The Physics of Music from Pythagoras to Microtones

<!--HTML--><p><span><strong>Abstract:</strong></span></p><p class="part">What are the physical foundations of Western music? Why are there 12 notes in an octave? Why is Equal Temperament so successful? What is the role of microtones in music composition? In this lecture series we will try to answer these and many other questions, that might have come to the mind of scientists playing an instrument from amateur to semi-professional level.&nbsp;<br><br>In the first lecture, starting from the case study of the vibrating string, we first review harmonic sounds and timbre in the context of Signal Theory. We then introduce the psychoacoustic notions of "roughness", Critical Bandwidth and Discrimination Limen. The sensations of consonance and dissonance for dyads are introduced by means of demonstrations and tests, including software simulations.&nbsp;<br><br>The second lecture is devoted to the physical theories trying to justify the Western music dyad's rankings for consonance and dissonance.&nbsp;<br>Starting from ancient Greece and following the historical path, we review the "compactness" and "roughness" theories, whose pioneers have been respectively G. Galilei and H. Helmholtz. The extension to triads is also detailed, in relation to the concept of tonality.&nbsp;<br><br>In the third lecture, we review the properties of the different scales that have been proposed over time. We discuss the Pythagorean scale, the Just Intonation scale and a number of temperaments, from the meantone to the equal one. We introduce microtones and temperaments with more than 12 notes per octave. Demonstration will be given for chords in the different temperaments and for microtonal chords.&nbsp;<br><br>At the end of the series, the scientist-musician will acquire a deeper awareness of the art of playing and composing music.</p><p class="part"><span><strong>Short bio:</strong></span></p><p class="part">Isabella Masina is a theoretical physicist, working in the fields of particle physics, cosmology and, more recently, the physics of music. She is associate professor at Ferrara University and her teaching activity includes a doctoral course entitled "Waves Acoustics and Music". She holds a Diploma in Harp and enjoys making transcriptions and arrangements for her instrument.</p><div><div>Giuseppe Lo Presti holds a PhD in Computer Engineering, and spent the last 18 years working for large-scale storage services for the CERN scientific community. He contributed to the development and operations of the tape storage system for the experiments at the LHC, and as of 2017 he joined the team that develops CERNBox, the cloud storage used by the whole CERN community. He plays piano since his childhood, and in his free time he enjoys exploring music theory issues and the history of instruments and musical temperaments. He recently contributed to the doctoral course "Waves Acoustics and Music" held at Ferrara University.</div></div>