Tuning ranges of regular temperaments: Difference between revisions

[[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 premiere issue of ''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 "nice" range was discussed in ''X_System'' in the Open University’s repository.  

In their writings these two tuning ranges are referred to simply as "valid" and "nice", and for some time and to some extent on the wiki and in the regular temperament community these names were used as-is. In May 2021 Milne agreed with a community effort to give them the more specific names "diamond valid" and "diamond nice" (or "diamond monotone" and "diamond pure", respectively), due to the fact that they are based on the effect the temperament has on a relevant tonality diamond. "Diamond strict" is the combination of both conditions.  

* [[diamond strict]]