"Music is the discipline which treats of numbers in their relation to those things which are found in sound." (Cassiodorus, cca. 6th century)
"Music is fashioned wholly in the likeness of numbers." (Anon, "Scholia Enchiriadis", cca. 900)
"There are certain pleasures which only fill the outward senses, and there are others also which pertain only to the mind or reason; but music is a delectation so put in the midst that both by the sweetness of the sounds it moveth the senses, and by the artificiousness of the number and proportions it delighteth reason itself." (John Northbrooke , "Against Dicing", 1577)
"Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics." (Jean-Philippe Rameau, "Treatise on Harmony reduced to its natural principles", 1722)
"Music is like geometric figures and numbers, which are the universal forms of all possible objects of experience." (Friedrich Nietzsche, "Birth of Tragedy", 1872)
"Music is an order of mystic, sensuous mathematics." (James Huneker, "Chopin: The Man and His Music", 1900)
"Music is mathematics, the mathematics of listening, mathematics for the ears." (Karlheinz Stockhausen, "Conversations with Stockhausen", 1987)
"Music is a science which should have definite rules; these rules should be drawn from an evident principle; and this principle cannot really be known to us without the aid of mathematics." (Jean-Philippe Rameau, Treatise on Harmony, 2012)
"Mathematics is music for the mind; Music is mathematics for the soul." (Stanley Gudder)
"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)
"The pleasure we obtain from music comes from counting, but counting unconsciously. Music is nothing but unconscious arithmetic." (Gottfried W Leibniz)
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