The dualism between continuous and discrete is relevant in music theory as well as in performance practice of musical instruments. Geometry has been used since longtime to represent relationships between notes and chords in tonal system. Moreover, in the field of mathematics itself, it has been shown that the continuity of real numbers can arise from geometrical observations and reasoning. Here, we consider a geometrical approach to generalize representations used in music theory introducing continuous pitch. Such a theoretical framework can be applied to instrument playing where continuous pitch can be naturally performed. Geometry and visual representations of concepts of music theory and performance strengthen the relationship between music and images: in this way, we can connect a theremin or violin performance with a study on perspective, always through mathematical ideas and paradigms. So can math explain musical concepts, and, on the contrary, can music explain mathematical concepts? Can music and math together give rise to visual arts in ever more innovative ways? In this paper, we try to connect different topics such as musical performance on instruments with continuous pitch, and the paradigm of geometry and continuity.

Author/Artist Bio

Maria Mannone earned Masters in Theoretical Physics, Orchestral Conducting, Composition, and Piano in Italy, and the Master 2 ATIAM at IRCAM-UPMC Paris VI Sorbonne. She achieved the Ph.D. in Composition at the University of Minnesota, where she developed an interdisciplinary research between mathematics and music. Author and co-author of books and articles, she gave invited lectures in USA, Asia, and Europe. Irene Iaccarino began to study the violin at the age of 5 years and graduated very young with honors. She collaborates with several orchestras and performs as a soloist both in Europe and in the United States of America. She graduated in Arts, Music and Entertainment Disciplines and is about to get the master degree in Musicology at the “Sapienza” University in Rome. She is professor at High School of Music. Rosanna Iembo is mathematician, poet, theologian, performing artist and university professor. In USA she is a MAA member and SIGMAA ART member since 2006 and AMS lifetime member. In 2013 she got a PHD honoris causa in letters in Cambridge, England. Website: www.rosannaiembo.it

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.