Douglas Blumeyer's RTT How-To: Difference between revisions

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maps the fourth (4/3, {{vector|2 -1 0 }}) to {{vector|0 1}}. That form is called [[mingen]] form.

But there are still more forms! One very important form is called '''[[canonical form]]'''.

But there are still more forms! One very important form is called [[defactored Hermite form]], or we may call it here '''canonical form''' for short.

It’s often the case that a temperament’s nullity is greater than 1 or its rank is greater than 1, and therefore we have an infinitude of equivalent ways of expressing the comma-basis or the mapping-row-basis. This can be problematic, if we want to efficiently communicate about and catalog temperaments. It’s good to have a standardized form in these cases. The approach RTT takes here is to get these matrices into canonical form. In plain words, this just means: we have a function which takes in a matrix and spits out a matrix of the same shape, and no matter which matrix we input from a set of matrices which we consider all to be equivalent to each other, it will spit out the same result. This output is thereby “canonical”, and it can therefore uniquely identify a temperament.

@@ Line 1,080: / Line 1,080: @@
 maps the fourth (4/3, {{vector|2 -1 0 }}) to {{vector|0 1}}. That form is called [[mingen]] form.
-But there are still more forms! One very important form is called '''[[canonical form]]'''.
+But there are still more forms! One very important form is called [[defactored Hermite form]], or we may call it here '''canonical form''' for short.
 It’s often the case that a temperament’s nullity is greater than 1 or its rank is greater than 1, and therefore we have an infinitude of equivalent ways of expressing the comma-basis or the mapping-row-basis. This can be problematic, if we want to efficiently communicate about and catalog temperaments. It’s good to have a standardized form in these cases. The approach RTT takes here is to get these matrices into canonical form. In plain words, this just means: we have a function which takes in a matrix and spits out a matrix of the same shape, and no matter which matrix we input from a set of matrices which we consider all to be equivalent to each other, it will spit out the same result. This output is thereby “canonical”, and it can therefore uniquely identify a temperament.