandcamp. Up until now I have kept this alias a secret and only shown these tunes to a few people, but I figured it's been long enough. Here is Nocturnes:

Nocturnes was made entirely in Audacity using the "sound dumplings" method described in an earlier post. This was a total 180 from my usual workflow, which is to synthesize everything with SuperCollider code.

Prior to Nocturnes, I released another EP You Deserve To Be All Alone. The final track "Tennessee" was the first Interstate Hydra track to be produced, and its relative success motivated me to develop these Audacity mashups into a serious project. The first track "We Were Young" opens with the first ever proper sound dumpling created for the project. Other than that, it's fairly barren and not really worth listening to.

"For Ellie" is a single released months after Nocturnes, and is formally the simplest Interstate Hydra track, comprising a row of sound dumplings in arch form.

I don't plan on returning to the Interstate Hydra alias for quite some time, but I hope you enjoy these tracks. Thank you for listening.

# A Closer Look at Clarence Barlow's ISIS

In 2005, Clarence Barlow published a paper on Intra-Samplar Interpolating Sinusoids (ISIS), an audio analysis-synthesis algorithm. It did not make much of a splash, with the paper having only 7 citations in Google Scholar. Nevertheless, it produces some interesting sounds, so let's dive into it.

First, some context. The precursor to ISIS is a technique Barlow calls spectastics. In this method, the short-time Fourier transform is computed of an audio signal, and at each frame, the magnitude spectrum is resampled logarithmically to 12EDO and used as a probability distribution to select a pitch. The pitch sequence forms an extremely rapid melody, which can be synthesized or played on a robotic instrument. Barlow describes the spectasized melody as "remarkably like the original sound recording."

In ISIS, this concept is taken to an extreme by making the "melody" a constant amplitude sine wave whose frequency is changed every sample. Given a digital signal that doesn't exceed ±1, we can interpolate between any two successive samples with a partial cycle of a sine wave. An image helps here; the dots show the sampled digital signal.

For example, if the samples are 0 and 1, as seen in the first two samples in the image, we can interpolate with a quarter sine wave with a period of 4 samples and a frequency of 1/4th the sample rate. There are actually infinitely many ways to do this interpolation. For example, from 0 to 1 we can also have a sine wave that completes 5/4ths of a cycle. We can even assume that the initial phase of the sine wave is $\pi$ and the final phase $5\pi/2$, or have the sine wave going backwards with phase ramping from 0 to $-3\pi/2$.

To resolve the ambiguity, ISIS restricts the frequency to be always nonnegative so the phase never goes backward, and always assumes the phase at every sample point is in the range $[-\pi/2, \pi/2]$ modulo $2\pi$. There are other approaches, such as picking the minimum possible nonnegative frequency or the frequency of minimum absolute value, which may produce interesting alternative sounds. I won't get into these (this is a relatively low-effort post), but feel free to try them out.

# An Approach to Sound Synthesis with L-Systems

An early obsession of mine when I was first learning about music tech was a paper by Stelios Manousakis titled "Non-Standard Sound Synthesis with L-Systems," published 2009 in Leonardo Music Journal. At the time I was a snob about making strictly "academic" electronic music (think Stockhausen or Xenakis) and viewed things like FM and subtractive as too plebian, so synthesis methods that branded themselves as "non-standard" were very alluring. If I could give my younger self some advice, I'd tell him that you have to build foundations as a sound designer first before you can get to the crazy experimental stuff. How are you going to make a cool alien soundscape from another dimension if you can't make a nice snare from scratch? Every good post-tonal composer understands tonality, if only to know how to avoid it. You have to know what rules you're breaking.

With more artistic maturity under my belt, I revisited Manousakis' paper recently and still found it interesting, so I decided to do some riffing on it. In this post, I'll quickly explain what L-systems are (there are lots of better explanations online) and walk through a complete, "minimum viable" system for generating sound with them. Sound examples are embedded.

