Defactoring: Difference between revisions

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* '''preserves genuine unit-fraction-of-an-prime periods''': at first glance, when a pivot is not equal to 1, it might trigger you to think that the mapping is enfactored. But temperaments can legitimately have generators that divide primes evenly, such as 5-limit Blackwood, {{vector|{{map|5 8 0}} {{map|0 0 1}}}}, which divides the octave into 5 parts.<ref>Any form that enforces pivots all be 1's would fail this criteria.</ref>

==== mingen ====

==== exclusion of generator size target criteria; mingen form ====

Initially, Dave and Douglas considered the proposal of a new standard RTT mapping form as an opportunity to include everything and the kitchen sink — in this case, to additionally massage generator sizes to fit a desirable rubric. It was ultimately decided to stay conceptually focused when drafting the proposal, leaving generator size out of the mix. Also, the particular generator size target they sought turned out to be a bit of a rabbit hole, especially above rank-2, both in terms of mathematical reality and engineering practicality. The results of those efforts are documented here: [[Generator size manipulation#mingen_form]]

Initially, Dave and Douglas considered the proposal of a new standard RTT mapping form as an opportunity to include everything and the kitchen sink — in this case, to additionally massage generator sizes to fit a desirable rubric. It was ultimately decided to stay conceptually focused when drafting the proposal, leaving generator size out of the mix. Also, the particular generator size target they sought — named "mingen" — turned out to be a bit of a rabbit hole, especially above rank-2, both in terms of mathematical reality and engineering practicality. The results of those efforts are documented here: [[Generator size manipulation#mingen_form]]

=== relationship between various matrix echelon forms ===

@@ Line 214: / Line 214: @@
 * '''preserves genuine unit-fraction-of-an-prime periods''': at first glance, when a pivot is not equal to 1, it might trigger you to think that the mapping is enfactored. But temperaments can legitimately have generators that divide primes evenly, such as 5-limit Blackwood, {{vector|{{map|5 8 0}} {{map|0 0 1}}}}, which divides the octave into 5 parts.<ref>Any form that enforces pivots all be 1's would fail this criteria.</ref>
-==== mingen ====
+==== exclusion of generator size target criteria; mingen form ====
-Initially, Dave and Douglas considered the proposal of a new standard RTT mapping form as an opportunity to include everything and the kitchen sink — in this case, to additionally massage generator sizes to fit a desirable rubric. It was ultimately decided to stay conceptually focused when drafting the proposal, leaving generator size out of the mix. Also, the particular generator size target they sought turned out to be a bit of a rabbit hole, especially above rank-2, both in terms of mathematical reality and engineering practicality. The results of those efforts are documented here: [[Generator size manipulation#mingen_form]]
+Initially, Dave and Douglas considered the proposal of a new standard RTT mapping form as an opportunity to include everything and the kitchen sink — in this case, to additionally massage generator sizes to fit a desirable rubric. It was ultimately decided to stay conceptually focused when drafting the proposal, leaving generator size out of the mix. Also, the particular generator size target they sought — named "mingen" — turned out to be a bit of a rabbit hole, especially above rank-2, both in terms of mathematical reality and engineering practicality. The results of those efforts are documented here: [[Generator size manipulation#mingen_form]]
 === relationship between various matrix echelon forms ===