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Tonal Gravity and the Major Scale

In my last post, I proposed a simple way to graph tonal gravity against the octave. 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…

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Three Flavors of Seventh Chord

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…

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Premature Nostalgia: Making Friends With Equal Temperament

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…

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Tonal music is music that has a particular key center, or home note. Not all music is tonal, but most is, worldwide. The key note is at the center of the lattice of fifths and thirds. All other notes are generated from this one. I call it the 1. It’s also called the tonic. When we say…


Another Comma

One more comma shows up in the central portion of the lattice. In equal temperament, three major thirds adds up to an octave. The major third is an interval of four piano keys (out of 12) or 400 cents. Three of them is 1200 cents, exactly an octave. In just intonation, this is not the…

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Another Major Second: The 10/9

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…

Saturn’s Rings

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….