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…
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…
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 have a favorite note. Don’t tell the others. It’s the septimal flat five, or septimal tritone. I call it 7b5 on the lattice. There are many reasons why I love this note. One is that Jimi played it, and he’s my favorite musician of them all. Another is that this note is rarely discussed…
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…
For every note on the lattice (except the 1), there is another note, the same distance away from the center and exactly opposite it. The harmonic moves for the two notes are the same, but the directions are opposite. Mirror twins are reciprocals of each other. Flipping a note’s ratio upside down will produce its…
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…