Path-based goodness: Difference between revisions

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Path-based goodness is a metric for judging the accuracy and simplicity of temperaments. To compute path-based goodness, we can apply the following steps:

# Choose values for the parameters <code>error_power</code>, <code>complexity_fondness</code>, <code>inaccuracy_fondness</code>, and ~~<code>~~target_score~~</code>~~. The canonical values are:

# Choose values for the parameters <code>error_power</code>, <code>complexity_fondness</code>, <code>inaccuracy_fondness</code>, and target_score. The canonical values are:

::: <code>error_power</code> = 1.5,

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::: <code>target_score</code> = 0.02.

# Let ''g'' be a variable. Assign to every JI interval (except 1/1) n/d with error e (in cents) a score equal to <code>inaccuracy_fondness</code>^(e^<code>error_power</code>) * <code>complexity_fondness</code>^(n+d) / ''g''.

# Let ''g'' be a variable. Assign to every JI interval (except 1/1) n/d with error e (in cents) a score equal to <code>inaccuracy_fondness</code>^(e^<code>error_power</code></code>) * <code>complexity_fondness</code>^(n+d) / ''g''.

# Assign to every ordered list of JI intervals a score equal to the product of the scores of all of its steps.

# Assign to every temperament with tuning a score equal to the sum of the scores of all the paths that yield a comma when the intervals are stacked.

# Assign to every temperament with tuning a ''goodness'' equal to the value ''g'' such that the score is equal to the ~~<code>~~target_score~~</code>~~.

# Assign to every temperament with tuning a ''goodness'' equal to the value ''g'' such that the score is equal to the target_score.

# Assign to every temperament a ''goodness'' equal to the largest goodness of that temperament across all generator tunings. In this way, path-based goodness also provides optimal tunings for temperaments.

@@ Line 1: / Line 1: @@
 Path-based goodness is a metric for judging the accuracy and simplicity of temperaments. To compute path-based goodness, we can apply the following steps:
-# Choose values for the parameters <code>error_power</code>, <code>complexity_fondness</code>, <code>inaccuracy_fondness</code>, and <code>target_score</code>. The canonical values are:
+# Choose values for the parameters <code>error_power</code>, <code>complexity_fondness</code>, <code>inaccuracy_fondness</code>, and target_score. The canonical values are:
 ::: <code>error_power</code> = 1.5,
@@ Line 8: / Line 8: @@
 ::: <code>target_score</code> = 0.02.
-# Let ''g'' be a variable. Assign to every JI interval (except 1/1) n/d with error e (in cents) a score equal to <code>inaccuracy_fondness</code>^(e^<code>error_power</code>) * <code>complexity_fondness</code>^(n+d) / ''g''.
+# Let ''g'' be a variable. Assign to every JI interval (except 1/1) n/d with error e (in cents) a score equal to <code>inaccuracy_fondness</code>^(e^<code>error_power</code></code>) * <code>complexity_fondness</code>^(n+d) / ''g''.
 # Assign to every ordered list of JI intervals a score equal to the product of the scores of all of its steps.
 # Assign to every temperament with tuning a score equal to the sum of the scores of all the paths that yield a comma when the intervals are stacked.
-# Assign to every temperament with tuning a ''goodness'' equal to the value ''g'' such that the score is equal to the <code>target_score</code>.
+# Assign to every temperament with tuning a ''goodness'' equal to the value ''g'' such that the score is equal to the target_score.
 # Assign to every temperament a ''goodness'' equal to the largest goodness of that temperament across all generator tunings. In this way, path-based goodness also provides optimal tunings for temperaments.