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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…

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Polarity

The following video compares the perfect fifth with the perfect fourth. These notes are the next-door neighbors of the tonic. They are equally close to the center. They are both harmonious. Yet there is a great difference in their character. The difference between these two intervals is polarity. I learned this term from W.A. Mathieu,…

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Polarity Experiment

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…