In her online article Quantum Music, Katie McCormick addresses music in a way connected to quantum mechanics. She also draws on Pythagoras and Galileo. But the subtitle: What if dissonance yields better results? is key. In my own terms, all things have vibrations, waves or harmonics; these are absolutely natural to everything.

This picture was taken by Mark Ruffin and shows a Memorial at Ripon Cathedral where our Choir sang in 2019. About two-thirds of the way down you can make out “Easter Day” and the date “169 4/5” This isn’t a mistake, but when the Gregorian Calendar was adopted in Yorkshire. Hence the engraver wasn’t sure of the year.

Pythagoras realized the scale cannot be broken into 12 or thirteen (a repeat of 1) equal parts. Octaves should meet and the fourth and fifth should be perfect, but then everything else falls apart. Bach had this problem (thus writing his Well-Tempered Clavier) and any music before the baroque period had to favor certain keys in order to be playable, or to be listenable. The unacceptable keys were said to have a “wolf” because the dissonance “howled,” and Bach would purposely play in these keys to encourage mathematicians and tuners to devise a more universal tuning method. As science progressed they were able to break down the 12 (13) notes into perfectly divided pitches, which meant every single interval was impure and wrong, and we became inured to it. You hear the greatest concert pianists playing on a piano that is purposely totally out of tune, but our ears accept it. Now, when we hear pure tonalities we think it sounds sour.
If we tune a system based on perfect fifths (which is how we tune) C to G, then G to D, etc., we eventually get back to the original C (13) but that C 13 is wildly out of tune with the original C thus proving perfection is not real, and dissonance is perfect. To make it fit (beat it into submission) each interval has to be drawn in by a fiftieth (doesn’t sound much) to make the Cs meet.
Enter Galileo. Until recent times the Church refused to embrace science. The world was flat, and Earth was the center of the Universe. Around 1582 the Church had no choice but to flip from the Julian Calendar (named after Julius Caesar) to the Gregorian Calendar – the Eastern Orthodox are still unhappy about it. Galileo could tell from his study of the Solar System that something was off, and it was big leap for Pope Gregory XIII to make this change. However, it took until 1992 for the Vatican to acknowledge Galileo was correct all along! Nevertheless, even now the day isn’t exactly 24 hours long (it’s 24 hours and 26 seconds) and every four years we need to make an adjustment – the leap year.
In recent times, with the advent of nuclear microscopy, we have learned that fractal patterns constantly evolve but never end. The closer you get, the more the pattern develops. This is the same with the harmonic series and the universe. There may be a beginning but there’s certainly no end. It could be a simile for the Christian Life.