Wednesday, July 3, 2013

The math in the twelve-tone


First number the pitches in order from 0 to 11 to name the intervals of twelve in the circle with twelve referring dots. When you draw lines connecting the first and the last intervals of a serial, which are both minor thirds, you can have several parallel lines with arrows on them. If we don’t move the dots and rotate the lines by 180 degrees, the blue line between D and C# would end up being line from G# to G with the arrow pointing the other direction. The same thing is true for all the other lines. This is not an accident. It is the principle with triton of twelve-tone.

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