Defactoring: Difference between revisions

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=== criteria ===

~~### talk about the criteria, like has to be integer, full-rank~~

In addition to being canonical and defactored, DCF has other important properties, which probably go without saying in the context of RTT mappings, but here they are just in case:

In addition to being canonical and defactored, DCF has other important properties:

* '''integer''': contains only integer terms.

* '''full-rank''': removes rank deficiencies, or in other words, rows that are all zeros

* '''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 ====

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]]

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

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### show the examples we tried, like in the big defactoring table

~~=== generator size manipulation ===~~

Initially Dave and I considered using 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. We ultimately decided no, because it was too much, and rabbit-hole ###

=== sum-and-difference defactoring ===

### explain our failed attempt at the sum-and-difference (SAD) defactoring... I think I can nab it mostly out of that message to Joe

@@ Line 209: / Line 209: @@
 === criteria ===
-### talk about the criteria, like has to be integer, full-rank
+In addition to being canonical and defactored, DCF has other important properties, which probably go without saying in the context of RTT mappings, but here they are just in case:
-In addition to being canonical and defactored, DCF has other important properties:
 * '''integer''': contains only integer terms.
 * '''full-rank''': removes rank deficiencies, or in other words, rows that are all zeros
 * '''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 ====
+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]]
 === relationship between various matrix echelon forms ===
@@ Line 418: / Line 420: @@
 ### show the examples we tried, like in the big defactoring table
-=== generator size manipulation ===
-Initially Dave and I considered using 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. We ultimately decided no, because it was too much, and rabbit-hole ###
 === sum-and-difference defactoring ===
 ### explain our failed attempt at the sum-and-difference (SAD) defactoring... I think I can nab it mostly out of that message to Joe