## L-systems and turtle graphics

Briefly, L-systems (short for "Lindenmayer systems") generate a sequence of words (strings) using rewriting rules applied repeatedly to an initial word called the axiom. A classic L-system is given by the rules a → ab and b → a with the axiom a. At each iteration, each symbol in the word is replaced by the right-hand side of its corresponding rule. The first few iterations of this L-system are:

a
ab
aba
abaab
abaababa
abaababaabaab
abaababaabaababaababa

Most L-systems that are objects of study undergo approximately exponential growth in this way. L-systems can produce simple patterns like abababab as well as aperiodic results like the above, generating apparent randomness while being completely deterministic.

A popular use of L-systems is to apply them to turtle graphics. To do so, each symbol in the L-system corresponds to an instruction to a turtle in 2D space, such as "move forward one unit" or "turn left 30 degrees." Following the instructions sequentially from one string and plotting the turtle's trajectory in space produces a drawing. Organic-looking fractals may result.

In "Non-Standard Sound Synthesis with L-Systems" as well as his more detailed 2006 master's thesis Musical L-Systems, Manousakis proposes a lot of different possibilites to explore, but the basic idea is that he's sonifying turtle graphics produced by L-systems and mapping the turtle's state over time (position, orientation, etc.) to synthesis parameters. These L-systems operate at different time scales, from microsound to the form of an entire piece.

# TopMod, Blender, and Curved Handles

I've been working on a big project using Blender. More on that in a future post, but here's a preview. The project has gotten me into a 3D art headspace, and I took a detour recently from this major project to work on a small one.

Blender isn't my first exposure to 3D. When I was a kid, I played around a lot with POV-Ray -- an outdated program even back when I was using it, but still a fun piece of history. I also found out about something called TopMod, which is an obscure research 3D modeling program. I was interested in it primarily because of Bathsheba Grossman, who used it in a series of lovely steel sculptures based on regular polyhedra.

The core idea of TopMod is that, unlike other 3D modeling programs, meshes are always valid 2-manifolds, lacking open edges and other anomalies like doubled faces. This is ensured with a data structure called the Doubly Linked Face List or DLFL. In practice, TopMod is really a quirky collection of miscellaneous modeling algorithms developed by Ergun Akleman's grad students. These features give a distinctive look to the many sculptures and artworks made with TopMod. I identify the following as the most important:

Subdivision surfaces. TopMod implements the well-known Catmull-Clark subdivision surface algorithm, which rounds off the edges of a mesh. However, it also has a lesser known subsurf algorithm called Doo-Sabin. To my eyes, Doo-Sabin has a "mathematical" look compared to the more organic Catmull-Clark.

Rind modeling. This feature makes the mesh into a thin crust, and punches holes in that crust according to a selected set of faces.

Curved handles. In this tool, the user selects two faces of the mesh, and TopMod interpolates between those two polygons while creating a loop-like trajectory that connects them. The user also picks a representative vertex from each of the two polygons. Selecting different vertices allows adding a "twist" to the handle.

The combination of these three features, as pointed out by Akleman et al., allows creating a family of cool-looking sculptures in just a few steps:

3. Perform one iteration of Doo-Sabin.

4. Apply rind modeling, removing contiguous loops of quadrilateral faces.

5. Perform one or more iterations of Catmull-Clark or Doo-Sabin.

(I would like to highlight step 3 to point out that while Doo-Sabin and Catmull-Clark look similar to each other in a final, smooth mesh, they produce very different results if you start manipulating the individual polygons they produce, and the choice of Doo-Sabin is critical for the "TopMod look.")

TopMod has other features, but this workflow and variants thereof are pretty much the reason people use TopMod. The program also has the benefit of being easy to learn and use.

The catch to all this is that, unfortunately, TopMod doesn't seem to have much of a future. The GitHub has gone dormant and new features haven't been added in a long time. Plus, it only seems to support Windows, and experienced users know it crashes a lot. It would be a shame if the artistic processes that TopMod pioneered were to die with the software, so I looked into ways of emulating the TopMod workflow in Blender. Let's go feature by feature.

