8539edo: Difference between revisions

While it may strike many people as too large to be practical, 8539edo 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 [[interval size measure|unit of interval measure]], the '''tina'''. This is because it is a very strong higher-limit system, distinctly [[consistent]] through the 27-odd-limit. It is a [[The Riemann zeta function and tuning #Zeta EDO lists|strict zeta]] tuning, and is also the first [[Trivial temperament|non-trivial]] EDO to be consistent in the 27-[[Odd prime sum limit|odd-prime-sum-limit]]. In the 13-limit, the only smaller systems with a lower logflat badness are {{EDOs|72, 270, 494, 5585 and 6079}}; in the 17-limit, that becomes {{EDOs|72, 494, 1506, 3395 and 7033}}. In the 19-limit, where it really shines, nothing beats it in terms of logflat badness until {{EDOs|20203}}. Some 17-limit commas it tempers out are [[28561/28560]], [[31213/31212]] and [[37180/37179]]; in the 19-limit it tempers out [[27456/27455]] and [[43681/43680]].

{{Harmonics in equal|8539}}