Music and Mathematics VII

"Every intelligent musician should be familiar with the physical laws which underline his art." (Clarence G Hamilton, "Sound and Its Relation to Music", 1912)

"There exists a passion for comprehension, just as there exists a passion for music. That passion is rather common in children but gets lost in most people later on. Without this passion, there would be neither mathematics nor natural science." (Albert Einstein, Scientific American Vol. 182 (4), 1950)

"One of the mysteries is how the human mind can hear a piece of music, a symphony from the beginning to the end, before beginning; or see a sculpture finished all the way round, when it doesn't exist. Now these faculties are the sort faculties which are needed in sciences, math, and medicine and all kind of things. But if one has them, one has to learn to use them." (Barbara Hepworth, "Art Talk, conversations with 15 woman artists", 1975)

"In our travels, we have come across many equations - math for understanding the universe, for making music, for mapping stars, and also for tipping, which is important." (Libba Bray, "Going Bovine", 2009)

"Music can capture human emotions to a degree beyond anything that we can convey with equations." (Jim Bell, The Interstellar Age: Inside the Forty- Year Voyager Mission, 2015)

"[...] the relations between the two [mathematics and music] disciplines were never truly symmetric. Yes, there are many similarities between the two. For example, mathematics and music both depend on an efficient system of notation - a set of written symbols that convey a precise, unambiguous meaning to its practitioners (although in music this is augmented by a large assortment of verbal terms to indicate the more emotional aspects of playing)." (Eli Maor, "Music by the Numbers: From Pythagoras to Schoenberg", 2018)

"The significance of Fourier’s theorem to music cannot be overstated: since every periodic vibration produces a musical sound (provided, of course, that it lies within the audible frequency range), it can be broken down into its harmonic components, and this decomposition is unique; that is, every tone has one, and only one, acoustic spectrum, its harmonic fingerprint. The overtones comprising a musical tone thus play a role somewhat similar to that of the prime numbers in number theory: they are the elementary building blocks from which all sound is made." (Eli Maor, "Music by the Numbers: From Pythagoras to Schoenberg", 2018)

"Ultimately, music is meant to move our souls, to stir our emotions, to arouse us to swing by its rhythms, and this cannot be achieved by mathematical principles alone." (Eli Maor, "Music by the Numbers: From Pythagoras to Schoenberg", 2018)

"But we have higher mathematics, haven't we? This gives me freedom from my senses. The language of mathematics is even more inborn and universal than the language of music; a mathematical formula is crystal clear and independent of all sense organs. I therefore built a mathematical laboratory, set myself in it as if I were sitting in a car, and moved along with a beam of light." (Albert Einstein)

"Musical form is close to mathematics - not perhaps to mathematics itself, but certainly to something like mathematical thinking and relationships." (Igor Stravinsky)