[Real Girl, posted 20 Aug 13]

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 is showcased often in the melody.This scale contains a sharp dissonance, between the b6 and the 7.  I go back and forth between those two notes a lot, with a stop on the 1 in between to help ease the transition.Watch how the melody and bass chase each other around. When the melody is below and to the left of the bass, the energy is reciprocal, tense. Then one or the other moves so that the melody is above and to the right, the energy becomes overtonal, and the tension resolves.

Another fun thing to watch is the alternating bass. Roots and fifths are right next to each other on the lattice. The red lens swings like a pendulum throughout the verses.

[Be Love, posted 6 Jun 13]

Be Love is a simpler song than Flying Dream, and it illustrates the lattice well. Note the shift in mode between verse and chorus, how it looks on the lattice, and how it feels in the music. I’ve added a green lens to the palette, for the guitar lick.

[Flying Dream, posted 28 Oct 12]

This may have been the most intense art project of my life. Some time early in 2012, I got it into my head to create a stop-motion animation of my song Flying Dream, moving in harmonic space. I’ve spent the past five months working like crazy on it. The song is carefully arranged using the lattice of fifths and thirds, sung and played in just intonation, and animated using colored lenses, rice paper and a flashlight.

This video encompasses almost everything I’ve learned in the past couple of years. I’ve described the lattice, and something of how it works, in my blog.

[Mozart, animated on the lattice, posted 6 Jan 13]

In one of my favorite passages in Harmonic Experience (p. 104-105), W.A. Mathieu points out that by the time Mozart came around, equal temperament was well enough established that a D# and an Eb could be thought of as the same note. So when Mozart wanted his melody to go back and forth between an Eb and an E, he wrote (spelled) the notes as D# and E, probably to make the music easier to read. In just intonation, D# is an entirely different note, and makes less harmonic sense than Eb.

I got curious as to how the two spellings would sound and look on the lattice. I also made one in equal temperament. They are quite different, and I think it’s fun to compare them. These are on YouTube with the following descriptions:


A passage from Sonata in F, K. 332. This is the spelling suggested by W.A. Mathieu, Harmonic Experience, p. 105. The melody moves between the major and minor third. Listen to the major/minor interplay in just intonation. This is in slow motion — the actual passage goes by in a few seconds.


A passage from Sonata in F, K. 332. This is how Mozart spelled it, with a #2 instead of a b3. He likely did this to make it easier to read. This video shows how that spelling would look, and sound, in just intonation, if taken literally. The melody moves by a diatonic semitone (112 cents) rather than by a chromatic semitone (70 cents), and the effect is quite different.


A passage from Sonata in F, K. 332, in equal temperament. In ET, the b3 and #2 are both tuned to a compromise pitch, in between the two. I think the ear turns it into a b3 here, but the affect is off, the note is quite flat. The whole passage feels different than it does in either of the JI versions.

How beautiful Mozart’s music is! I have watched the first video, in JI with the major/minor pair, many times. Try following just the orange one a couple of times, then just the yellow one.