8539edo: Difference between revisions

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{{EDO intro|8539}} While it may strike many people as too large to be practical, it has seen actual use as a bookkeeping device to keep track of higher-limit intervals which have been allowed to freely modulate, and has been proposed as a unit of interval measure, the [[tina]] (see [http://www.tonalsoft.com/enc/t/tina.aspx ~~http://www.tonalsoft.com/enc/t/tina.aspx~~]). This is because it is a very strong higher-limit system, distinctly [[consistent]] through the 27-odd-limit, and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, zeta integral, and zeta gap]] tuning. In the 13-limit, the only smaller systems with a lower logflat badness are 72, 270, 494, 5585 and 6079; in the 17-limit, that becomes 72, 494, 1506, 3395 and 7033. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until 20203. Some 17-limit commas it tempers out are 28561/28560, 31213/31212 and 37180/37179; in the 19-limit it tempers out are 27456/27455 and 43681/43680. 8539 is a prime number, and the tina as a unit of measure could be criticized on that basis; however some people prefer primes for this sort of job, as they do not imply a preference for one smaller edo over another.

{{EDO intro|8539}} While it may strike many people as too large to be practical, it has seen actual use as a bookkeeping device to keep track of higher-limit intervals which have been allowed to freely modulate, and has been proposed as a unit of interval measure, the [[tina]] (see [http://www.tonalsoft.com/enc/t/tina.aspx Tonalsoft Encyclopedia | ''Tina'']). This is because it is a very strong higher-limit system, distinctly [[consistent]] through the 27-odd-limit, and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, zeta integral, and zeta gap]] tuning. In the 13-limit, the only smaller systems with a lower logflat badness are 72, 270, 494, 5585 and 6079; in the 17-limit, that becomes 72, 494, 1506, 3395 and 7033. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until 20203. Some 17-limit commas it tempers out are 28561/28560, 31213/31212 and 37180/37179; in the 19-limit it tempers out are 27456/27455 and 43681/43680. 8539 is a prime number, and the tina as a unit of measure could be criticized on that basis; however some people prefer primes for this sort of job, as they do not imply a preference for one smaller edo over another.

=== Prime harmonics ===

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 {{Infobox ET}}
-{{EDO intro|8539}} While it may strike many people as too large to be practical, it has seen actual use as a bookkeeping device to keep track of higher-limit intervals which have been allowed to freely modulate, and has been proposed as a unit of interval measure, the [[tina]] (see [http://www.tonalsoft.com/enc/t/tina.aspx http://www.tonalsoft.com/enc/t/tina.aspx]). This is because it is a very strong higher-limit system, distinctly [[consistent]] through the 27-odd-limit, and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, zeta integral, and zeta gap]] tuning. In the 13-limit, the only smaller systems with a lower logflat badness are 72, 270, 494, 5585 and 6079; in the 17-limit, that becomes 72, 494, 1506, 3395 and 7033. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until 20203. Some 17-limit commas it tempers out are 28561/28560, 31213/31212 and 37180/37179; in the 19-limit it tempers out are 27456/27455 and 43681/43680. 8539 is a prime number, and the tina as a unit of measure could be criticized on that basis; however some people prefer primes for this sort of job, as they do not imply a preference for one smaller edo over another.
+{{EDO intro|8539}} While it may strike many people as too large to be practical, it has seen actual use as a bookkeeping device to keep track of higher-limit intervals which have been allowed to freely modulate, and has been proposed as a unit of interval measure, the [[tina]] (see [http://www.tonalsoft.com/enc/t/tina.aspx Tonalsoft Encyclopedia | ''Tina'']). This is because it is a very strong higher-limit system, distinctly [[consistent]] through the 27-odd-limit, and is both a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, zeta integral, and zeta gap]] tuning. In the 13-limit, the only smaller systems with a lower logflat badness are 72, 270, 494, 5585 and 6079; in the 17-limit, that becomes 72, 494, 1506, 3395 and 7033. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until 20203. Some 17-limit commas it tempers out are 28561/28560, 31213/31212 and 37180/37179; in the 19-limit it tempers out are 27456/27455 and 43681/43680. 8539 is a prime number, and the tina as a unit of measure could be criticized on that basis; however some people prefer primes for this sort of job, as they do not imply a preference for one smaller edo over another.
 === Prime harmonics ===