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Impact cultural mathematics
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Tuesday, 06 May 2008
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Artistic expression
Cover Treaty harmony reduced to its principles of natural Jean-Philippe Rameau.
The notes that sound good together to a Western ear, are sons whose fundamental vibration frequencies are in simple reports. For example, the octave is a doubling of frequency, a fifth-fold increase 3 / 2.
 This link between the frequency and harmony was particularly detailed in the Treaty of harmony reduced to its natural principles (Paris, 1722, reprinted in IBSN 2865631575 or ISBN 205100787X) by Jean-Philippe Rameau, french baroque composer and theorist music. It is based in part on analysis of harmonics (rated 2 to 15 in the following figure) of a sound fundamental Do serious (note 1), the first harmonics and their ringing octaves between them.
The harmonics on a staff.
 If the curve traced in red, which follows the notes harmonics, a speed log, it is the relationship between two phenomena. On the one hand, representing the height of a sound by our auditory system, which is proportional to the logarithm of the frequency sound (a frequency double is always the same distance sound "called octave). On the other hand, harmonic frequencies that are multiples of the fundamental frequency.
Fractal
We can see that it involves a certain beauty to the symmetrical figures. A symmetry of a geometrical figure is, intuitively, that there is a reason for the figure that repeats itself following a specific rule, while being partially processed. Mathematically, a symmetry is the existence of a non-trivial action of a group, often by isometry, ie that preserves the distances on the figure. In other words, the intuition of the rule is mathematically achieved by the fact that this is a group that acts on the figure, and the feeling that a rule governs the symmetry is precisely due to the algebraic structure of this group .
For example, the group linked to the mirror symmetry is all \ Z/2Z = \ (0.1 \). A Rorschach test is a figure invariant this symmetry, as well as a butterfly and, more generally, the bodies of animals, at least on the surface. When drawing the sea surface, the whole wave has a symmetry with translation: move our gaze on the length between two crests of waves does not change the view that it was the sea Another case of symmetry, this time not isometric, is one presented by the fractal: a certain pattern repeats itself at all scales of vision.
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