51edo: Difference between revisions

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== Theory ==

51 = 3 × 17, ~~and~~ 51edo shares its [[3/2|fifth]] with [[17edo]]. Compared to other multiples of 17edo, notably [[34edo]] and [[68edo]], 51edo's harmonic inventory seems lacking, getting few harmonics very well considering its step size. However, it does possess excellent approximations of [[11/10]] and [[21/16]], only about 0.3 cents off in each case.

Since {{nowrap|51 {{=}} 3 × 17}}, 51edo shares its [[3/2|fifth]] with [[17edo]]. Compared to other multiples of 17edo, notably [[34edo]] and [[68edo]], 51edo's harmonic inventory seems lacking, getting few harmonics very well considering its step size. However, it does possess excellent approximations of [[11/10]] and [[21/16]], only about 0.3 cents off in each case.

Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an archeotonic [[6L 1s]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.

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 {{Infobox ET}}
-{{EDO intro|51}}
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 == Theory ==
-= 3 × 17, and 51edo shares its [[3/2|fifth]] with [[17edo]]. Compared to other multiples of 17edo, notably [[34edo]] and [[68edo]], 51edo's harmonic inventory seems lacking, getting few harmonics very well considering its step size. However, it does possess excellent approximations of [[11/10]] and [[21/16]], only about 0.3 cents off in each case.
+Since {{nowrap|51 {{=}} 3 × 17}}, 51edo shares its [[3/2|fifth]] with [[17edo]]. Compared to other multiples of 17edo, notably [[34edo]] and [[68edo]], 51edo's harmonic inventory seems lacking, getting few harmonics very well considering its step size. However, it does possess excellent approximations of [[11/10]] and [[21/16]], only about 0.3 cents off in each case.
 Using the [[patent val]], 51et [[tempering out|tempers out]] [[250/243]] in the [[5-limit]], [[225/224]] and [[2401/2400]] in the [[7-limit]], and [[55/54]] and [[100/99]] in the [[11-limit]]. It is the [[optimal patent val]] for [[sonic]], the rank-3 temperament tempering out 55/54, 100/99, and 250/243, and also for the rank-4 temperament tempering out 55/54. It provides an alternative tuning to [[22edo]] for [[porcupine]], with a nice fifth but a rather flat major third, and the optimal patent val for the 7- and 11-limit [[porky]] temperament, which is sonic plus 225/224. 51 contains an archeotonic [[6L&nbsp;1s]] scale based on repetitions of 8\51, creating a scale with a whole-tone-like drive towards the tonic through the 17edo semitone at the top.