Tuning ranges of regular temperaments: Difference between revisions

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[[Andrew Milne]], [[Bill Sethares]] and [[James Plamondon]] defined some important tuning ranges. Their "valid" range was defined in ''Tuning Continua and Keyboard Layouts'' in the ''Journal of Mathematics and Music''<ref>Andrew Milne, William Sethares & James Plamondon (2008) Tuning continua and keyboard layouts, Journal of Mathematics and Music, 2:1, 1-19, DOI: [https://doi.org/10.1080/17459730701828677 10.1080/17459730701828677]</ref>; according to Milne, this tuning range was Sethares's contribution. Their "purer" range was discussed in the technical report ''X_System'' in the Open University’s repository.

In 2014, these tuning ranges ~~went through much discussion,~~ by Milne, Gene Ward Smith, and others. The "valid" range was proposed names such as "lax", "monotone", and "normal", while the "purer" range was proposed to be named "strict", and the combination proposed to be named "nice". After some churn (in the edit history of this page), valid/lax/monotone/normal became "valid", while purer/strict became "nice", and the combination became "strict". In other words, "nice" and "strict" for some reason got switched, and for some time and to some extent on the wiki and in the regular temperament community that's how they stuck.

In 2014, these tuning ranges were discussed by Milne, Gene Ward Smith, and others. The "valid" range was proposed names such as "lax", "monotone", and "normal", while the "purer" range was proposed to be named "strict", and the combination proposed to be named "nice". After some churn (in the edit history of this page), valid/lax/monotone/normal became "valid", while purer/strict became "nice", and the combination became "strict". In other words, "nice" and "strict" for some reason got switched, and for some time and to some extent on the wiki and in the regular temperament community that's how they stuck.

In May 2021 Milne agreed with a community effort to revise the names to be more specific, descriptive, and closer to their original meaning. So the original "valid" became "diamond monotone", the original "purer" become "diamond tradeoff", and the combination of these two was left unnamed.

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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 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.

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 impossible 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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 [[Andrew Milne]], [[Bill Sethares]] and [[James Plamondon]] defined some important tuning ranges. Their "valid" range was defined in ''Tuning Continua and Keyboard Layouts'' in the ''Journal of Mathematics and Music''<ref>Andrew Milne, William Sethares & James Plamondon (2008) Tuning continua and keyboard layouts, Journal of Mathematics and Music, 2:1, 1-19, DOI: [https://doi.org/10.1080/17459730701828677 10.1080/17459730701828677]</ref>; according to Milne, this tuning range was Sethares's contribution. Their "purer" range was discussed in the technical report ''X_System'' in the Open University’s repository.
-In 2014, these tuning ranges went through much discussion, by Milne, Gene Ward Smith, and others. The "valid" range was proposed names such as "lax", "monotone", and "normal", while the "purer" range was proposed to be named "strict", and the combination proposed to be named "nice". After some churn (in the edit history of this page), valid/lax/monotone/normal became "valid", while purer/strict became "nice", and the combination became "strict". In other words, "nice" and "strict" for some reason got switched, and for some time and to some extent on the wiki and in the regular temperament community that's how they stuck.
+In 2014, these tuning ranges were discussed by Milne, Gene Ward Smith, and others. The "valid" range was proposed names such as "lax", "monotone", and "normal", while the "purer" range was proposed to be named "strict", and the combination proposed to be named "nice". After some churn (in the edit history of this page), valid/lax/monotone/normal became "valid", while purer/strict became "nice", and the combination became "strict". In other words, "nice" and "strict" for some reason got switched, and for some time and to some extent on the wiki and in the regular temperament community that's how they stuck.
 In May 2021 Milne agreed with a community effort to revise the names to be more specific, descriptive, and closer to their original meaning. So the original "valid" became "diamond monotone", the original "purer" become "diamond tradeoff", and the combination of these two was left unnamed.
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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 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.
+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 impossible 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]]).