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Dyadic chord/Pattern of essentially tempered chords: Difference between revisions

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Turns out ptolemismic isn't of pattern 1 since the 3's can be stacked to 9
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* 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''d''<sub>1</sub>/''d''<sub>2</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>, and its inverse
* 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''d''<sub>1</sub>/''d''<sub>2</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>, and its inverse
* 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>.  
* 1-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>-''n''<sub>1</sub>/''d''<sub>2</sub>-''n''<sub>2</sub>/''d''<sub>1</sub> with steps ''d''<sub>1</sub>/''n''<sub>2</sub>-''n''<sub>2</sub>/''n''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>2</sub>-''d''<sub>2</sub>/''d''<sub>1</sub>-''d''<sub>1</sub>/''n''<sub>1</sub>.  
=== Defective ===
Defective pattern 1 is where some of these chords turn out essentially just. [[Ptolemismic chords]] are of this category, as it only has a palindromic triad, two pairs of inversely related tetrads, and a pair of inversely related pentads.


== Pattern 2 ==
== Pattern 2 ==
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