The Harmonic Lattice can be viewed as a map of harmonic space. Music moves in harmonic space, just as it moves in melodic space (the world of scales and keyboards). The two spaces are very different from each other. In melodic space, such as a piano keyboard, when two notes are close together, it means…
In my last post, I proposed a simple way to graph tonal gravity against the octave. Overtonal notes, generated by multiplying, are restful, stable — they have positive polarity, pulling toward the center. Reciprocal notes, generated by division, are restless, unstable — they push. I call this negative polarity. Mixed-polarity notes have both, and I’ve…
I believe the sensation of tonal gravity is the most important driver of tension and resolution in tonal music, music that has a central key note. The tonic is like a sun, creating a gravitational field around it. The lattice is a beautiful map of this gravitational field, in harmonic space. Tonal gravity acts like…
Major and minor chords look like triangles on the lattice. They are closed loops, which I think contributes to their stable feeling. Up a major third, up a minor third, and down a fifth (due West on the lattice) brings you right back where you started. The intervals interlock, and they are all consonant, reinforcing…
My new song video, Real Girl, contains many examples of consonance and dissonance, tension and resolution. In my last post, I extracted a phrase from the song and slowed it way down to illustrate how the bass and melody dance, creating and resolving tension in several different ways. Here is the last half of that…
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…
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…
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…
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,…