Owen Plant is my friend, and an outstanding singer/songwriter. He’s the artist-in-residence at a Georgia resort, a completely engrossing performer, and he has written many beautiful songs.
Owen commissioned me to animate the title cut from his new album, “I Was On The Moon,” cowritten by Owen and Christopher Tyng. It turned out to be a beautiful one visually. I especially like the chromatic “Wagon Wheel” runs in the bass (5 – b6 -6), the way passing notes in the acoustic guitar (orange) anticipate chord changes, and how the melody and vocal harmony chase each other around like butterflies.
The colors are:
Red = bass
Green = electric guitar and vibraphone
Orange = acoustic guitar and synths
Yellow light = melody
Yellow unlit = harmony vocal
It’s another labor of love, thousands of photographs of colored lenses, rice paper, and a yellow LED. Enjoy.
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 they are close in pitch.
In a harmonic space, such as the lattice, when two notes are close together, it means they are harmonically related.
“Harmonically related” means that one note can be converted into the other note by multiplying and dividing by small whole numbers. A note vibrating at 100 cycles per second is closely related to a note at 300 cycles per second. In melodic space, these two notes are far apart, but in harmonic terms they are right next door to each other — they harmonize.
In my video, Flying Dream, I animated the movement of one of my songs on the lattice. Now I’ve animated a composition of W. A. Mathieu’s.
Mathieu is the author of Harmonic Experience, an astonishing book that takes music back to its origins in resonance and pure harmony, and then uses the lattice concept to bring that harmonic understanding forward into the world of equal temperament. For me, the book opened the study of music like a flower.
The lattice, and my stop-motion animations, have given me a sort of musical oscilloscope. Instead of the music being some sort of black box, I can see inside it, get a visual image of what is going on harmonically. The new tool has made songwriting, improvising and arranging much easier.
I’ve animated Example 22.10 from the book. It’s intended to be an illustration of unambiguous harmony — the chord progression moves by short distances on the lattice, so it is clear to the eye and ear where you are. I think it’s a beautiful piece of music in its own right, a one-minute tour of a huge area of the lattice. It uses 28 different notes!
There are two versions of the video. The first one, in ET, has a soundtrack of Allaudin Mathieu playing the piece on his beautifully tuned piano. This is perfect equal temperament. It uses twelve notes to approximate the twenty-eight notes that the piece visits.
For the second one, in JI, I retuned the piano to the actual pitches of the lattice notes. Now, magically, the piano has all 28 notes. There is a whole new dimension to the music. In the JI version, I feel:
Slight vertigo when the music moves quickly
Satisfaction when a spread-out (tense) pattern collapses to a compact (resolved) one
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 chosen to simply add their overtonal and reciprocal components together to get the total polarity.
Here again is the graph of the 13 most central notes of the lattice.
The stable notes are gravity wells, and the unstable ones are peaks. Melodies and harmonies dance in this gravity field. Higher points represent tension, lower ones resolution, and the lower they are, the more resolved and stable. The tonic major triad, most stable of all, occupies the lowest spots — 1, 3 and 5.
The polarity map of the major scale looks like this:
The notes are all overtonal except the 4, which is strongly reciprocal, and the 6, which is mixed and slightly unstable.
Here’s a split screen video showing the major scale, against a tonic drone, on both the lattice and the octave. This is an example of how the lattice serves as a Rosetta Stone, a translator between harmonic and melodic space.
Can you hear the push/pull quality of the notes? Each note has its own feeling against the steady 1.
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 darker, more dissonant note than its comma sibling, the 2.
The b7 is dissonant and gorgeous — check out the sequence at the end of this post.
Each note is a compound of three legs on the lattice — two fifths, or a factor of 9, and a major third, a factor of 5. By the logic of the last post, the short leg should predominate, which would make the 2- slightly overtonal and stable, and the b7 slightly reciprocal and unstable.
I’m setting up here for a map of the tonal gravity field. I think I can put some numbers on this stuff. Coming soon. I’ll use that new song animation as a basis — it’s full of fleeting dissonances and polarity flips.
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 and x3.
The next overtonal note out from the center is the major seventh, or 7. Its ratio is 15/1, or x3, x5.
The 7 has its mirror twin too, the b2-, at 112 cents. Its ratio is 1/15.
Here is how they sound:
For me, the pattern continues. The 7 is stable, but less so than the notes we’ve heard so far, and it’s getting dissonant as well, because it’s farther from the center. The b2- is both dissonant and unstable.
These notes each traverse two legs of the lattice, a 3 and a 5. The 7 is two legs “up,” or multiplying, and the b2- is two “down,” or dividing.
How will this affect stability and instability? I’ll guess that since 3 is a shorter distance than 5 is, and closer to the center means stronger gravity, the factor of 3 will dominate the blend.
So 3/5, the minor third, should lean toward the overtonal, and 5/3, the major sixth, should lean toward the reciprocal.
This hypothesis is supported by the long tradition that the minor third is a stable note, less so than the major third but OK to end a song with.
That is indeed what I hear, although it’s less clear than it is with earlier intervals.
All four of these intervals use the same prime factors, and cover the same harmonic distance. The difference between them is polarity.
