Some... agreeing with Philolaus, believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that 'geometric harmony' is the cube because it is harmonized in all three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion... (Nicomachus)

Some... agreeing with Philolaus, believe that the proportion is called harmonic because it attends upon all geometric harmony, and they say that 'geometric harmony' is the cube because it is harmonized in all three dimensions, being the product of a number thrice multiplied together. For in every cube this proportion is mirrored; there are in every cube 12 sides, 8 angles and 6 faces; hence 8, the [harmonic] mean between 6 and 12, is according to harmonic proportion...

Related topics

believe cube harmonic harmony mean number three

Related quotes

Conservatism, though a necessary element in any stable society, is not a social program; in its paternalistic, nationalistic and power adoring tendencies it is often closer to socialism than true liberalism; and with its traditionalistic, anti-intellectual, and often mystical propensities it will never, except in short periods of disillusionment, appeal to the young and all those others who believe that some changes are desirable if this world is to become a better place.

Friedrich Hayek

It is the duty of all troops and police in my command to adopt the severest measures. Every act of violence committed by partisans must be punished immediately. Reports submitted must also give details of countermeasures taken. Wherever there is evidence of a considerable number of partisan groups a proportion of the male population of the area will be arrested, and in the event of an act of violence being committed these men will be shot.

Albert Kesselring

I made a very bad mistake; I miscounted these scraps of information on the record as 92, and in continual homage to this man who had been so influential to me, I began creating or constructing my own films on this so-called "magic" number of 92 ... but when I eventually made a film about John Cage and met him, I explained this to him, and he found it very amusing because there are only 90 stories on the two sides of the record, and I'd based three years of my filmic career on this mathematical error!

Peter Greenaway

I have never said that human society ought to be aristocratic, but a great deal more than that. What I have said, and still believe with ever-increasing conviction, is that human society is always, whether it will or no, aristocratic by its very essence, to the extreme that it is a society in the measure that it is aristocratic, and ceases to be such when it ceases to be aristocratic. Of course I am speaking now of society and not of the State.

José Ortega y Gasset

In lecturing on cookery, as on housebuilding, I divide the subject into, not four, but five grand elements: first, Bread; second, Butter; third, Meat; fourth, Vegetables; and fifth, Tea - by which I mean, generically, all sorts of warm, comfortable drinks served out in teacups, whether they be called tea, coffee, chocolate, broma, or what not. I affirm that, if these five departments are all perfect, the great ends of domestic cookery are answered, so far as the comfort and well-being of life are concerned.

Harriet Beecher Stowe