8539edo: Difference between revisions
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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, [[consistency|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 [[odd prime sum limit|27-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 [[20203edo|20203]]. | 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, [[consistency|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 [[odd prime sum limit|27-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 [[20203edo|20203]]. | ||
Some of the simpler commas it [[tempering out|tempers out]] include [[123201/123200]] in the 13-limit; [[28561/28560]], [[31213/31212]], [[37180/37179]] in the 17-limit; 27456/27455, 43681/43680, 89376/89375 in the 19-limit; 12168/12167, 16929/16928, 19551/19550, 21736/21735, [[25025/25024]], 43264/43263 among others in the 23-limit. | It tempers out the [[Senior|Senior comma]] in the [[5-limit]], [[Very high accuracy temperaments#Sepbizo-asegu (171 & 3566 & 4973)|[-3 2 -17 14⟩]] in the [[7-limit]], [[3294225/3294172]] in the [[11-limit]]. | ||
Some of the simpler commas it [[tempering out|tempers out]] include [[123201/123200]] in the [[13-limit]]; [[28561/28560]], [[31213/31212]], [[37180/37179]] in the [[17-limit]]; 27456/27455, 43681/43680, 89376/89375 in the [[19-limit]]; 12168/12167, 16929/16928, 19551/19550, 21736/21735, [[25025/25024]], 43264/43263 among others in the [[23-limit]]. | |||
Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]]. | Since it tempers out 12168/12167, it allows [[vicetertismic chords]] in the [[23-odd-limit]]. | ||