Tuning ranges of regular temperaments: Difference between revisions

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== Other tuning ranges ==

The diamond tuning ranges, though they have historical momentum, do not preclude definition of other validity ranges for the tuning of temperaments. The topic of tuning ranges is relatively subjective. Milne himself has described the diamond tuning ranges as "convenient mathematical fictions", and proposed that the reality would be to define some sort of empirically obtained range of tunings over which a sample of participants can correctly identify that ~~tunings~~ intervals in the way prescribed by the mapping. But realistically, that is an almost possible question to even ask of participants, and relies upon all sorts of a priori assumptions about categorizations of intervals by their ratio, which is quite possibly an entirely bogus notion.

The diamond tuning ranges, though they have historical momentum, do not preclude definition of other validity ranges for the tuning of temperaments. The topic of tuning ranges is relatively subjective. Milne himself has described the diamond tuning ranges as "convenient mathematical fictions", and proposed that the reality would be to define some sort of empirically obtained range of tunings over which a sample of participants can correctly identify that tuning's intervals in the way prescribed by the mapping. But realistically, that is an almost possible question to even ask of participants, and relies upon all sorts of a priori assumptions about categorizations of intervals by their ratio, which is quite possibly an entirely bogus notion.

[[Paul Erlich]] has proposed other tuning ranges, such as the set of regular tunings in which the temperament has up to 2×, 5×, 10× etc. its optimal damage under some metric (such as [[Kees_height|KE]]), or a set of absolute cutoffs on damage applied across all temperaments, though there could be no objective value for such cutoffs that would be both amenable to the entire community as well as useful for the entire set of regular temperaments (including extreme cases like [[macrotemperaments]] and [[microtemperaments]]).

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 == Other tuning ranges ==
-The diamond tuning ranges, though they have historical momentum, do not preclude definition of other validity ranges for the tuning of temperaments. The topic of tuning ranges is relatively subjective. Milne himself has described the diamond tuning ranges as "convenient mathematical fictions", and proposed that the reality would be to define some sort of empirically obtained range of tunings over which a sample of participants can correctly identify that tunings intervals in the way prescribed by the mapping. But realistically, that is an almost possible question to even ask of participants, and relies upon all sorts of a priori assumptions about categorizations of intervals by their ratio, which is quite possibly an entirely bogus notion.
+The diamond tuning ranges, though they have historical momentum, do not preclude definition of other validity ranges for the tuning of temperaments. The topic of tuning ranges is relatively subjective. Milne himself has described the diamond tuning ranges as "convenient mathematical fictions", and proposed that the reality would be to define some sort of empirically obtained range of tunings over which a sample of participants can correctly identify that tuning's intervals in the way prescribed by the mapping. But realistically, that is an almost possible question to even ask of participants, and relies upon all sorts of a priori assumptions about categorizations of intervals by their ratio, which is quite possibly an entirely bogus notion.
 [[Paul Erlich]] has proposed other tuning ranges, such as the set of regular tunings in which the temperament has up to 2×, 5×, 10× etc. its optimal damage under some metric (such as [[Kees_height|KE]]), or a set of absolute cutoffs on damage applied across all temperaments, though there could be no objective value for such cutoffs that would be both amenable to the entire community as well as useful for the entire set of regular temperaments (including extreme cases like [[macrotemperaments]] and [[microtemperaments]]).