## 100 Girlfriends

There is a passage, in my song Real Girl, that clearly showcases both kinds of dissonance — the kind that comes from harmonic distance, and the kind that comes from reverse polarity. This melodic passage occurs many times in the song, and it contains a rather dizzying series of tensions and resolutions. My friend Jody…

## Real Girl, Animated

Here is my third stop-motion animation of a full song. Real Girl uses a custom nine-note scale. It occupies the Southeast quadrant of the lattice, the zone of the natural minor, with two added notes — the 7, which allows for a major V chord in the progression, and the 7b5, a blue note that…

## One More Mirror Pair

I’m almost done with the next full-song video. In the meantime, here’s one more pair of mirror twins for consideration. The 2- is a common melody note in my songs, and in the blues. It goes well with the blue note 7b3 — there is an extremely common melody that goes 7b3, 2-, 1. It’s a…

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…

## Why Can We Hear Harmony?

My friend Scott is an expert river rafter. I went down the American River with him once. We had about five crew. It was a big raft, and well-behaved, so he decided he’d leave the driving to us, sit in the bottom of the boat, and go through one of the rapids with his…

## More Mirror Twins

Mirror twins are pairs of intervals, exactly opposite each other on the lattice. The two intervals are reciprocals of each other, which means their ratios are flipped — if one is 5/3, the other is 3/5. Harmonic distance is the same for each interval — the only difference is polarity. Listening to mirror twin pairs gives…

## Polarity

The following video compares the perfect fifth with the perfect fourth. These notes are the next-door neighbors of the tonic. They are equally close to the center. They are both harmonious. Yet there is a great difference in their character. The difference between these two intervals is polarity. I learned this term from W.A. Mathieu,…

## Mirror Twins

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. Mirror twins are reciprocals of each other. Flipping a note’s ratio upside down will produce its…

## Harmonic Distance

Harmonic distance is the total length of the connection between two notes on the lattice, as measured on the solid lines. The more tinkertoy sticks you traverse to get from one note to the other, the greater the harmonic distance. It’s not the same thing as melodic distance, which is a difference in pitch. Two notes can…

## Polarity Experiment

In the last post I did a consonance experiment, listening to intervals with wider and wider spacing. In that experiment, I kept the axis (3) and direction (multiplication, overtonal) the same, and increased the distance. This time I’ll keep the axis and the distance the same, and switch direction. Each illustration will compare a note with…