On Vibrations I

"The length of strings is not the direct and immediate reason behind the forms [ratios] of musical intervals, nor is their tension, nor their thickness, but rather, the ratios of the numbers of vibrations and impacts of air waves that go to strike our eardrum." (Galileo Galilei, "Two New Sciences", 1638)

"The atomic theory plays a part in physics similar to that of certain auxiliary concepts in mathematics: it is a mathematical model for facilitating the mental reproduction of facts. Although we represent vibrations by the harmonic formula, the phenomena of cooling by exponentials, falls by squares of time, etc, no one would fancy that vibrations in themselves have anything to do with circular functions, or the motion of falling bodies with squares." (Ernst Mach, "The Science of Mechanic", 1893)

"The making of things to a high measure of accuracy is not just a test of workmanship. It is a fundamental to service production. In such production there can be no fitting of parts in assemblies or in repairs. Every crankshaft must be exactly like any other crankshaft. Of course no two parts are ever absolutely alike, except by accident, for it does not pay to try for accuracy beyond a certain point. But any kind of a machine which has moving parts must be accurately made or there will be an amount of vibration through play that will shorten the life of the machine and also decrease its running efficiency." (Henry Ford, "Moving Forward", 1930)

"In the realm of physics it is perhaps only the theory of relativity which has made it quite clear that the two essences, space and time, entering into our intuition, have no place in the world constructed by mathematical physics. Colours are thus 'really' not even æther-vibrations, but merely a series of values of mathematical functions in which occur four independent parameters corresponding to the three dimensions of space, and the one of time." (Hermann Weyl, "Space, Time, Matter", 1952)

"[…] the equation of small oscillations of a pendulum also holds for other vibrational phenomena. In investigating swinging pendulums we were, albeit unwittingly, also investigating vibrating tuning forks." (George Pólya, "Mathematical Methods in Science", 1977)

"Nature is never perfectly symmetric. Nature's circles always have tiny dents and bumps. There are always tiny fluctuations, such as the thermal vibration of molecules. These tiny imperfections load Nature's dice in favour of one or other of the set of possible effects that the mathematics of perfect symmetry considers to be equally possible." (Ian Stewart & Martin Golubitsky, "Fearful Symmetry: Is God a Geometer?", 1992)

"The mystery of sound is mysticism; the harmony of life is religion. The knowledge of vibrations is metaphysics, the analysis of atoms is science, and their harmonious grouping is art. The rhythm of form is poetry, and the rhythm of sound is music. This shows that music is the art of arts and the science of all sciences; and it contains the fountain of all knowledge within itself." (Inayat Khan, "The Mysticism of Sound and Music", 1996)

"Whereas symmetry can create beauty, its breaking does not necessarily destroy beauty; instead, it may even create another kind of beauty." (Guozhen Wu, "Nonlinearity and Chaos in Molecular Vibrations", 2005)

"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)