paper.bib

@book {Lewin:1987,
    AUTHOR = {Lewin, David},
     TITLE = {Generalized Music Intervals and Transformations},
    SERIES = {},
 PUBLISHER = {Yale University Press},
      YEAR = {1987},
}

@article{Lewin:1982,
author = {Lewin, David},
title = {Transformational Techniques in Atonal and Other Music Theories},
journal = {Perspectives of New Music},
volume = {21},
number = {1-2},
pages = {312--381},
year = {1982},
doi = {10.2307/832879}
}

@Inbook{Fiore:2011,
author="Fiore, Thomas M.
and Noll, Thomas",
editor="Agon, Carlos
and Andreatta, Moreno
and Assayag, G{\'e}rard
and Amiot, Emmanuel
and Bresson, Jean
and Mandereau, John",
title="Commuting Groups and the Topos of Triads",
bookTitle="Mathematics and Computation in Music: Third International Conference, MCM 2011, Paris, France, June 15-17, 2011. Proceedings",
year="2011",
publisher="Springer Berlin Heidelberg",
address="Berlin, Heidelberg",
pages="69--83",
abstract="The goal of this article is to clarify the relationship between the topos of triads and the neo-Riemannian PLR-group. To do this, we first develop some theory of generalized interval systems: 1) we prove the well known fact that every pair of dual groups is isomorphic to the left and right regular representations of some group (Cayley's Theorem), 2) given a simply transitive group action, we show how to construct the dual group, and 3) given two dual groups, we show how to easily construct sub dual groups. Examples of this construction of sub dual groups include Cohn's hexatonic systems, as well as the octatonic systems. We then enumerate all ℤ12-subsets which are invariant under the triadic monoid and admit a simply transitive PLR-subgroup action on their maximal triadic covers. As a corollary, we realize all four hexatonic systems and all three octatonic systems as Lawvere--Tierney upgrades of consonant triads.",
isbn="978-3-642-21590-2",
doi="10.1007/978-3-642-21590-2_6",
url="https://doi.org/10.1007/978-3-642-21590-2_6"
}

@incollection {Noll:2005,
AUTHOR = {Noll, Thomas},
EDITOR = {Fripertinger, Harald and Reich, Ludwig},
TITLE = {The Topos of Triads},
BOOKTITLE = {Colloquium on Mathematical Music Theory},
SERIES={Grazer Math. Ber.},
YEAR = {2005},
volume = {347},
PAGES = {103--135},
}

@article{Mazzola:2006,
 ISSN = {00316016},
 URL = {http://www.jstor.org/stable/25164629},
 author = {Guerino Mazzola and Moreno Andreatta},
 journal = {Perspectives of New Music},
 number = {2},
 pages = {88-113},
 publisher = {Perspectives of New Music},
 title = {From a Categorical Point of View: K-Nets as Limit Denotators},
 volume = {44},
 year = {2006}
}

@incollection {Popoff:2015,
AUTHOR = {Popoff, Alexandre and Andreatta, Moreno and Ehresmann, Andr{\'e}e},
EDITOR = {Collins, Tom and Meredith, David and Volk, Anja},
TITLE = {A Categorical Generalization of Klumpenhouwer Networks},
BOOKTITLE = {Mathematics and Computation in Music: 5th International Conference, MCM 2015, London, UK, June 22-25, 2015, Proceedings},
YEAR = {2015},
   SERIES = {Lecture Notes in Computer Science},
    VOLUME = {9110},
PUBLISHER = {Springer International Publishing},
PAGES = {303--314},
ISBN={978-3-319-20603-5},
DOI = {10.1007/978-3-319-20603-5_31},
URL = {http://dx.doi.org/10.1007/978-3-319-20603-5_31}
}

@article{Popoff:2016,
ISSN = {00316016},
 URL = {http://www.jstor.org/stable/10.7757/persnewmusi.54.2.0005},
 author = {Popoff, Alexandre and Agon, Carlos and Andreatta, Moreno and Ehresmann, Andr\'ee},
 journal = {Perspectives of New Music},
 number = {2},
 pages = {5-63},
 publisher = {Perspectives of New Music},
 title = {From K-nets to PK-nets: a Categorical Approach},
 volume = {54},
 year={2016},
 doi={10.7757/persnewmusi.54.2.0005}
}

@book{Lehman:2018,
  title={Hollywood Harmony: Musical Wonder and the Sound of Cinema},
  author={Lehman, F.},
  isbn={9780190606435},
  lccn={2017041598},
  series={Oxford music/media series},
  year={2018},
  publisher={Oxford University Press}
}

@book{Gollin:2010,
  title={The Oxford Handbook of Neo-Riemannian Music Theories},
  author={Gollin, E. and Rehding, A.},
  isbn={9780199717477},
  lccn={2010017175},
  series={Oxford Handbooks},
  year={2010},
  publisher={Oxford University Press}
}

@book{Cohn:2012,
  title={Audacious Euphony: Chromatic Harmony and the Triad's Second Nature},
  author={Cohn, R.},
  isbn={9780199772698},
  lccn={2011008754},
  series={Oxford Studies in Music Theory},
  year={2012},
  publisher={Oxford University Press, USA}
}