The work with spatial audio has grown almost naturally out of my interests in algebraic geometry.
The work is centered around algorithmic spatialization. Waveguide meshes are modeled from projections
of higher dimesional algebraic and geometric structures. At this moment the work is realized as very
large Pure Data externals. Encoding to ambisonics happens directly in the objects.
Hypercubes dimensions 4-8 graphical animation: https://vimeo.com/282543243
Compositions
For binaural renderings it is necessary to listen with headphones. Stereo can be played on speakers or via headphones.
Room Extractions #1
7th order ambisonics fixed media + stereo version. 2024-25.
A work from an spatial synthesis artist residency at ICST, Zurich, 2024.
Quite some additional work is done in 2025 for presentation at the ICST 20 yrs. anniversary.
It can be considered a framework for a poetic and algorithmic transcription of data from a room into immersive audio.
The symmetry and geometry of the 6D hypercube is used to reflect the room data into a geometric fantasy in 6 dimensions.
There are many creative choices to make when navigating through the vast possibilities these geometries offer.
And there is a personal experience of the room that influences the path. The ICST is located in an huge former
industrial building in Zurich, which used to be a squat. Half way through the residency I realized that it was exactly
in this building I had been back in 2006, performing at some experimental festival. Hardcore, but also great.
The best I ever heard on brain waves was there… A special stereo version was made for an ICST release.
Binaural rendering from 3D version, only for headphones:
Stereo version produced for ICST anniversary release:
Phe noType
7th order ambisonics fixed media. 4 min 32. 2024-25.
Cutups from current scientific publications on genetics.
Voice: Walker Smith, recorded at CCRMA Stanford November 2024. Finished in Denmark 2025. All spatialization and other
audio processes take place through a gigantic audio effect wave guide mesh structured after the 8D hypercube.
Binaural rendering, only for headphones:
Netop som Digter
2025. Computer generated spatial audio and acoustic voice. 7th order ambisonics. 13Min45.
2025. 7th order ambisonics fixed media and live acoustic voice. 14 min.
Performed at NOTAM Oslo April and SMC conference at Mumuth Graz July 2025. The generative computer music structures explore
the mathematical object : the E8. The 3D projection space is constantly rotated which gives new views on the E8.
There are as well transformations between affine and projective 3-space, which include some wraps around infinities. The work is realized as one large external object for Pure Data. This object is handling all audio processes and the encoding to ambisonics. The work is generated offline due to computational intensity.
The fixed media is performed with acoustic voice.
The text for the vocal performance is taken from S. Kierkegaard’s book ‘Gjentagelsen’ / ‘The Repetition’, written under the pseudonym
Constantin Constantius. The book lingers over the question whether anything repeats and if anything can be repeated. The fragments are
taken towards the end where the writer speaks about a poet he has invented for this book, a poet who writes poetry of his own.
Regarding the recording, then it is sort of a ‘demo reference’ , where the vocals are spatialized algorithmically.
In live performance the voice must be acoustic in space
Binaural rendering, only for headphones:
ES QC – using mathematical quasicrystals to inform spatial audio
Concert presentation at the Speculative Synthesis Symposium, Graz, September 2024.
7th order ambisonics and acoustic voice. An algorithmic spatial audio work which explores non-periodic order
and quasicrystals for synthesis and spatialization. The structure of the famous 4-dimensional Elser-Sloane quasicrystal
forms the base. There is a short paper as well :
https://speculativesoundsynthesis.iem.sh/symposium/docs/proceedings/broch/
The piece was performed with a little bit of acoustic vocals, so well.. you are invited to hum along with this new sort of synthesis.
Binaural rendering, only for headphones:
Video from Speculative Synthesis Concert at Mumuth, Graz
Alloys of the Vast
7th order ambisonics 9min27. Algorithmic compositions based on the mathematical object : 'the E8'. This work has been under way for a few years.
And it will most likely be ongoing.
It includes developing quite some machinery to handle and approach this gigantic and awe-inspiring structure. Everything
is generated with data from the rotating and projected E8: Synthesis, spatialization and time structures are all one.
I have aimed at a purety wrt. composing the chosen algorithms since the E8 is vast and divinely rich in possibilities in itself.
The title has a small reference to mathematical quasicrystals though these do no appear directly here.
Alloys 2, 2024
Binaural rendering, only for headphones:
Alloys 1, 2023
Binaural rendering, only for headphones:
Stereo:
graphical animation of the Gosset polytope (E8) - no sound - made to test some of the math. Though it is a 3D projection it
explores the Coxeter plane and other planes of unusual symmetry.
