The numbers one to four also have another important quality:|
Pythagoras discovered that the most simplest, regularly proceeding ratios 2:1, 3:2, and 4:3, which contain the first numbers, correspond to the basic intervals in music: octave, fourth and fifth. You see that numbers also rule the musical harmonies.
According to legends Pythagoras has made this discovery as he passed a smithy; he has heard that the bangs of the hammer have been only fourths and fifths. When he weighed the hammers he found out the ratios above.
Pythagoras discovers the connections between ratios and tone frequencies.
He experimented with bells, glasses of water, strings and pipes of different sizes. His Hebrew person opposite Jubal hammers at an amboss.
woodcuts from F. Gaffurio, Theoria musica, milano 1492
More likely to be true seems the dicovery at the monochord (lat.:"one string"), a wooden box with one string tightened on top of it.
If the string has a certain tone, e.g. c´, and you tear it in half
, that means a ratio of 2:1, the string sounds one octave higher,
you can hear a c´´. |
If you divide it in a ratio of 3:2, you get a fifth (c´-g´).
If you divide in 4:3, you get a fourth (c´-f´).
So you can measure with a monochord (count) and hear tones; the most simplest proportions of measures are the basis of the most harmonical, basic intervals: the mathematical harmony has a musical harmony as its consequence. "harmony" is a Greek word and originally means "clip" (tool of carpenters), "connection", "structure", also "symmetry" (right proportions), "harmony".
Just like in terms of music this ratios can also be found in the distances and rotation times of stars,
this discovery resulted in the theory of "spherical harmonies": it was believed
that the rotating stars make tones, which -with the help of simple proportions- create a so called "Spherical music".
This collection of celestial bodies forms the "cosmos" ("pretty order").
The theory of spherical harmonies has expounded a great impact: in a magnificient way it was the main thought of Kepler's studies of the orbits of planets in his main work "Harmonices mundi" ("world's harmony",1619), it is also found in Goethes "Faust":
In Brudersphären Wettgesang,
Und ihre vorgeschriebne Reise
Vollendet sie mit Donnergang."
Press at the single notations to hear the "Spherical harmonies"
The discovery of these simple and to musical harmonies that basical proprotions at the monochord seemed to be overwhelming to Pythagoras that he told his pupils when he layed dying always to play the monochord.