Picking up the fifth hammer

This is a post that I had originally published on Medium on December 31, 2020. It has since fallen behind a paywall and so I am republishing it here.

There is a well-known conservative pundit who doesn’t believe that rap is music. To him, the statement “rap is not music” is a “fact” because he was told by his father — who studied music theory — that music has three elements: harmony, melody, and rhythm. Rap lacks harmony and melody and so ergo, it is not music.

Let’s put aside the absurdity that an application of logic can somehow invalidate the decisions of millions of people who have chosen hiphop to be the soundtrack of their lives. Applying logic to music feels absurd but there is historical precedent for the inclination to do so. Pythagoras, the ancient Greek philosopher that most of us associate with triangles, was known as both The Father of Mathematics and The Father of Music. Perhaps though it would be more accurate to call him The Father of Music Theory for his discovery that musical intervals are created by the length of an instrument (such as strings in a lyre) that follow simple numeric ratios.

These particular ratios produced pleasing sounds. The music became more beautiful because it fit a theory that was itself considered beautiful and pleasing to Pythagoras because the ratios were made up of whole numbers that added up to ten.

You should watch Adam Neely’s illuminating September 2020 YouTube video “Music Theory and White Supremacy” if you want to learn how the music theory of Ancient Greece progressed until it ossified into the cudgel of The Harmonic Style of 18th Century European Musicians that continues to be used to bash jazz, hiphop, and other forms of non-European music to this day.

Neely’s explainer of how music theory has been weaponized is robust enough that even a non-musician like myself now feels like I can readily defend my musical tastes from logic.

But in one particular way, I don’t believe that Neely goes far enough.

Let me tell you a little-known story about Pythagoras’ discovery of the mathematics behind harmonics and his music theory: it was based on a lie of omission.

An ancient tradition holds that Pythagoras invented harmony. It is said that one day, he wandered by a forge and, hearing a wondrous sound come from within, ventured in to investigate. He found five men hammering with five hammers. To his astonishment, he discovered that four of the five hammers stood in a marvelous set of proportions, which, when combined, allowed him to reconstruct the laws of music. But there was also a fifth hammer. Pythagoras saw and heard it, but he could not measure it; nor could he reason its discordant sound. He therefore discarded it.

a rusty hammer

When what we see doesn’t match up with the ideal that we have been told, we throw out that disharmonious part of the world. It becomes unseen.

But if you look closely and if you work hard to describe what’s in front of you before casting judgement on what you immediately see… you will find a world that has fifth hammers scattered everywhere.

Here’s my favourite example. The zodiac is defined as the path of the Earth’s orbit around the Sun (as they are experienced in the Northern Hemisphere) that brings a series of groups of stars called constellations into view. It was the ancient Babylonians who gave names to 12 of these constellations that we now associate with the signs of our horoscopes. The number 12 is significant. The Babylonians gravitated to numbers that fit into their sexagesimal number system, which means that they built their mathematics around a base of 60. We are so used to basing our numbers on ten (the decimal system) that twelve feels unnecessarily complicated. Yet we too have found it useful to divide our clocks into 60 minutes because it is so useful to divide an hour up in halves, quarters, and in five minute increments. And we too, like the Babylonians, have chosen to ignore the 13th constellation — Ophiuchus the Serpent Bearer — that also exists in the path of the Zodiac.

It is one thing to completely dismiss stars in the sky that everyone can see. It is an entirely other matter to look at people who do not fit a prescribed category and announce them as deformed. It has been estimated that 1.7% of the world’s population is intersex but they are not considered as natural as the 1.5% of the world that are redheads. It is not coincidence that the same people who don’t believe that rap is music also have very strong viewpoints on the categories of gender.

I have resolved that in 2021, I will look out for more fifth hammers. I will record more observations that will bring into question the supposed ideals of the status quo and share them here, on Medium.