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:

Path-based goodness is a measure of your ability as a composer to create music recognizable as tempered JI. we assume a composer wants to return to previously written pitches; otherwise, they would just use JI. so their music contains multiple paths from a tone to the same tone. They are likelier to use a path if the intervals within it are simple and close to just. So path-based goodness is a measure of how much total ''option'' (which I use as a mass noun here because there is an infinite number of options and some paths are more of a compositional option for them than others) a composer has when writing music. brb going to put that on the path-based goodness page

The parameters are calibrated according to what I believe best reflects the preferences of composers (how much they use simple intervals, and how much unjustness they're willing to tolerate). If a composer works under different aesthetic criteria, they may want to use different parameters. For example, if one uses timbres less sensitive to mistuning, one may want to increase inaccuracy fondness. If one is interested in essentially tempered chords more than long comma pumps, one may want to lower target_score. hkm has found that changing target_score by an order of magnitude affects rankings minimally; changing the other parameters changes the rankings in a predictable and small way. (For example, if we increase inaccuracy_fondness, all scores go up, but scores for less accurate systems increase more.) We do not treat some JI intervals as having more room for error than others, because it is not entirely agreed upon whether they do.

== Method of computation ==

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:

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Path-based goodness can also be calculated for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment.

=== Path-based goodnesses, ideal GPVs, and octave stretches for the equal temperaments 1-140: ===

== Path-based goodnesses, ideal GPVs, and octave stretches for the equal temperaments 1-140: ==

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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:
+Path-based goodness is a measure of your ability as a composer to create music recognizable as tempered JI. we assume a composer wants to return to previously written pitches; otherwise, they would just use JI. so their music contains multiple paths from a tone to the same tone. They are likelier to use a path if the intervals within it are simple and close to just. So path-based goodness is a measure of how much total ''option'' (which I use as a mass noun here because there is an infinite number of options and some paths are more of a compositional option for them than others) a composer has when writing music. brb going to put that on the path-based goodness page
+The parameters are calibrated according to what I believe best reflects the preferences of composers (how much they use simple intervals, and how much unjustness they're willing to tolerate). If a composer works under different aesthetic criteria, they may want to use different parameters. For example, if one uses timbres less sensitive to mistuning, one may want to increase inaccuracy fondness. If one is interested in essentially tempered chords more than long comma pumps, one may want to lower target_score. hkm has found that changing target_score by an order of magnitude affects rankings minimally; changing the other parameters changes the rankings in a predictable and small way. (For example, if we increase inaccuracy_fondness, all scores go up, but scores for less accurate systems increase more.) We do not treat some JI intervals as having more room for error than others, because it is not entirely agreed upon whether they do.
+== Method of computation ==
+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:
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 Path-based goodness can also be calculated for scales without JI interpretations; we assign to each note and just interval a tempered interval rooted on that note, and compute the goodness of the best assignment.
-=== Path-based goodnesses, ideal GPVs, and octave stretches for the equal temperaments 1-140: ===
+== Path-based goodnesses, ideal GPVs, and octave stretches for the equal temperaments 1-140: ==
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