One of the beautiful qualities of the lattice is that the patterns repeat everywhere. Notes that are in the same relationship to each other on the lattice will always have the same difference in pitch, no matter how where you go. For example, a move of one space to the right will always be a…
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…
As I’ve analyzed my songs on the lattice, and written new music using it as a tool, I have found that I have a certain palette of notes in my mind, a territory of the lattice that I can hear and think with. The notes in this portion are distinct individuals for me. Each one…
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….
Resonance, in general, is the tendency of a system to vibrate more strongly at some frequencies than at others. A great example of this is a playground swing. Like any pendulum, the swing “wants” to swing at a particular frequency, its resonant frequency. You can make yourself go higher and higher without a lot of…
I recently read Mickey Hart’s beautiful book, Drumming at the Edge of Magic. Hart is best known as one of the two drummers of the Grateful Dead. His book tells the story of his lifelong fascination with percussion, and of his investigations into the ancient connection between rhythm and the human spirit. Toward the end…
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…
A closer look at the untempered 12-note scale reveals some interesting patterns. Here’s the scale on the lattice again. This time, I’ve colored the notes as follows: Red = notes from the central, Pythagorean row, or spine, of the lattice. They are generated by multiplying and dividing by 3. Green = notes from the next row…
The familiar 12-note scale is also called the chromatic scale. There are many ways to generate an untempered version of such a scale. The oldest way seems to be Pythagorean tuning. When you multiply a frequency by 3, you get a new note, an octave plus a fifth above. Multiply by 3 again, and you get…