@MISC{MUSIC_S1.MIZ,
    TITLE = {{P}ythagorean Tuning: Pentatonic and Heptatonic Scale},
    AUTHOR = {Coghetto, Roland},
    ADDRESS1 = {Rue de la Brasserie 5\\7100 La Louvi\`ere, Belgium},
      SUMMARY = {Using Mizar \cite{Mizar-State-2015}, we define a structure
       \cite{bancerek2003structure,grabowski2016algebraic} in order to build a
       Pythagorean pentatonic scale and a Pythagorean heptatonic scale
       (\url{https://en.wikipedia.org/wiki/Pythagorean_tuning},
        \cite{baskevitch2008representations,parzysz1984musique}).},
  DAY = {29},
  MONTH = {September},
  YEAR = {2018},
  ACKNOWLEDGEMENT = {I would like to thank H\'el\`ene Cambier (professor of
      music history at the music academy of La Louvi\`ere) and Marie
      Barbier (Recorder (musical instrument)) for suggestions.},
    MSC2010 = {00A65 97M80 03B35},
    KEYWORDS = {Music; Pythagorean Tuning, pentatonic scale, heptatonic scale}}

@article{bancerek2003structure,
  title={On the structure of Mizar types},
  author={Bancerek, Grzegorz},
  journal={Electronic Notes in Theoretical Computer Science},
  volume={85},
  number={7},
  pages={69--85},
  year={2003},
  publisher={Elsevier}
}

@inproceedings{grabowski2016algebraic,
  title={On algebraic hierarchies in mathematical repository of Mizar},
  author={Grabowski, Adam and Korni{\l}owicz, Artur and Schwarzweller, Christoph},
  booktitle={Computer Science and Information Systems (FedCSIS), 2016 Federated Conference on},
  pages={363--371},
  year={2016},
  organization={IEEE}
}

@phdthesis{baskevitch2008representations,
  title={Les repr{\'e}sentations de la propagation du son, d'Aristote {\`a} l'Encyclop{\'e}die},
  author={Baskevitch, Fran{\c{c}}ois},
  year={2008},
  school={Universit{\'e} de Nantes}
}

@book{parzysz1984musique,
  title={Musique et math{\'e}matique:(suivi de) Gammes naturelles},
  author={Parzysz, Bernard and Hellegouarch, Yves}
  year={1984},
  number={53},
  publisher={Association des Professeurs de Math\'ematiques de l'Enseignement Public (APMEP) Paris}
}
