Normal forms: Difference between revisions

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add more context and examples
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If the ''i''-th entry in the result is negative, change the signs of every entry in the corresponding row of the mapping.
If the ''i''-th entry in the result is negative, change the signs of every entry in the corresponding row of the mapping.


The "mapping" (though not the "Map to lattice") listed on temperament pages of this wiki are in this form. The generators in canonical form of septimal meantone is positive already, so its positive generator form is the same as its canonical form, [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10 }}], corresponding to generators of ~2/1 and ~3/1.  
The "mapping" (though not the "map to lattice") listed on temperament pages of this wiki are in this form. The generators in canonical form of septimal meantone is positive already, so its positive generator form is the same as its canonical form, [{{val| 1 0 -4 -13 }}, {{val| 0 1 4 10 }}], corresponding to generators of ~2/1 and ~3/1. An example of positive generator form that is different from the canonical form is the porcupine temperament, elaborated below.  


For an example of finding the positive generator form from the canonical form, the canonical mapping for porcupine is
The canonical mapping for porcupine is


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