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…
Chords and other collections of notes have consistent, recognizable shapes on the lattice. A major chord is a triangle sitting on its base, a minor chord is a triangle on its point. Yesterday’s post has videos showing these chords. In the songs I know and write, the next most common chords after major and minor…
A chord is a collection of three or more notes sounded at the same time. Arpeggios, in which the notes are sounded one after the other, are considered chords too. Two notes sounded at once are generally called an interval rather than a chord. Chords make patterns on the lattice. A given kind of chord…
I want to show you some lattice movies of how I’ve used blue tritones in my own music. Real Girl has several examples. The clearest is a guitar lick in the chorus: That 7b5 is tasty over the bVI chord. For an instant, it makes a “barbershop seventh,” the 7th harmonic of the root. Here…
I just recorded a new song, and it’s a perfect example of how equal temperament and just intonation can get along together. Here’s the cut: Reading this blog might give you the impression that I’m “against” equal temperament and “for” just intonation, or untempered music. True, discovering untempered music has been like sailing to…
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…
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…
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…