Ternary scale theorems: Difference between revisions

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Write ''s''<sub>1</sub> for the scale word made from stacked 2-steps from the 0-degree, and let ''s''<sub>2</sub> be the scale word of stacked 2-steps from the 1-degree.
Write ''s''<sub>1</sub> for the scale word made from stacked 2-steps from the 0-degree, and let ''s''<sub>2</sub> be the scale word of stacked 2-steps from the 1-degree.
* In the singly even case, since ''s''<sub>2</sub> is the same as the circular word of 2-steps starting at the (n/2)-degree, we know that they differ only by interchanging '''y''' and '''z''', hence that they have the same period. Hence both ''s''<sub>1</sub> and ''s''<sub>2</sub> are primitive.
* In the singly even case, let ''s''<sub>2</sub> be the circular word of 2-steps starting at the (n/2)-degree. We know that they differ only by interchanging '''y''' and '''z''', hence that they have the same period. Hence both ''s''<sub>1</sub> and ''s''<sub>2</sub> are primitive.
* In the doubly even case, let ''s''<sub>2</sub> be offset at the generator, which has the same dyad class as some generator of the MOS 2aX 2cZ.
* In the doubly even case, let ''s''<sub>2</sub> be offset at the generator, which has the same dyad class as some generator of the MOS 2aX 2cZ.