"There is geometry in the humming of the strings; there is music in the spacing of the spheres." (Pythagoras, cca. 6th century BC)
"And so they have handed down to us clear knowledge of the speed of the heavenly bodies and their risings and settings, of geometry, numbers and, not least, of the science of music. For these sciences seem to be related." (Archytas of Tarentym, 4th c. BC)
"Music submits itself to principles which it derives from arithmetic." (St. Thomas d'Aquin,” Summa theologica”, 1485)
"Musicke I here call that Science, which of the Greeks is called Harmonie. Musicke is a Mathematical Science, which teacheth, by sense and reason, perfectly to judge, and order the diversities of soundes hye and low." (John Dee, 1570)
"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)
"For many parts of Nature can neither be invented with sufficient subtlety, nor demonstrated with sufficient perspicuity, nor accommodated to use with sufficient dexterity, without the aid and intervention of Mathematic: of which sort are Perspective, Music, Astronomy, cosmography, Architecture, Machinery, and some others." (Sir Francis Bacon, De Augmentis, Bk. 3 [The Advancement of Learning], 1605)
"Mathematics make the mind attentive to the objects which it considers. This they do by entertaining it with a great variety of truths, which are delightful and evident, but not obvious. Truth is the same thing to the understanding as music to the ear and beauty to the eye. The pursuit of it does really as much gratify a natural faculty implanted in us by our wise Creator as the pleasing of our senses: only in the former case, as the object and faculty are more spiritual, the delight is more pure, free from regret, turpitude, lassitude, and intemperance that commonly attend sensual pleasures." (John Arbuthnot, "An Essay on the Usefulness of Mathematical Learning", 1701)
"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. Notwithstanding all the experience I may have acquired in music from being associated with it for so long, I must confess that only with the aid of mathematics did my ideas become clear and did light replace a certain obscurity of which I was unaware before." (Jean-Philippe Rameau, "Treatise on Harmony reduced to its natural principles", 1722)
"Music is a science which should have secure rules; these rules should be drawn from an evident principle, and this principle can scarcely be known to us without the aid of mathematics. Thus I must admit that despite all the experience I could get from music in practicing it for so long a time, nevertheless it is only by the help of mathematics that my ideas have grown clear." (Jean-Philippe Rameau, "Traite de l'harmonie", 1722)
"But mathematics, certainly, does not play the smallest part in the charm and movement of the mind produced by music. Rather is it only the indispensable condition (conditio sine qua non) of that proportion of the combining as well as changing impressions which makes it possible to grasp them all in one and prevent them from destroying one another, and to let them, rather, conspire towards the production of a continuous movement and quickening of the mind by affections that are in unison with it, and thus towards a serene self-enjoyment." (Immanuel Kant, "The Critique of Judgment", 1790)
Note: The quotes have been reordered chronologically.
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