Normal forms: Difference between revisions

Dave Keenan (talk | contribs)
Normal val lists: Replaced "list of 𝑟 vals as an" with "list of vals (mapping) as a". Replaced "are the vals" with "are the vals (maps)". It's not initially limited to "𝑟", and since DHF is a D&D thing, it should include D&D terminology.
Cmloegcmluin (talk | contribs)
Defactored Hermite form: remove link to information that was removed
Line 196: Line 196:


=== Defactored Hermite form ===
=== Defactored Hermite form ===
Given a matrix of ''p''-limit intervals, we can find its defactored Hermite form in much the same way as a mapping. The only difference is that they must be put in an "antitranspose sandwich", or in other words, antitransposed<ref>See a discussion of the antitranspose here: [[Dave Keenan & Douglas Blumeyer's guide to RTT: exploring temperaments#Antinullspace]].</ref> once at the beginning, and then antitransposed again at the end.
Given a matrix of ''p''-limit intervals, we can find its defactored Hermite form in much the same way as a mapping. The only difference is that they must be put in an "antitranspose sandwich", or in other words, antitransposed once at the beginning, and then antitransposed again at the end.


For example, suppose we have the comma basis for septimal meantone:
For example, suppose we have the comma basis for septimal meantone: