Rosewindow frequency/resonance/energy

The quote "there is geometry in the humming of the strings" is attributed to Pythagoras, an ancient Greek philosopher and mathematician. It describes his observation that musical harmony is based on mathematical ratios. Specifically, the lengths of strings, the tension, and other factors directly relate to the pitch and intervals of the resulting sound. This quote is part of a larger statement, "There is geometry in the humming of the strings, there is music in the spacing of the spheres".

Pythagoras experimented with strings of different lengths and found that when two strings of a certain length ratio were made to vibrate, they produced a harmonious chord or interval. For instance, a string half the length of another would play an octave higher, and strings in ratios of 4:3 and 3:2 would produce a perfect fourth and fifth, respectively.

These ratios (2:1, 4:3, 3:2) are the foundation of Western musical scales and harmonies. Pythagoras believed that music was inherently mathematical and that certain ratios produced pleasing sounds due to their mathematical simplicity.

Pythagoras's theory extended beyond musical instruments to the cosmos, suggesting that the planets also moved in accordance with mathematical ratios, producing a "music of the spheres". This idea, though poetic, reflects his belief in a harmonious and ordered universe governed by mathematical principles.

The physical dimensions of a string instrument, like the length of the string, the distance between the bridge and the nut, and the thickness of the string, all have geometric properties that affect the resulting pitch and quality of the sound.

Pythagoras PDF
https://www.academia.edu/74646356/PYTHAGORAS