Defactoring: Difference between revisions

Line 32:

# It does not have any obvious musical or mathematical meaning in this context (whereas enfactored and defactored do have obvious mathematical meaning).

# It has another unrelated meaning within xenharmonics: https://en.xen.wiki/w/Anomalous_saturated_suspension

# The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in.

# Research on the tuning list archives suggests that [[Gene Ward Smith]] chose the word "saturation" because it was used in the mathematical software he was using at the time, Sage<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18026.html and https://doc.sagemath.org/html/en/reference/search.html?q=index_in_saturation</ref>. However, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>. We think we should avoid propagating Sage's decision to overload matrix saturation with a second meaning.

@@ Line 32: / Line 32: @@
 # It does not have any obvious musical or mathematical meaning in this context (whereas enfactored and defactored do have obvious mathematical meaning).
+# It has another unrelated meaning within xenharmonics: https://en.xen.wiki/w/Anomalous_saturated_suspension
 # The most common everyday usage of that word is for "saturated fats", which are the bad kind of fats, so it has negative associations, despite "saturation" being the ''good'' state for a matrix to be in.
 # Research on the tuning list archives suggests that [[Gene Ward Smith]] chose the word "saturation" because it was used in the mathematical software he was using at the time, Sage<ref>See: https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18026.html and https://doc.sagemath.org/html/en/reference/search.html?q=index_in_saturation</ref>. However, there is another common but conflicting sense of saturation for matrices which clamps entry values to between -1 and 1<ref>See https://math.stackexchange.com/questions/1964814/linear-transformation-of-a-saturated-vector and https://faculty.uml.edu//thu/tcs01-june.pdf</ref>. We think we should avoid propagating Sage's decision to overload matrix saturation with a second meaning.