38ed7/3: Difference between revisions
Hotcrystal0 (talk | contribs) fix wording |
m Re-organize |
||
| Line 2: | Line 2: | ||
{{ED intro}} | {{ED intro}} | ||
While 38ed7/3 fails to accurately represent low | == Theory == | ||
While 38ed7/3 fails to accurately represent low [[prime interval|prime harmonics]], it provides great approximations of the [[13/1|13th]], [[17/1|17th]], [[19/1|19th]], and a multitude of higher primes, and also handles the interval of [[5/3]] well. But 38ed7/3 should, most of all, be noted for the exceptional quality of its approximation to [[11/9]], which is a mere 0.0088 cents off from just. Its natural subgroup in the [[19-limit]] is 5/3.7/3.11/9.13.17.19, but this can extend to include higher primes, especially [[29/1|29]], [[31/1|31]], and [[37/1|37]]. | |||
38ed7/3 possesses a shimmering octave at 31 steps in, therefore making this a potential octave-compressed version of [[31edo]], one that sacrifices its notable accuracy in the [[7-limit]] (though a number of 7-limit intervals are still portrayed passably due to the common flat tendency of harmonics 2, 3, 5, and 7) in favor of a huge number of high primes. | 38ed7/3 possesses a shimmering octave at 31 steps in, therefore making this a potential octave-compressed version of [[31edo]], one that sacrifices its notable accuracy in the [[7-limit]] (though a number of 7-limit intervals are still portrayed passably due to the common flat tendency of harmonics 2, 3, 5, and 7) in favor of a huge number of high primes. | ||
=== Harmonics === | |||
{{Harmonics in equal|38|7|3|columns=11}} | |||
{{Harmonics in equal|38|7|3|columns=12|start=12|collapsed=1|title=Approximation of harmonics in 38ed7/3 (continued)}} | |||
== Intervals == | == Intervals == | ||
| Line 241: | Line 246: | ||
|1466.8709 | |1466.8709 | ||
|} | |} | ||