From Xenharmonic Wiki
Jump to: navigation, search

The 8539 equal temperament divides the octave into 8539 equal parts of 0.1405 cents each. While it may strike many people as too large to be practical, it's seen actual use as a bookeeping 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.) This is because it is a very strong higher limit system, distinctly consistent through the 27 limit, and is both a zeta peak and zeta integral 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 don't imply a preference for one smaller edo over another.