Temperament addition: Difference between revisions

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=Versus temperament merging=

Like [[~~tempermaent~~ merging]], temperament arithmetic takes temperaments as inputs and finds a new temperament sharing properties of the inputs. And they both can be understood as, in some sense, ''adding'' these input temperaments together.

Like [[temperament merging]], temperament arithmetic takes temperaments as inputs and finds a new temperament sharing properties of the inputs. And they both can be understood as, in some sense, ''adding'' these input temperaments together.

But there is a big difference between temperament arithmetic and merging. Temperament arithmetic is done using ''entry-wise'' addition (or subtraction), whereas merging is done using ''concatenation''. So the temperament sum of mappings with two rows each is a new mapping that still has exactly two rows, while the other hand, the merging of mappings with two rows each is a new mapping that has a total of four rows<ref>At least, this mapping would have a total of four rows before it is reduced. After reduction, it may end up with only three (or two if you map-merged a temperament with itself for some reason).</ref>.

@@ Line 187: / Line 187: @@
 =Versus temperament merging=
-Like [[tempermaent merging]], temperament arithmetic takes temperaments as inputs and finds a new temperament sharing properties of the inputs. And they both can be understood as, in some sense, ''adding'' these input temperaments together.
+Like [[temperament merging]], temperament arithmetic takes temperaments as inputs and finds a new temperament sharing properties of the inputs. And they both can be understood as, in some sense, ''adding'' these input temperaments together.
 But there is a big difference between temperament arithmetic and merging. Temperament arithmetic is done using ''entry-wise'' addition (or subtraction), whereas merging is done using ''concatenation''. So the temperament sum of mappings with two rows each is a new mapping that still has exactly two rows, while the other hand, the merging of mappings with two rows each is a new mapping that has a total of four rows<ref>At least, this mapping would have a total of four rows before it is reduced. After reduction, it may end up with only three (or two if you map-merged a temperament with itself for some reason).</ref>.