The angle in a semicircle is a right angle. In harmony, the three lines representing the three musical notes constituting a chord are the three sides of an isosceles right triangle.
A right triangle is made up of two perpendicular lines: a horizontal line and a vertical line. The third line is the resultant of the two lines.
An isosceles right triangle is a right triangle (a right-angled triangle) with two equal sides and two equal angles. The two equal angles are called base angles.
Base angles of isosceles triangles are equal.
This means that if the base angles of an isosceles triangle are X and Y respectively,
X = Y (base angles)
The isosceles right triangle is the hybrid of an isosceles triangle and a right triangle. Since the isosceles right triangle is a right triangle, the three sides of the triangle are the following three sides of a right triangle:
- Opposite (Opp)
- Adjacent (Adj)
- Hypotenuse (Hyp)
The opposite is the vertical side, the adjacent is the horizontal, and the line connecting the opposite and adjacent sides is the hypotenuse.
The hypotenuse is the line dividing the circle into two equal halves or two semicircles. This means that the hypotenuse is the diameter of the circle.
The two perpendicular lines of the right angle and the diameter of the circle are the three sides of a right triangle in a semicircle. Hence, the angle in a semicircle is a right triangle (a right-angled triangle).
From Pythagorean theorem, the diameter of the circle is equal to the square root of the sum of the square of the opposite side and the square of the adjacent side. This means that the hypotenuse (the diameter of the circle) is the reflection of the other two sides.
The diameter is the chord if the other two sides of the right triangle are equal. Equality here implies agreement. The angle in a semicircle is a symbol of conflict resolution if the two perpendicular sides are equal.
The vertical line and the horizontal line are two notes, and the third line (the diameter) is the third note. When sounded together, the three lines will produce harmony. This means that the isosceles right triangle in the semicircle symbolizes harmony between two groups or two individuals.