First we have subdivision surfaces. Blender's Subdivision Surface modifier only supports Catmull-Clark (and a "Simple" mode that subdivides faces without actually smoothing out the mesh). However, a Doo-Sabin implementation is out there, and I can confirm that it works in Blender 3.3. An issue is that this Doo-Sabin implementation seems to produce duplicated vertices, so you have to go to edit mode and hit Mesh -> Merge -> By Distance, or you'll get wacky results doing operations downstream. This may be fixable in the Doo-Sabin code if someone wants to take a stab at it. Also worth noting is that this implementation of Doo-Sabin is an operator, not a modifier, so it is destructive.

EDIT: Turns out, Doo-Sabin can be done without an addon, using Geometry Nodes! This StackExchange answer shows how, using the setup in the image below: a Subdivide Mesh (not a Subdivision Surface) followed by a Dual Mesh. The Geometry Nodes modifier can then be applied to start manipulating the individual polygons in the mesh.

Rind modeling can be accomplished by adding a Solidify modifier, entering face select mode, and simply removing the faces where you want holes punched. An advantage over TopMod is that modifiers are nondestructive, so you can create holes in a piecemeal fashion and see the effects interactively. To actually select the faces for rind modeling, TopMod has a tool to speed up the process called "Select Face Loop;" the equivalent in Blender's edit mode is entering face select mode and holding down Alt while clicking an edge.

Curved handles have no equivalent in Blender. There is an unresolved question on the Blender StackExchange about it. To compensate for this, I spent the past few days making a new Blender addon called blender-handle. It's a direct port of code in TopMod and is therefore under the same license as TopMod, GPL.

My tool is a little awkward to use -- it requires you to select two vertices and then two faces in that order. TopMod, by comparison, requires only two well-placed clicks to create a handle. I'm open to suggestions from more experienced Blender users on how to improve the workflow. That said, this tool also has an advantage over TopMod's equivalent: parameters can be adjusted with real-time feedback in the 3D view, instead of having to set all the parameters prior to handle creation as TopMod requires. The more immediate the feedback, the more expressive an artistic tool is.

Installation and usage instructions are available at the README. blender-handle is 100% robust software entirely devoid of bugs of any kind, and does not have a seemingly intermittent problem where sometimes face normals are inverted.

The rest of this post will be a nerdy dive into the math of the handle algorithm, so I'll put that after the break. Enjoy this thing I made in Blender with the above methods (dodecahedron base, six handles with 72-degree twists, Doo-Sabin, rind modeling, then Catmull-Clark):

# Sound Dumplings: a Sound Collage Workflow

Most of the music I produce doesn't use any samples. I'm not prejudiced against sample-based workflows in any way; I just like the challenge of doing everything in SuperCollider, which naturally encourages synthesis-only workflows (as sample auditioning is far more awkward than it is in a DAW). But sometimes, it's fun and rewarding to try a process that's the diametric opposite of whatever you do normally.

Two things happened in 2019 that led me to the path of samples. The first was that I started making some mixes, solely for my own listening enjoyment, that mostly consisted of ambient and classical music, pitch shifted in Ardour so they were all in key and required no special transition work. I only did a few of these mixes, but with the later ones I experimented a bit with mashing up multiple tracks. The second was that I caught up to the rest of the electronic music fanbase and discovered Burial's LPs. I was wowed by his use of Sound Forge, a relatively primitive audio editor.

Not long into my Burial phase, I decided I'd try making sample-based ambient music entirely in Audacity. I grabbed tracks from my MP3 collection (plus a few pirated via youtube-dl), used "Change Speed" to repitch them so they were all in key, threw a few other effects on there, and arranged them together into a piece. I liked the result, and I started making more tracks and refining my process.

Soon I hit on a workflow that I liked a lot. I call this workflow sound dumplings. A sound dumpling is created by the following process:

1. Grab a number of samples, each at least a few seconds long, that each fit in a diatonic scale and don't have any strong rhythmic pulse.

