Tuning ranges of regular temperaments: Difference between revisions

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== Diamond tuning ranges ==

[[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>Milne, A. J., Sethares, W. A., and Plamondon, J. (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; this was Milne's contribution. Today these are known as [[diamond monotone]] and [[diamond tradeoff]], respectively.

[[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>Milne, A. J., Sethares, W. A., and Plamondon, J. (2008). [https://www.researchgate.net/publication/228091827_Tuning_continua_and_keyboard_layouts Tuning continua and keyboard layouts]. Journal of Mathematics and Music, 2(1):1–19.</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; this was Milne's contribution. Today these are known as [[diamond monotone]] and [[diamond tradeoff]], respectively.

=== History ===

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 == Diamond tuning ranges ==
-[[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>Milne, A. J., Sethares, W. A., and Plamondon, J. (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; this was Milne's contribution. Today these are known as [[diamond monotone]] and [[diamond tradeoff]], respectively.
+[[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>Milne, A. J., Sethares, W. A., and Plamondon, J. (2008). [https://www.researchgate.net/publication/228091827_Tuning_continua_and_keyboard_layouts Tuning continua and keyboard layouts]. Journal of Mathematics and Music, 2(1):1–19.</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; this was Milne's contribution. Today these are known as [[diamond monotone]] and [[diamond tradeoff]], respectively.
 === History ===