July 29, 2023
Guest Writers: Dr. Joel Plaag
A musing on Psalm 8:3. When I consider the heavens, the work of your fingers, the moon and stars which you have set in place...
I really didn't like physics class. I think part of the reason was, even though the teacher was the mother of one of my classmates, I never quite understood all of the directions. The math wasn't fun. The subject seemed uninteresting. That feeling colored my perception of physics of music in college, where I groaned through long lectures about wavelengths with the interest of a five-year-old at a United Nations Treaty readthrough.
But then an ironic thing happened - I took a course on the history of music theory - one of my favorite topics. I had been introduced to amazing concepts like the mathematical properties of Equal Temperament - the bending of notes from pure tuning to approximate, equidistant tuning. (¹²√2)⁸⁴=2⁷=128
I had learned about the story of Pythagoras hearing the clanging of a blacksmith's hammer on an anvil and coming up with the overtone series. I had learned the ratios of string lengths to pitches; 2 to 1 was an octave, 4 to 3 was a perfect fifth and 9 to 8 was a whole step. I learned of the Pythagorean comma, which is the difference between "pure" whole steps and "pure" octaves, and the discrepancy between them, represented mathematically, which is: 531441⁄524288 ≈ 1.01364
And I think to myself - why are there all of these rules in music? Who came up with the ideas that could be expressed mathematically like this?
Today I'd have to go back and review how to perform a square root function without a calculator. I'd need a lot more fingers and toes to create exponential functions. But today I also know that a graph for x² looks like this, and can be seen in ranks of pipes, who also follow this formula.
Check out the row of pipes near the back and compare it to the x² line.
These kinds of orderly progressions are fascinating to me. Did they happen by random chance? Hardly. Some people, when they look at a set of organ pipes, see the handiwork of the organ builder, the beautiful woodworking, or the exacting way that an organ has been placed in a space that is seemingly too small to fit. But I see God's handiwork. I see that x² line, and I think of evidence of God who created structures for us, and I'm continually amazed.
Rev. Bruce Frogge