Pythagoras is the source of their mathematical philosophy found in music. Its system of order and beauty, built on harmonies octaves, fifths and fourths, which is the chaotic continuum ear available interval divides its konsonantnošču and simple mathematical form. Octave interval is achieved by vibration wire length which are in the ratio of 2:1, the fifth being exercised by the ratio of 3:2, a ratio of 4:3 fourth interval (upper third has a ratio of 5:4, 6:5 and small).
But if the principle cake boxes of musical order and beauty of mathematical form (mathematical harmony), then is not the natural order, with its undoubted beauty, is also reducible to a similar or even identical to the principle? Pythagoras the answer is yes. The nature of the cosmos, cake boxes that order and beauty, and his principle number.
(Often mystified Pythagorean formula: "Everything is number" means just that math the key to understanding everything, or, closer to today's expression, that mathematics is the foundation of every science. Taj Pythagorean insight that comes from early childhood science and philosophy still managed science as its supreme principle.)
Pythagoras distinguished three types of music. If you use the Latin terminology of his followers, to the musica instrumentalis (common cake boxes music pianos, trumpets, cake boxes etc.), musica humana (constant though silent music of each individual, which are particularly important consensus or conflict between spirit and body), and musica mundana, music universe that is created by rotating celestial sphere (and is therefore known as the music of the spheres).
Despite our distinct differentiation of these areas, for Pythagoras all three music one and the same music. Trumpet and celestial bodies can literally play the same scale as this is a matter of pure mathematics. And the music do not differ more than they are different polygons that make fighting cake boxes a human palm of polygons that make up the constellation of certain stars in the sky or a melodic line of some musical themes. Eternal, a mathematical idea is polygon and all its manifestations does the same.
Do we have that in mind we can better understand the Pythagorean method of treatment. Musica instrumentalis and musica humana are just manifestations of the same truth. Sounds lira because the same cause vibrations in the "human instrument" that people can act badly or well. For example, listening to music composed in the Phrygian scale can cause violence, but it can also dispel the transition to a calming spondaic rhythm. We can remember the essential unity musicae instrumentalis and musicae Humanae perhaps we can understand Kepler issue of subheadings harmony of the world:
However, the most lasting contribution to the Pythagorean theory of music, but these findings are consonant intervals of octaves, fifths and fourths the simple arithmetic ratios of 2:1, 3:2 and 4:3 (5:4 and 6:5 applies to large and small humming) .
According to legend, Pythagoras was passing a blacksmith heard consonant intervals of fourths, fifths and octaves produced shocks different cake boxes hammer on an anvil. Explored this phenomenon found that the weight hammers that produce tones arranged in these intervals, cake boxes refer to 4:3, 3:2 and 2:1. Continuing experiments with lyre and monokordom (single-wire instrument) cake boxes found that the same is true for the length of wire.
(Vincenzo Galilei, father of Galileo Galilei, demonstrated in 1589. Hammers that story can not be true, because the weight of the hammer must be regarded as a square with monokorda to produce the same intervals. Thus, the fourth, the fifth and the octave products hammers to weight ratio 4 2 3 2 2 2 1 second Vincenzo said that the same proportions apply to weight lifting that burden on one and the same wire, as well as for different cake boxes wire diameters of the same kind, it is all true. was also argued that the same intervals obtained on wind instruments, if appropriate volumes of the column of air in the pipes instruments are in the ratio 4:3:2:1, ie if the length of the columns in cubic ratio 4 3 3 3 2 3 1 3rd That's not true because the pitch is only dependent on the length of the column, not on the volume.)
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