Geometric Music

         Geometry is used in many ways in the world. A great example of geometry is actually music. Most teenagers who are in geometry classes, and dislike the topic, do not realize this fact. Geometry is used in the making of instruments and is present in the sound of the music itself. Geometry and mathematics can be used to find out what makes great music great. It’s all in the geometry of music.

         Geometry must be used in the making of most musical instruments. The people who make guitars and other stringed instruments need to use circles, rectangles, triangles, and many other shapes to make musical instruments. Makers of musical instruments need to know exact angle measurements, so that the person playing the instrument will find it comfortable to play. They also need to take into account the sound of the instrument. Different sizes and shapes produce different vibrations or sounds. An upright piano, which is composed mostly of squares, sounds different from a grand piano, which is a combination of many shapes, mostly circles. Hence, geometry must be used, else the instruments will not sound right, feel right, or look right.

         Geometry can be heard. In a chromatic scale, all the notes are geometrically located on a series of perfect expanding circles. The major cord can actually be drawn as a triangle. There are ratios at each of the vertices of this triangle, 1/1, 5/4, and 3/2. A minor cord is a triangle with a vertex facing the opposite direction as the major cord. The ratios at its vertices are opposite those of the major cord, 1/1, 4/5, and 2/3. These triangles can be made into a 3d pyramid with 3 faces. The 3rd vertex being 7/4. Using non-Euclidean geometry and topology, a man was able to answer the question of how music works. He used mathematics, which is applied to problems of extradimensional physics. He described music as a lattice of points in a symmetrical, folded-up space known as an orbifold in which the points are the tiny particles in the vibrations of music.

         Geometry can be used to discover what music is good and what is simply noise. If the music makes even, patterned shapes in its sound, then it will most likely sound nice. However, if someone is banging on a keyboard, the patterns made by the vibrations of the music will be uneven and hard to decipher. When I lived in Germany, I went to a museum of light and sound. In the museum, there was a small, circular table covered with sand. If you rubbed a violin bow against the table, the sand would actually move around to form different shapes that resembled flowers made up of geometric shapes. This only worked if the violin bow was rubbed a certain way. Similarly, musical vibrations are only appealing if they are made a certain way.

         Therefore, geometry is actually more interesting and useful than most people think, and it will most likely be beneficial to anyone who learns it. Geometry can be found in the making of musical instruments and the actual sound of the music. It can also be used as a means of deciphering what music is good and what music is bad. Geometry is truly amazing.