Music for Möbius Strip

Two-part tonal musical piece whose upper line covers one half of the surface of a Mobius strip and the lower one (in a bass key) the other. If someone wanted to try it, the game is not as simple as it may seem: when you write, you must already consider that the final product must play well (or at least in a way consistent with the laws of traditional harmony) not only if read from the bottom towards the beginning (reversible or double-faced) but also by turning the score 180° (rotatable). In fact, since the strip cannot be oriented, it is not possible to distinguish a clockwise or counterclockwise direction: if we imagined dancing a waltz along the whole tape we would find ourselves, arrived at the starting point, turning in the opposite direction from our departure. Throwing random notes here and there and applying these rules would not result in problems of execution but nothing would make sense from the point of view of classical music theory: applying this principle to dodecaphony for example, the drafting of the piece would involve many less problems because they would eliminate all harmonic consonances or resolutions of some part movements.

Bibliography:

- L’infinito circolare. Borges, Bach, Escher: tre artefici di narrazioni perpetue, in «Punto Zero», n. 11, supplemento al n. 116 di «Nexus New Times», 2015, pp. 68-75 (parziale riedizione online il 04.11.2019 https://www.nexusedizioni.it/it/CT/escher-bach-borges-il-cerchio-la-spirale-e-leterno-ritorno-5960).

- Musica per nastro di Möbius, scheda didattica per il dipartimento formazione e apprendimento, Scuola Universitaria Professionale della Svizzera Italiana (SUPSI), 30 gennaio 2019, https://www.matematicando.supsi.ch/risorse-didattiche/musica-per-il-nastro-di-mobius/

- Musica per nastro di Möbius. Regole per la costruzione di un brano tonale reversibile, bustrofedico, bifronte e scomponibile, in «MatematicaMente», n. 256, 2 luglio 2019, http://www.mathesis.verona.it/wp-content/uploads/2018/Numeri/Nume256.pdf.