Music and Mathematics I (Unsourced)

"Although some older art, music or wines may be better than the newer, it is rather unlikely that this would often apply to science or mathematics." (William F Lucas)

"Architecture is akin to music in that both should be based on the symmetry of mathematics." (Frank L Wright)

"Besides language and music, mathematics is one of the primary manifestations of the free creative power of the human mind." (Hermann Weyl)

"In music, mathematics appears formally, as revelation, as creative idealism. All enjoyment is musical, consequently mathematical. The highest life is mathematics." (Novalis)

"It is Proportion that beautifies everything, the whole Universe consists of it, and Musicke is measured by it." (Orlando Gibbons)

"Little comes to us through time as a complete monument; much comes as remnants; much as techniques, as practical manual; some things because of their close affinity to man, like mathematics; other things because they are always encouraged, like astronomy and geography; other things because of man’s needs, like medicine; and finally some things, because the human being, without wanting to, continues to produce them, like music and the other fine arts." (Johann Wolfgang von Goethe)

"[…] mathematics has liberated itself from language; and one who knows the tremendous labor put into this process and its ever-recurring surprising success, cannot help feeling that mathematics nowadays is more efficient in it particular sphere of the intellectual world than, say, the modern languages in their deplorable condition of decay or even music are on their fronts." (Andreas Speiser)

"Mathematics is music for the mind;
Music is mathematics for the soul." (Stanley Gudder)

"Mathematics is, as it were, a sensuous logic, and relates to philosophy as do the arts, music, and plastic art to poetry." (Friedrich von Schlegel)

"May not Music be described as the Mathematics of sense, and Mathematics as the Music of reason?" (James J Sylvester)

"Music is architecture translated or transposed from space into time; for in music, besides the deepest feeling, there reigns also a rigorous mathematical intelligence." (Georg W F Hegel)

"Music is the arithmetic of sounds as optics is the geometry of light." (Claude Debussy)

"Music is the hidden arithmetical exercise of a soul unconscious that it is calculating." (Gottfried W Leibniz)

"Music is the pleasure the human soul experiences from counting without being aware it is counting." (Gottfried W Leibniz)

"The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (Gottfried W Leibniz)

"The Pythagoreans considered all mathematical science to be divided into four parts: one half they marked off as concerned with quantity, the other half with magnitude; and each of these they posited as twofold. A quantity can be considered in regard to its character by itself or in relation to another quantity, magnitudes as either stationary or in motion. Arithmetic, then, studies quantity as such, music the relations between quantities, geometry magnitude at rest, spherics magnitude inherently moving." (Diadochus Proclus)

"There is geometry in the humming of the strings; there is music in the spacing of the spheres." (Pythagoras, cca. 6th century BC)

See also:
Music and Mathematics II
Music and Mathematics III
The Music of Numbers