Akerselvas Sang
Made in Oslo, at NOTAM, september 2022. The sound is based on a mono recording of the Aker river, a river which runs
down through Oslo, and passes right behind the NOTAM studio. Techniques include some subtractive synthesis and large
waveguide meshes for resonance and spatialization. There is a fast moving algoritmically generated spectral / integer series
which control the filters and some amount of entrainment is happening in the waveguide meshes
Binaural rendering, only for headphones:
Stereo:
The Copenhagen Interpretation
The work fluctuates between noise and spectral harmonies. Double bass : Jimmi Roger Pedersen - a variation on the Danish song:
Jeg ved en laerkerede by C. Nielsen.
Text qoutes from the works of S. Kierkegaard. Field recordings from Copenhagen.
Ambisonics. Finished 2024.
Binaural rendering, only for headphones:
Stereo:
17-19
Harmonic structures from the numbers 17 and 19. Recorded for 7th order ambisonics - 6min01
Finished 2022 January.
Binaural rendering for headphones:
Stereo version:
Forfatteren - The Author
2022-2024 , 7min30 , original 7th order ambisonics
Spatial Audio composition with text excerpts from Om min Forfatter-Virksomhed and Synspunktet for min Forfatter-Virksomhed
by Søren Kierkegaard (!! Danish text!!)
This piece came about partly as an early study for a music theater project, and partly as an application of new developments in spatial audio.
Recordings of the text are let loose in the 8D hypercube waveguide mesh. This is a very large reverberation effect,
which creates instrumental room and algorithmic spatialization, - and a bit of artifacts plus a non-linear distance mapping in the 3D projection.
Binaural rendering, only for headphones:
Stereo:
7sphere Revisited,
I revisited the world of the octonions and refined the tools.
The unit length octonions make up the unit 7sphere.
In a way one could say that this is a field recording on the
7sphere. I know that things are well behaved within a certain framework, but the
way it is set up, then there are always new things to encounter. The piece was made during an artist residency at IEM in 2021.
It was played at ICMC 2022 Limerick
and a few more places.
Stereo :
Binaural :
picture of the IEM CUBE. Studio for spatial audio.
Thanks to the IEM institute for letting me work there the summer of 2021
Entartung Entkörperung Entgeistigung,
The harmonic structure for this piece started by looking at some tiny fragments
from Arnold Schönberg's opus 23 which is now written exactly 100 years ago.
After that the movements transformed much and got woven into a microtonal
spectral structure. Anyway, every time I look at some of Schönberg's music I
perceive that he has had premonitions of jazz to come up through the century. So
maybe that is what it became: little echos of distant premonitions. The text is by
Rudolf Steiner, from lectures 1916 and 1917. So the piece brings together some very
different, both highly visionary, aspects of Austrian culture. Made at IEM 2021.
Voice: Jannick Knyrim. text and English translation
Stereo :
Binaural :
E8 work in progress
_
The E8 is a mathematical object which was discovered more than 100 years ago.
But just the last few decades it has become very popular among physicists who try
to use it to explain various mysteries.
Algorithmically the 'sound test' follows more or less what is happening
in this animation: Gosset polytope - E8 - 3D projections .
Stereo :
Binaural :
Syntropy 77
Binaural rendering of composition for 5th order ambisonics - 5min15
The compositional structure for this piece was made winter 2021. But it is here reworked at the IEM summer 2021.
Spatialization is realized through the Simplex23 waveguide mesh described on the IEM blog. The piece explores
harmonic structures generated from the numbers 7 and 11, which usually do not have a place in traditional
tuning systems. The synthesis has bits af quasicrystal waveforms, non-periodic order.
CCRMA 2020 Stanford
7sphere Karma, 2020, practically everything in this piece is
generated with the 8 dimensional octonion algebra. FM synthesis plays an
important role, here octonion orbits are modulating the phases of other
octonion orbits. The piece was made during
a stay at CCRMA, Stanford
binaural:
Syntropy 7times8, 2020, A spectral composition
binaural:
Efflux, 2019, The 6 dimensional hypercube rotated and projected
onto 3D creates the resonant framework, the synthesis
has bits from mathematical quasicrystals
binaural:
Attempt at plotting the symmetry of the 240 largest 3D tetrahedra, which are inside the 6D hypercube. The symmetry is used in transformations of space in the
test file for processed vocals : Det Almene.
Det Almene. (The Ordinary) A test. 1st order ambisonics recording of vocals is put into a resonance unit
modeled after the 6D hypercube. There are many options for placing and transforming a 3D tetrahedron inside the 6D structure.
The recording and programming is made during a residency at IAC Malmoe, January 2026.
The space is perspective which creates wraps around a geometric infinity as the projection rotates, That is left audible.
The text is a fragment from S. Kerkegaard's 'Gjentagelsen' (The Repetion). The text is about the ordinary and the exception. The one is possibly inside the other.
binaural:
