171edo: Difference between revisions

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All intervals with an odd limit below 10,000,000 in the 7-limit are mapped consistently by 171edo. Because of its accuracy in the 7-limit, the 171et mapping is an excellent and relatively simple way to classify commas by size. For example, one step represents [[225/224]], two steps [[126/125]], three steps [[81/80]], and four steps [[64/63]].

171edo is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-3 temperament [[jove]], which tempers out [[243/242]] (rastma) and [[441/440]], not to mention [[540/539]] and 2401/2400. Jove can be extended by adding [[364/363]] for the 13-limit and [[595/594]] for the 17-limit, which 171edo also supports. Alternatively, the 171e val can be used, which tempers out [[385/384]]. In the 2.3.13 subgroup, it provides the optimal patent val for [[Glacier comma|glacier]], and is generally a great [[2.3.5.13 subgroup|2.3.5.13]] and 2.3.5.13.17 subgroup temperament.

171edo is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-3 temperament [[jove]], which tempers out [[243/242]] (rastma) and [[441/440]], not to mention [[540/539]] and 2401/2400. Jove can be extended by adding [[364/363]] for the 13-limit and [[595/594]] for the 17-limit, which 171edo also supports. Alternatively, the 171e val can be used, which tempers out [[385/384]]. In the 2.3.13 subgroup, it provides the optimal patent val for [[Glacier comma|glacier]], and is generally a great [[2.3.5.7.13 subgroup|2.3.5.7.13]] and 2.3.5.7.13.17 subgroup temperament.

171edo is an excellent tuning for the [[Carlos Gamma]] scale, since the difference between 5 steps of 171edo and 1 step of Carlos Gamma is only -0.010823 cents.

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 All intervals with an odd limit below 10,000,000 in the 7-limit are mapped consistently by 171edo. Because of its accuracy in the 7-limit, the 171et mapping is an excellent and relatively simple way to classify commas by size. For example, one step represents [[225/224]], two steps [[126/125]], three steps [[81/80]], and four steps [[64/63]].
-edo is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-3 temperament [[jove]], which tempers out [[243/242]] (rastma) and [[441/440]], not to mention [[540/539]] and 2401/2400. Jove can be extended by adding [[364/363]] for the 13-limit and [[595/594]] for the 17-limit, which 171edo also supports. Alternatively, the 171e val can be used, which tempers out [[385/384]]. In the 2.3.13 subgroup, it provides the optimal patent val for [[Glacier comma|glacier]], and is generally a great [[2.3.5.13 subgroup|2.3.5.13]] and 2.3.5.13.17 subgroup temperament.
+edo is much less accurate in the 11-limit, but still quite useful as it is a good tuning (emphasizing accuracy in the 7-limit) for the important rank-3 temperament [[jove]], which tempers out [[243/242]] (rastma) and [[441/440]], not to mention [[540/539]] and 2401/2400. Jove can be extended by adding [[364/363]] for the 13-limit and [[595/594]] for the 17-limit, which 171edo also supports. Alternatively, the 171e val can be used, which tempers out [[385/384]]. In the 2.3.13 subgroup, it provides the optimal patent val for [[Glacier comma|glacier]], and is generally a great [[2.3.5.7.13 subgroup|2.3.5.7.13]] and 2.3.5.7.13.17 subgroup temperament.
 edo is an excellent tuning for the [[Carlos Gamma]] scale, since the difference between 5 steps of 171edo and 1 step of Carlos Gamma is only -0.010823 cents.