3. Use Audacity's "Change Speed" to get them all in a desired key. Use variable speed playback, not pitch shifting or time stretching.

4. Arrange the samples into a single gesture that increases in density, reaches a peak, then decreases in density. It's dense in the middle -- hence, dumpling.

5. Bounce the sound dumpling to a single track and normalize it.

The step that is most difficult is repitching. A semitone up is a ratio of 1.059, and a semitone down is 0.944. Memorize those and keep doing them until the sample sounds in key, and use 1.5 (a fifth up) and 0.667 (a fifth down) for larger jumps. It's better to repitch down than up if you can -- particularly with samples containing vocals, "chipmunk" effects can sound grating. Technically repeated applications of "Change Speed" will degrade quality compared to a single run, but embrace your imperfections. Speaking of imperfections, don't fuss too much about the fades sounding unnatural. You can just hide it by piling on more samples.

Most sound dumplings are at least 30 seconds long. Once you have a few sound dumplings, it is straightforward to arrange them into a piece. Since all your sound dumplings are in the same key, they can overlap arbitrarily. I like to use a formal structure that repeats but with slight reordering. For example, if I have five sound dumplings numbered 1 through 5, I could start with a 123132 A section, then a 454 B section, then 321 for the recap. The formal process is modular since everything sounds good with everything.

Sound dumplings are essentially a process for creating diatonic sound collages, and they allow working quickly and intuitively. I think of them as an approach to manufacturing music as opposed to building everything up from scratch, although plenty of creativity is involved in sample curation. Aside from the obvious choices of ambient and classical music, searching for the right terms on YouTube (like "a cappella" and "violin solo") and sorting by most recent uploads can get you far. In a few cases, I sampled my previous sound dumpling work to create extra-dense dumplings.

The tracks I've produced with this process are some of my favorite music I've made. However, like my mixes they were created for personal listening and I only share them with friends, so I won't be posting them here. (EDIT: I changed my mind, see my music as Interstate Hydra.) If you do want to hear examples of sound dumpling music, I recommend checking out my friend Nathan Turczan's work under the name Equuipment. He took my sound dumpling idea and expanded on it by introducing key changes and automated collaging of samples in SuperCollider, and the results are very colorful and interesting.

If you make a sound dumpling track, feel free to send it my way. I'd be interested to hear it.

# Matrix Modular Synthesis

Today's blog post is about a feedback-based approach to experimental sound synthesis that arises from the union of two unrelated inspirations.

## Inspiration 1: Buchla Music Easel

The Buchla Music Easel is a modular synthesizer I've always admired for its visual appearance, almost more so than its sound. I mean, look at it! Candy-colored sliders, knobs, and banana jacks! It has many modules that are well explored in this video by Under the Big Tree, and its standout features in my view are two oscillators (one a "complex oscillator" with a wavefolder integrated), two of the famous vactrol-based lowpass gates, and a five-step sequencer. The video I linked says that "the whole is greater than the sum of the parts" with the Easel -- I'll take his word for it given the price tag.

The Music Easel is built with live performance in mind, which encompasses live knob twiddling, live patching, and playing the capacitive touch keyboard. Artists such as Kaitlyn Aurelia Smith have used this synth to create ambient tonal music, which appears tricky due to the delicate nature of pitch on the instrument. Others have created more out-there and noisy sounds on the Easel, which offers choices between built-in routing and flexible patching between modules and enables a variety of feedback configurations for your bleep-bloop-fizz-fuzz needs.

# Resource: "The Tube Screamer's Secret"

A few years ago I bookmarked Boğaç Topaktaş' 2005 article titled "The Tube Screamer's Secret," but today I was dismayed to discover that the domain had expired. This ensures that the page is now nearly impossible to find unless you already know the URL. I don't normally make posts that are just a link to a third party, but this valuable resource might be forgotten otherwise. Here's the page in the Wayback Machine:

https://web.archive.org/web/20180127031808/http://bteaudio.com/articles/TSS/TSS.html

# Pulsar Synthesis

Curtis Roads' book Microsound is a must-read for any nerdy music technologist. Despite its age, it contains many exciting techniques under the granular synthesis umbrella that still sound fresh and experimental. I recently started exploring one of these methods, called pulsar synthesis, and thought it'd be fun to write my own review of it and demonstrate how to accomplish it in SuperCollider or any similar environment.

