Knotty Oscillator: Breaking knot topology for a new physically-inspired sound generator

Sergey Kasich, and Emir Chacra

Proceedings of the International Conference on New Interfaces for Musical Expression

Abstract

In this paper, we present a new type of 1-D waveguide oscillator inspired by knots, mathematical knot theory, and physical modeling. The main idea behind this study was to model a self-intersecting resonator, imagining it as one crossing of a knot. The number of crossings is known to be an invariant of knot class, which means that we could potentially use knot theory to distinguish variations of such oscillators, while using all the flexibility of geometric parameters. The problem was that the topology of mathematical knots forbids intersections at the points of crossing, and without intersection any knotted waveguide is just a tube. That is why we had to break knot topology to model one crossing as a chain of two three-port junctions. In this text we describe the concepts, the speculations and show practical results, including resulting VST-plugin.

Citation

Sergey Kasich, and Emir Chacra. 2026. Knotty Oscillator: Breaking knot topology for a new physically-inspired sound generator. Proceedings of the International Conference on New Interfaces for Musical Expression. DOI: 10.5281/zenodo.20784090 [PDF]

BibTeX Entry

@inproceedings{nime2026_22,
 abstract = {In this paper, we present a new type of 1-D waveguide oscillator inspired by knots, mathematical knot theory, and physical modeling. The main idea behind this study was to model a self-intersecting resonator, imagining it as one crossing of a knot. The number of crossings is known to be an invariant of knot class, which means that we could potentially use knot theory to distinguish variations of such oscillators, while using all the flexibility of geometric parameters. The problem was that the topology of mathematical knots forbids intersections at the points of crossing, and without intersection any knotted waveguide is just a tube. That is why we had to break knot topology to model one crossing as a chain of two three-port junctions. In this text we describe the concepts, the speculations and show practical results, including resulting VST-plugin.},
 address = {London, United Kingdom},
 articleno = {22},
 author = {Sergey Kasich and Emir Chacra},
 booktitle = {Proceedings of the International Conference on New Interfaces for Musical Expression},
 doi = {10.5281/zenodo.20784090},
 editor = {Benedict Gaster and João Tragtenberg and Anna Xambó and Tom Mitchell},
 issn = {2220-4806},
 month = {June},
 note = {},
 numpages = {6},
 pages = {196--201},
 title = {Knotty Oscillator: Breaking knot topology for a new physically-inspired sound generator},
 track = {Paper},
 url = {http://nime.org/proceedings/2026/nime2026_22.pdf},
 year = {2026}
}