718edo: Difference between revisions

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== Theory ==

718edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]].

718edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit, with [[28/25]] and its octave complement [[25/14]] being the only inconsistencies in the [[35-odd-limit]]. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]].

As does 359et, 718et [[Tempering out|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1|3]]. In the 5-limit it [[tempering out|tempers out]] the gammic comma, {{monzo| -29 -11 20 }}, and the [[monzisma]], {{monzo| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].

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| [[Abigail]]

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<nowiki />* [[Normal ~~lists~~|Octave-reduced form]], reduced to the first half-octave, and [[~~Normal lists~~|minimal form]] in parentheses if distinct

<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct

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 {{Infobox ET}}
-{{EDO intro|718}}
+{{ED intro}}
 == Theory ==
-edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]].
+edo is [[consistency|distinctly consistent]] in the [[23-odd-limit]], and does well enough in the 31-limit, with [[28/25]] and its octave complement [[25/14]] being the only inconsistencies in the [[35-odd-limit]]. It is closely related to [[359edo]], but the mapping differs for [[5/1|5]], [[13/1|13]], [[17/1|17]] and [[31/1|31]].
 As does 359et, 718et [[Tempering out|tempers out]] the 359-comma in the 3-limit, rendering a very accurate [[harmonic]] [[3/1|3]]. In the 5-limit it [[tempering out|tempers out]] the gammic comma, {{monzo| -29 -11 20 }}, and the [[monzisma]], {{monzo| 54 -37 2 }}. In the 7-limit it tempers out [[4375/4374]]; in the 11-limit [[3025/3024]], [[9801/9800]] and [[131072/130977]]; in the 13-limit [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], [[6656/6655]] and [[10648/10647]]; in the 17-limit [[1275/1274]], [[2025/2023]]; in the 19-limit [[2432/2431]], 3250/3249, 4200/4199 and 5985/5984; and in the 23-limit 2024/2023, 2025/2024, 2185/2184, 3060/3059. It [[support]]s [[gammic]], [[monzismic]] and [[abigail]].
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 | [[Abigail]]
 |}
-<nowiki />* [[Normal lists|Octave-reduced form]], reduced to the first half-octave, and [[Normal lists|minimal form]] in parentheses if distinct
+<nowiki />* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct