Additive Synthesis and Spectral Modeling are in detail introduced in the corresponding sections of the Sound Synthesis Introduction. Since sounds are created by combining large numbers of spectral components, such as harmonics or noise bands, spatialization at synthesis stage is an obvious method. Listeners can thereby be spatially enveloped by a single sound, with spectral components being perceived from all angles. The continuous character, however, blurs the localization.

SOS

Spatio-operational spectral (SOS) synthesis (Topper, 2002) is an attempt towards a dynamic spatial additive synthesis, implemented in MAX/MSP and RTcmix. Partials are rotated independently within a 2D 8 channel speaker setup. A first experiment used a varying rate circular spatial path of the first eight partials of a square wave, as shown in Figure 1. Figure 2 shows the second experiment with one partial moving against the others.

/images/spatial/spatial_synthesis/sos_1.png — *Figure 1: First SOS experiment (Topper, 2002).*

/images/spatial/spatial_synthesis/sos_2.png — *Figure 2: Second SOS experiment (Topper, 2002).*

SMS

Spatial Modulation Synthesis (SMS), developed by Ryan McGee, is a synthesis framework that treats spatial trajectories as the primary control source for sound generation. In this model, the synthesis parameters are directly mapped to the physical properties of a sound's movement through space, such as its distance from a listener or its angular velocity. By coupling spatialization and synthesis into a single unified process, McGee's approach allows for "spatial timbres" that change dynamically based on motion, moving beyond traditional panning toward a truly multidimensional auditory experience:

https://lifeorange.com/SM/

GLOOO

GLOOO is a system for real-time expressive spatial synthesis with spectral models. A haptic interface allows the dynamic distribution of 100 spectral components, allowing a control over the spread and position of the resulting violin sound. The project is best documented in the following publications:

References

2017

Grimaldi, Vincent and Böhm, Christoph and Weinzierl, Stefan and von Coler, Henrik. Parametric Synthesis of Crowd Noises in Virtual Acoustic Environments. In Proceedings of the 142nd Audio Engineering Society Convention. Audio Engineering Society, 2017.
[details] [BibTeX▼]

@inproceedings{grimaldi2017parametric,
    author = {{Grimaldi, Vincent and B{\"o}hm, Christoph and Weinzierl, Stefan and von Coler, Henrik}},
    booktitle = "{Proceedings of the 142nd Audio Engineering Society Convention}",
    location = "Berlin, Germany",
    organization = "Audio Engineering Society",
    title = "{Parametric Synthesis of Crowd Noises in Virtual Acoustic Environments}",
    year = "2017"
}

2015

Stuart James. Spectromorphology and spatiomorphology of sound shapes: audio-rate AEP and DBAP panning of spectra. In Proceedings of the International Computer Music Conference (ICMC). 2015.
[details] [BibTeX▼]

@inproceedings{james2015spectromorphology,
    author = "James, Stuart",
    booktitle = "{Proceedings of the International Computer Music Conference (ICMC)}",
    location = "Denton, Texas, United States",
    title = "Spectromorphology and Spatiomorphology of Sound Shapes: audio-rate {AEP} and {DBAP} panning of spectra",
    year = "2015"
}

Ryan McGee. Spatial modulation synthesis. In Proceedings of the International Computer Music Conference (ICMC). 2015.
[details] [BibTeX▼]

@inproceedings{mcgee2015spatial,
    author = "McGee, Ryan",
    booktitle = "{Proceedings of the International Computer Music Conference (ICMC)}",
    location = "Denton, USA",
    title = "Spatial Modulation Synthesis",
    year = "2015"
}

2009

Alexander Müller and Rudolf Rabenstein. Physical modeling for spatial sound synthesis. In Proceedings of the International Conference of Digital Audio Effects (DAFx). 2009.
[details] [BibTeX▼]

@inproceedings{muller2009physical,
    author = {M{\"u}ller, Alexander and Rabenstein, Rudolf},
    booktitle = "{Proceedings of the International Conference of Digital Audio Effects (DAFx)}",
    location = "Como, Italy",
    title = "Physical Modeling for Spatial Sound Synthesis",
    year = "2009"
}

2008

Scott Wilson. Spatial swarm granulation. In Proceedings of the International Computer Music Conference (ICMC). 2008.
[details] [BibTeX▼]

@inproceedings{wilson2008spatial,
    author = "Wilson, Scott",
    booktitle = "{Proceedings of the International Computer Music Conference (ICMC)}",
    location = "Belfast, Ireland",
    title = "Spatial Swarm Granulation",
    year = "2008"
}

David Kim-Boyle. Spectral spatialization - an overview. In Proceedings of the International Computer Music Conference (ICMC). Belfast, UK, 2008.
[details] [BibTeX▼]

@inproceedings{kim2008spectral,
    author = "Kim-Boyle, David",
    address = "Belfast, UK",
    booktitle = "{Proceedings of the International Computer Music Conference (ICMC)}",
    title = "Spectral Spatialization - an Overview",
    year = "2008"
}

2004

Curtis Roads. Microsound. The MIT Press, 2004. ISBN 0262681544.
[details] [BibTeX▼]

@book{roads2004microsound,
    author = "Roads, Curtis",
    isbn = "0262681544",
    publisher = "The MIT Press",
    title = "{Microsound}",
    year = "2004"
}

2002

David Topper, Matthew Burtner, and Stefania Serafin. Spatio-operational spectral (SOS) synthesis. In Proceedings of the International Conference of Digital Audio Effects (DAFx). Singapore, 2002.
[details] [BibTeX▼]

@inproceedings{topper2003spatio,
    author = "Topper, David and Burtner, Matthew and Serafin, Stefania",
    address = "Singapore",
    booktitle = "{Proceedings of the International Conference of Digital Audio Effects (DAFx)}",
    location = "Hamburg, Germany",
    title = "Spatio-Operational Spectral ({SOS}) Synthesis",
    year = "2002"
}