For every note on the lattice (except the 1), there is another note, the same distance away from the center and exactly opposite it. The harmonic moves for the two notes are the same, but the directions are opposite.
Listening to these mirror twins helps demonstrate polarity.
The simplest ratios on the lattice, the ones with the smallest numbers in them, are 3:1 and 1:3, the perfect fifth and perfect fourth. Here they are:
Tonal gravity is strong here close to the sun. The fifth sounds remarkably resolved, like it’s part of the drone. In fact, this note shows up so strongly in the natural overtone series that it is part of the drone. If you listen carefully to that tonic drone by itself, you can hear it. The following video shows a 5 by itself, followed by the straight drone on the 1. I hear the fifth appear again, quietly, after the drone has a few seconds to settle in and bloom.
The fifth says, “You’re home, relax.”
The fourth also shows where home is, but in a very different way. Instead of saying, in effect, “Home is here, come on,” It is saying “Home is over there, now go.”
Our built-in audio processor is always looking for mathematical relationships between notes so we can tell which frequencies belong together, identify different sound sources and orient ourselves in our surroundings. I think this is why we hear harmony and why it sounds like a journey — it’s a part of our built-in orientation software.
Three cycles for every one is a “right” ratio. It strongly says, “These frequencies belong together, they are being made by the same thing.” But the ratio is upside down, 1/3, the exact opposite of the “right” sound, 3/1. It’s the shadow version of the 5, yin to its yang.
The 5 feels like this:
The 4 feels like this:
The beautiful stability of the 5, contrasted with the equally beautiful instability of the 4, is what I mean by polarity.