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…
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…
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…
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…
I just passed the 10,000 photo mark on the stop motion animations, good thing I’m not hand-drawing them like Winsor McCay! The one I’m working on, Real Girl, has a lot of dissonant notes in it. The melody ranges far from the roots and makes some slightly dizzying harmonic jumps. I want to use it…
The V chord, the major chord based on the 5, is a powerful compositional tool. It points, very clearly and with a lot of tension, directly at the tonic. If you want to lead the ear to the I, the V chord is the top-of-the-line triad. Why this is so is still a bit mysterious…
Be Love was written and arranged on the lattice. I consciously used the lattice as a tool to make the music do what I wanted it to do. Working with this song has taught me a lot about leading the ear. Different parts of the lattice have different sounds. The upper right, the northeast, is…
There are two basic directions on the lattice: multiplication and division. If I start with a note, and then multiply it by 3, or 5, or 7, I will get a harmony note with overtonal energy. Such a note is in the natural overtone series of the original note. Overtonal energy is stable, restful, it…
When I started exploring the extended lattice beyond the central 12 notes, the first note that was really new to me was the 10/9 major second, also called the minor or lesser whole tone. Now I call it the 2-. The lattice extends forever in all directions. When you continue multiplying and dividing, generating new notes beyond the boundaries…
I’ve described eleven notes now, and each one has a piano key to go with it, an equal tempered equivalent. The one remaining black key has a lot of names. It’s the note between the 4 and 5, right in the middle of the octave — the tritone, devil’s interval, flatted fifth, augmented fourth. In…