Generator form manipulation: Difference between revisions
Cmloegcmluin (talk | contribs) m update templates, fix typo, clarifying footnotes |
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So at this point, the generators are an octave and a negative perfect fifth. It's time for our second step. | So at this point, the generators are an octave and a negative perfect fifth. It's time for our second step. | ||
The second step of achieving a generator with the size of a perfect fourth should be familiar: we need to increase our negative perfect fifth to a perfect fourth, and so we need to add one octave, and therefore we need to change <math>𝒎_1</math> to be <math>𝒎_1 - | The second step of achieving a generator with the size of a perfect fourth should be familiar: we need to increase our negative perfect fifth to a perfect fourth, and so we need to add one octave, and therefore we need to change <math>𝒎_1</math> to be <math>𝒎_1 - 𝒎_2</math>, so we end up with: | ||
<math> | <math> | ||
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</math> | </math> | ||
And we're done, having found the mapping {{rket|{{map|1 2 4}} {{map|0 -1 -4}}}}. | And we're done, having found the mapping {{rket|{{map|1 2 4}} {{map|0 -1 -4}}}}. | ||
=== Beyond rank-2 === | === Beyond rank-2 === | ||