Generator embedding optimization: Difference between revisions

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Which brings us finally, to the "A" part of the initialism, for "abbreviated". Specifically, we only keep the first <math>r + 1</math> entries in these lists, and throw out the rest. This is where <math>r</math> is the [[rank]] of the temperament, or in other words, the count of generators it has. Again, this is the dimension of the tuning damage space we're searching, and so its the number of points required to specify a point within it.

Critically, for our purposes here, that means it's the maximum number of target-intervals we could possibly have minimaxed damage to at this time. That's why if these ADSLODs are identical all the way down, we need to try something else, in a new tuning damage space.

Critically, for our purposes here, that means it's the maximum number of target-intervals we could possibly have minimaxed damage to at this time; if we look any further down this list, then we can't ''guarantee'' that the damage values we're looking at are as low as they could possibly be at their position in the list. That's why if these ADSLODs are identical all the way down, we need to try something else, in a new tuning damage space.

We'll learn about this in the advanced tie-breaking section later on.

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 Which brings us finally, to the "A" part of the initialism, for "abbreviated". Specifically, we only keep the first <math>r + 1</math> entries in these lists, and throw out the rest. This is where <math>r</math> is the [[rank]] of the temperament, or in other words, the count of generators it has. Again, this is the dimension of the tuning damage space we're searching, and so its the number of points required to specify a point within it.
-Critically, for our purposes here, that means it's the maximum number of target-intervals we could possibly have minimaxed damage to at this time. That's why if these ADSLODs are identical all the way down, we need to try something else, in a new tuning damage space.
+Critically, for our purposes here, that means it's the maximum number of target-intervals we could possibly have minimaxed damage to at this time; if we look any further down this list, then we can't ''guarantee'' that the damage values we're looking at are as low as they could possibly be at their position in the list. That's why if these ADSLODs are identical all the way down, we need to try something else, in a new tuning damage space.
 We'll learn about this in the advanced tie-breaking section later on.