Pulsar synthesis produces periodic oscillations by alternating between a short, arbitrary waveform called the pulsaret (after "wavelet") and a span of silence. The reciprocal of the pulsaret's length is the formant frequency, which is manipulated independently of the fundamental frequency by changing the speed of the pulsaret's playback and adjusting the silence duration to maintain the fundamental. Roads calls this "pulsaret-width modulation" or PulWM. If the formant frequency dips below the fundamental frequency, the silence disappears and the pulsarets can either be truncated (regular PulWM) or overlapped (overlapped PulWM or OPulWM). Roads describes OPulWM as "a more subtle effect" due to phase cancellation.

The pulsaret signal can be anything. The book suggests the following, among others: a single sine wave cycle, multiple sine wave periods concatenated, and a bandlimited impulse (sinc function). Another option is to take the waveform from live input, transferring the timbre of input over to a quasiperiodic signal and behaving slightly more like an effect than a synth.

# "Switching" in Procedural Generation

A friend recently told me of an idea he had: what if a video game employing procedural generation could legitimately surprise its own developer? This applies to music as well -- I wish I had such moments more often in my algorithmic composition work.

Pondering this question made me think back to a recent video by producer Ned Rush: Melodic Phrase Generator in Ableton Live 11. In it, the artist starts with four C notes in the piano roll and uses a variety of MIDI filters to transform them into a shimmering pandiatonic texture with lots of variation. It's worth a watch, but one moment that especially made me think is where he pulls out an arpeggiator and maps a random control signal to its "Style" setting (timestamp). Ableton Live allows mapping control signals to discrete popup menus as well as continuous knobs, so this causes the arpeggiator to switch randomly between 18 arpeggiation styles, including Up, Down, UpDown, Converge, Diverge, Pinky Up, Chord Trigger, Random, and more.

This was the most important part of Ned Rush's patch, as these styles individually sound good and different from each other, so switching between them randomly sounds both good and diverse. From this, we can gather a valuable technique for procedural generation: switching or collaging among many individual algorithms, each of which has considerable care put into it. Imagine a "synthesizer" (or level generator, or whatever) with many different switched modes, coated in layers of "effects," each with their own switched modes. Even with simple, haphazard randomness controlling the modes, the system will explore numerous combinatorial varieties. If this wears itself out quickly, then the modes can be grouped into categories, with switching within a category happening on a smaller time scale (or space scale) and switching between categories happening on a larger time scale.

Switching is a handy way to aid in achieving those elusive moments where a generative system does something truly unexpected. I recommend experimenting with it next time you play with algorithmic creativity.

# Integer Ring Modulation

When I think of ring modulation -- or multiplication of two bipolar audio signals -- I usually think of a complex, polyphonic signal being ring modulated by an unrelated sine wave, producing an inharmonic effect. Indeed, this is what "ring modulator" means in many synthesizers' effect racks. I associate it with early electronic music and frankly find it a little cheesy, so I don't use it often.

But if both signals are periodic and their frequencies are small integer multiples of a common fundamental, the resulting sound is harmonic. Mathematically this is no surprise, but the timbres you can get out of this are pretty compelling.

I tend to get the best results from pulse waves, in which case ring modulation is identical to an XOR gate (plus an additional inversion). Here's a 100 Hz square wave multiplied by a second square wave that steps from 100 Hz, 200 Hz, etc. to 2000 Hz and back.

As usual, here is SuperCollider code:

(
{
var freq, snd;
freq = 100;
snd = Pulse.ar(freq) * Pulse.ar(freq * LFTri.ar(0.3, 3).linlin(-1, 1, 1, 20).round);
snd ! 2;
)