Physics of the Blues

What you get depends on how you pluck the string, but all shapes of a string are a sum of harmonics. The shape of each harmonic is a sine wave — a wave whose curve follows the ratio of the length of the side opposite an acute angle in a right triangle to the length of the hypotenuse.

And that's geometry, which takes us back once again to physics.

Musical scales involve notes that, sounded simultaneously (chords), sound good together. The result is the left brain meeting the right brain — a Pythagorean interval of overlapping notes. This synergy would suggest less difference between the working of the right brain and the left brain than common wisdom would dictate. The pleasing sound of harmony comes when two notes share a common harmonic, meaning that their frequencies are in simple integer ratios, such as 3/2 (G/C) or 5/4 (E/C).

For the great composers, of course, the harmonies and scales are a template — the creativity that the composers bring is what makes great music. While not all composers understand mathematics and physics, some do. Gibson cites Bach as an example of a great composer who understood the techniques he was using. The melodic line is intimately related to harmony.
For many musicians — and their listeners — the physics and mathematics of music are instinctive. When a musician learns music, he or she is unconsciously learning complex patterns of sound, harmony and rhythm. When really good musicians make mistakes, those mistakes are often hard to detect because they are so well integrated into the established patterns of the piece.

Gibson notes that harmonic analysis exists in both science and music and is in fact the basis of much science, including X-ray diffraction. The geometric quality of vibrations that make up music are harmonic in time. Similarly, the work of physics, such as at Argonne's Advanced Photon Source, which examines the structure of life itself, is focused on what is harmonic in space.

Gibson says that people who are drawn to science and art have much in common. Both disciplines attract creative minds. Both fields demand that their disciples master technique long before they can be great scientists or great artists.

Science, like art and beauty, is at its best when it is elegant and simple. Gibson asserts that the language of mathematics, as expressed in calculus, is the most powerful and beautiful language known to humans because of its basic simplicity. When a single formula is versatile enough to explain processes as different as an electric motor, lightning and the landing of a 747, that simple sentence is poetic.

Both artists and scientists rely on the principles of mathematics and physics, whether consciously or intuitively, to achieve their goals. And, at the same time, both science and art rely on the creative questioner to ask, “Why do we do it this way?” and “Why not try something else and see what happens?”

Because that's when something interesting shows up in music and science that makes the world a better place to live.