Subgroup temperament families, relationships, and genes: Difference between revisions

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 The most important genes are codimension-1. A codimension-1 gene is just the pairing of one subgroup and a comma tempered out on that subgroup and is called a ''base pair.'' It is fairly natural to extend the definition of genes to codimension-2, codimension-3, etc, but for now I will primarily focus on codimension-1 below.
-Genes, and base pairs in particular, are meant to generalize commas, which are ratios are tempered out by some temperament. Any subgroup temperament could hypothetically be a gene, much like any ratio of any kind could hypothetically be a comma, but in both situations the term has the added interpretation of suggesting that the "gene" or "comma" is particularly musically useful as the nucleation point for a subgroup family, i.e. it is low-complexity, low-error, and in this case, on a relatively simple subgroup. So much like 81/80, 64/63, and 243/242 are JI intervals that make for good commas, we have that 2.3.5 81/80, 2.3.7 64/63, 2.3.11 243/242 are subgroup temperaments that make for good genes.
+Genes, and base pairs in particular, are meant to generalize commas, which are ratios tempered out by some temperament. Any subgroup temperament could hypothetically be a gene, much like any ratio of any kind could hypothetically be a comma, but in both situations the term has the added interpretation of suggesting that the "gene" or "comma" is particularly musically useful as the nucleation point for a subgroup family, i.e. it is low-complexity, low-error, and in this case, on a relatively simple subgroup. So much like 81/80, 64/63, and 243/242 are JI intervals that make for good commas, we have that 2.3.5 81/80, 2.3.7 64/63, 2.3.11 243/242 are subgroup temperaments that make for good genes.
 Note that being a good gene is quite a bit stronger criterion than being a good comma. For instance, if we are only looking at rank-2 genes, note that the comma 64/63 does very well, with at least two good genes right away - 2.3.7 64/63 and 2.7.9 64/63. The "simpler" comma 36/35, on the other hand, doesn't lead to any good rank-2 genes at all. This is because there simply is not any decent rank-3 subgroup that has 36/35 in it to begin with; the simplest is 2.3.35. Another instance is 1029/1024, which does very well on the 2.3.7 subgroup with 2.3.7 1029/1024 (slendric), whereas the simplest rank-2 genes for the much "simpler" comma 126/125 are 14.3.5 126/125 and 2.5.63 126/125. Put another way, 126/125 really is kind of a rank-3 comma; the 2.3.5.7 126/125 (starling) temperament is very good, but it simply doesn't do well in the rank-2 setting unless some other comma is also added.