Sacred geometry

8) Geometry and music

8.1
Using the square as unity with both its side and area equal to 1, by crossing the \/2 with the (\/5)/2 and leading a perpendicular from the point of interesection up to the side, we divide unity into 1/3 and 2/3.

Arithmetic proportion:
1/3, 2/3, 1

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8.2
Use the square for unity and by means of an arc from the lower left corner,,, bring the length of side 1 down to intersect with the diagonal \/2. Then lead an arc from the upper right corner back up to the upper side of the square.

Harmonc proportion:
(\/2-1), (2 - \/2), 1

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Please enable Java for an interactive construction (with Cinderella).
8.3
Lead an arc from the point of intersection of the half-side with the semi-diagonal and the arc with radius equal to the half-side to the upper side of the square.

Geometric progression:
1/f², 1/f, 1

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Please enable Java for an interactive construction (with Cinderella).
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