User:Hkm/Sandbox: Difference between revisions

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== Badness ==

Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)**error_power) * complexity_fondness**(the complexity of the ~~motion~~) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.

Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93, and magic_number ~ 2.

Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)**error_power) * complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.

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 == Badness ==
-Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)**error_power) * complexity_fondness**(the complexity of the motion) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.
+Let min_cents ~ 35, error_power ~ 1.5, complexity_fondness ~ 0.93, and magic_number ~ 2.
+Let a "step" be any JI interval. We say that is the score of a "step" is equal to 1/(min_cents + (the step's error in cents)**error_power) * complexity_fondness**(the complexity of the step) / goodness_measurer. We then say that the score of a "path" is equal to the product of the scores of the steps. The score of a temperament with a list of generator tunings is equal to the sum of the scores of all paths that reach the original interval times those path lengths. The goodness of a temperament with a list of generator tunings is the goodness_measurer necessary to get a score of magic_number. (This also works for scales without JI interpretations; we assign a JI interpretation to each pair of notes and compute the goodness of the best assignment.) The goodness of a temperament on its own is the highest goodness that that temperament achieves; we can find optimal tunings for any temperament through this algorithm.