1178edo: Difference between revisions

BudjarnLambeth (talk | contribs)
mNo edit summary
m Adopt template: Factorization; misc. cleanup
Line 2: Line 2:
{{EDO intro|1178}}
{{EDO intro|1178}}


1178edo is a very strong 19-limit system, and is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak, integral and gap edo]]. It is also distinctly [[consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A basis for its 19-limit commas is [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4375/4374]], 4914/4913 and 5985/5984. It supports and provides a great tuning for [[semihemienneadecal]].  
1178edo is a very strong 19-limit system, and is a [[zeta edo|zeta peak, integral and gap edo]]. It is also [[consistency|distinctly consistent]] through to the [[21-odd-limit]], and is the first edo past [[742edo|742]] with a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]. A basis for its 19-limit [[comma]]s is [[2500/2499]], [[3025/3024]], 3250/3249, 4200/4199, [[4375/4374]], [[4914/4913]] and 5985/5984. It [[support]]s and provides a great tuning for [[semihemienneadecal]].  


=== Prime harmonics ===
=== Prime harmonics ===
Line 8: Line 8:


=== Subsets and supersets ===
=== Subsets and supersets ===
Since 1178 = 2 × 19 × 31, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.  
Since 1178 = {{factorization|1178}}, 1178edo is notable for containing both 19 and 31. Its subset edos are {{EDOs| 2, 19, 31, 38, 62, and 589 }}.  


[[Category:Enneadecal]]
[[Category:Enneadecal]]
[[Category:Hemienneadecal]]
[[Category:Hemienneadecal]]
[[Category:Semihemienneadecal]]
[[Category:Semihemienneadecal]]