Posted by Boy Wonder

Mon, 30 Apr 2007 18:21:46 GMT

From Wikipedia;
In mathematics and the arts, two quantities are in the golden ratio if the ratio between the sum of those quantities and the larger one is the same as the ratio between the larger one and the smaller. This ratio can be expressed as a mathematical constant, usually denoted by the Greek letter (phi), which is the algebraic irrational number with its approximate value.
The figure of a golden section illustrates the defining geometric relationship, expressed algebraically.
At least since the Renaissance, many artists and architects have proportioned their works to approximate the golden ratio — especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio —believing this proportion to be aesthetically pleasing. Mathematicians have studied the golden ratio because of its unique and interesting properties.

Other names frequently used for or closely related to the golden ratio are golden section (Latin: sectio aurea), golden mean, golden number, and the Greek letter phi (f).
Other terms encountered include extreme and mean ratio, medial section, divine proportion (Italian: proporzione divina), divine section (Latin: sectio divina), golden proportion, golden cut, and mean of Phidias.
In Ancient Times, numbers were magical and held the secret of the Music of the Spheres - Musica universalis (lit. universal music, or music of the spheres) is an ancient philosophical concept that regards proportions in the movements of celestial bodies — the Sun, Moon, and planets — as a form of musica (the Medieval Latin name for music). This 'music' is not literally audible, but simply a harmonic and/or mathematical concept.
The Greek mathematician and astronomer Pythagoras is frequently credited with originating the concept, which stemmed from his semi-mystical, semi-mathematical philosophy and its associated system of numerology of Pythagoreanism. According to Johannes Kepler

Posted by Immutable Name, of Toll-X

Mon, 30 Apr 2007 13:53:44 GMT

Not necessarily. There are various aspects of music that have mathematical relations that you also find in geometry. For example, the three main notes in a major chord obey Pythagoras’ rule, not just the right-angled triangle.

Mathematical ratios that are “pleasing” in geometry (and thus archetecture and design) are very often the same ratios found to be pleasing in music (and indeed in visual art, such as the “golden ratio”).

Musical secret uncovered in chapel carving

Posted by Boy Wonder

Posted by Immutable Name, of Toll-X