718edo: Difference between revisions

Line 3:

== 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 [[31-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]].

@@ Line 3: / Line 3: @@
 == 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 [[31-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]].