In the last few posts, I’ve been exploring mirror twins — notes at the same harmonic distance from the center, but of opposite polarity.

The notes explored so far are 3/1, 5/1, 7/1, 9/1, and their reciprocals, 1/3, 1/5, 1/7 and 1/9. The 9/1 and 1/9 are made up of two legs on the lattice, x3 and x3.

The next overtonal note out from the center is the major seventh, or 7. Its ratio is 15/1, or x3, x5.

The 7 has its mirror twin too, the b2-, at 112 cents. Its ratio is 1/15.

Here is how they sound:

For me, the pattern continues. The 7 is stable, but less so than the notes we’ve heard so far, and it’s getting dissonant as well, because it’s farther from the center. The b2- is both dissonant and unstable.

These notes each traverse two legs of the lattice, a 3 and a 5. The 7 is two legs “up,” or multiplying, and the b2- is two “down,” or dividing.

What if one stick goes up and the other one down?

These notes are the minor third, 3/5, and the major sixth, 5/3. They are compounds of overtonal and reciprocal energy.

How will this affect stability and instability? I’ll guess that since 3 is a shorter distance than 5 is, and closer to the center means stronger gravity, the factor of 3 will dominate the blend.

So 3/5, the minor third, should lean toward the overtonal, and 5/3, the major sixth, should lean toward the reciprocal.

This hypothesis is supported by the long tradition that the minor third is a stable note, less so than the major third but OK to end a song with.

That is indeed what I hear, although it’s less clear than it is with earlier intervals.

All four of these intervals use the same prime factors, and cover the same harmonic distance. The difference between them is polarity.

Next: One More Mirror Pair