742edo: Difference between revisions

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The ''742 equal ~~division~~'' divides the octave into 742 equal parts of 1.617 ~~cents~~ each. It is a very strong 19-limit system and a [[~~The_Riemann_Zeta_Function_and_Tuning~~#Zeta EDO lists|zeta peak tuning]], and is uniquely [[~~consistent|~~consistent]] in the 21-limit. It has a lower 19-limit [[Tenney-~~Euclidean_temperament_measures~~#TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.

The '''742 equal divisions of the octave''' ('''742edo''') divides the [[octave]] into 742 [[equal]] parts of 1.617 [[cent]]s each. 742edo is a very strong 19-limit system and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent]] in the [[21-odd-limit]]. It has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], 2058/2057, [[2601/2600]], 4914/4913, [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.

~~It is a multiple of~~ [[53edo]] and [[14edo]].

742 = 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]].

[[Category:~~zeta~~]]

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Zeta]]

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-The ''742 equal division'' divides the octave into 742 equal parts of  1.617 cents each. It is a very strong 19-limit system and a [[The_Riemann_Zeta_Function_and_Tuning#Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent|consistent]] in the 21-limit. It has a lower 19-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out 2401/2400 in the 7-limit, 9801/9800 in the 11-limit, 4096/4095, 6656/6655, 10648/10647 in the 13-limit, 1701/1700, 2058/2057, 2601/2600, 4914/4913, 5832/5831 in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.
+The '''742 equal divisions of the octave''' ('''742edo''') divides the [[octave]] into 742 [[equal]] parts of 1.617 [[cent]]s each. 742edo is a very strong 19-limit system and a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak tuning]], and is uniquely [[consistent]] in the [[21-odd-limit]]. It has a lower 19-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until [[1178edo|1178]]. It tempers out [[2401/2400]] in the 7-limit, [[9801/9800]] in the 11-limit, [[4096/4095]], [[6656/6655]], [[10648/10647]] in the 13-limit, [[1701/1700]], 2058/2057, [[2601/2600]], 4914/4913, [[5832/5831]] in the 17-limit, 2376/2375, 2432/2431, 2926/2925, 3136/3135, 4200/4199, 5776/5775, 5929/5928, 5985/5984, 6860/6859 in the 19-limit.
-It is a multiple of [[53edo]] and [[14edo]].
+= 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]].
-[[Category:zeta]]
+=== Prime harmonics ===
+{{Primes in edo|742}}
+[[Category:Equal divisions of the octave]]
+[[Category:Zeta]]