I keep working my way closer to recording in strict just intonation. Here’s one I did today, of my song Breakup Songs. The acoustic guitar is in equal temperament, and the bass and vocals are untempered. I love singing harmony when the fretless bass is playing lattice notes. Sometimes I feel like I’m sliding…
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 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…
The picture to the right shows the lattice of fifths and thirds, a map of untempered harmonic space, extending to infinity. The map shows how to venture farther and farther from home, the tonic, and stay perfectly in tune no matter how far you roam. Every single note in this infinite matrix is tuned to a different…
The lattice goes on forever in every direction. It starts with the tonic, the 1, the Big Bang of the musical universe. Multiplying and dividing the tonic by 3 generates the horizontal axis. This is the familiar circle of fifths, although in just intonation, it doesn’t quite come out exact. If you multiply by 3,…
Why are the rings of Saturn so beautiful? The photo to the right was taken by the Cassini spacecraft when the sun was behind the planet, and backlighting the rings and the edge of the atmosphere. A type of solar eclipse never before seen by humans! The rings are composed of millions of small particles, mostly ice, orbiting Saturn….
Yesterday, I described a simple way to hear, and more importantly, feel, the difference between equal temperament and just intonation, by singing Frère Jacques over an open G chord with ET major thirds, and then over a G chord that has only roots and fifths in it. The second half of the experiment is called singing over…
It would be natural to read these posts and wonder why I’m so passionate about intonation, and why I’m going to so much trouble to explore it in this blog and in real life. After all, we’re talking about tiny differences in tuning here, why be so picky when it’s the heart that counts? It’s…
The simplest untempered tuning of the major scale is: 1 — 0 cents 2 — 204 3 — 386 4 — 498 5 — 702 6 — 884 7 — 1088 Here’s how that tuning compares with the equal tempered scale: The black numbers show the pitches of 12-tone equal temperament. They are equally…