148418edo: Difference between revisions

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148418edo is a ~~[[zeta peak edo]]~~, distinctly [[consistent]] through the [[39-odd-limit]]. It marks the first equal temperament with lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]s after [[16808edo|16808]] in the 23-, 29-, and 31-limit, the first after 83096 in the 37-limit, and the first after 95524 in the 41-limit. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.

148418edo is a very strong higher-limit tuning, distinctly [[consistent]] through the [[39-odd-limit]], and is a [[zeta peak edo]]. It marks the first equal temperament with lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]s after [[16808edo|16808]] in the [[23-limit|23-]], [[29-limit|29-]], and [[31-limit]], the first after 83096 in the [[37-limit]], and the first after 95524 in the [[41-limit]]. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.

=== Prime harmonics ===

{{Harmonics in equal|148418|intervals=prime|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 148418edo (continued)}}

=== Subsets and supersets ===

Since 148418 factors into 2 × 74209, 148418edo has subset edos 2 and 74209.

Since 148418 factors into primes as {{nowrap| 2 × 74209 }}, 148418edo has subset edos 2 and 74209.

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 {{ED intro}}
-edo is a [[zeta peak edo]], distinctly [[consistent]] through the [[39-odd-limit]]. It marks the first equal temperament with lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]s after [[16808edo|16808]] in the 23-, 29-, and 31-limit, the first after 83096 in the 37-limit, and the first after 95524 in the 41-limit. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.
+edo is a very strong higher-limit tuning, distinctly [[consistent]] through the [[39-odd-limit]], and is a [[zeta peak edo]]. It marks the first equal temperament with lower [[Tenney-Euclidean temperament measures #TE simple badness|relative error]]s after [[16808edo|16808]] in the [[23-limit|23-]], [[29-limit|29-]], and [[31-limit]], the first after 83096 in the [[37-limit]], and the first after 95524 in the [[41-limit]]. Some of the simpler commas it tempers out include 408761/408760, 453376/453375, 509796/509795, 601426/601425, 633556/633555, 709632/709631, 949026/949025, 1154440/1154439, 1163800/1163799, 1255501/1255500, 2023425/2023424, 2307361/2307360, 2697696/2697695, 3897166/3897165, 4096576/4096575, and 5909761/5909760.
 === Prime harmonics ===
-{{Harmonics in equal|148418}}
+{{Harmonics in equal|148418|intervals=prime|columns=9}}
+{{Harmonics in equal|148418|intervals=prime|columns=9|start=10|collapsed=true|title=Approximation of prime harmonics in 148418edo (continued)}}
 === Subsets and supersets ===
-Since 148418 factors into 2 × 74209, 148418edo has subset edos 2 and 74209.
+Since 148418 factors into primes as {{nowrap| 2 × 74209 }}, 148418edo has subset edos 2 and 74209.