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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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Putting Some Numbers on Tonal Gravity

I believe the sensation of tonal gravity is the most important driver of tension and resolution in tonal music, music that has a central key note. The tonic is like a sun, creating a gravitational field around it. The lattice is a beautiful map of this gravitational field, in harmonic space. Tonal gravity acts like…

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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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More Mirror Twins

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…