742edo: Difference between revisions

Cleanup; clarify the title row of the rank-2 temp table
Adopt template: Factorization; misc. cleanup
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== Theory ==
== Theory ==
742edo is a very strong 19-limit system and a [[zeta peak edo]], and is uniquely [[consistent]] in the [[21-odd-limit]]. It tempers out the vishnuzma and the fortune comma in the 5-limit, supporting [[vishnu]] and [[fortune]]; [[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.
742edo is a very strong 19-limit system and a [[zeta peak edo]], and is [[consistency|distinctly consistent]] in the [[21-odd-limit]]. The equal temperament [[tempering out|tempers out]] the [[vishnuzma]] and the fortune comma in the 5-limit, [[support]]ing [[vishnu]] and [[fortune]]; [[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.


=== Prime harmonics ===
=== Prime harmonics ===
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=== Subsets and supersets ===
=== Subsets and supersets ===
742 = 2 × 7 × 53, so it notably contains [[53edo]] and [[14edo]]. It supports [[silicon]] temperament (224 & 742) with period 14 in the 13-limit, and [[iodine]] temperament (159 & 742) with period 53 in the 17-limit.
Since 742 factors into {{factorization|742}}, 742edo has subset edos {{EDOs| 2, 7, 14, 53, 106, and 371 }}, of which [[7edo]], [[14edo]] and [[53edo]] are very notable. It supports [[silicon]] (224 & 518) with period 14 in the 13-limit, and [[iodine]] (159 & 583f) with period 53 in the 17-limit.


== Regular temperament properties ==
== Regular temperament properties ==
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! Generator*
! Generator*
! Cents*
! Cents*
! Associated<br>Ratio
! Associated<br>Ratio*
! Temperaments
! Temperaments
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