38ed7/3: Difference between revisions

fix wording
m Re-organize
Line 2: Line 2:
{{ED intro}}
{{ED intro}}


While 38ed7/3 fails to accurately represent low primes, it provides great approximations of the 13th, 17th, 19th, and a multitude of higher prime harmonics, 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 7/3.5/3.11/9.13.17.19, but this can extend to include higher primes, especially 29, 31, and 37.
== 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
|}
|}
== Harmonics ==
{{Harmonics in equal
| steps = 38
| num = 7
| denom = 3
| intervals = prime
}}
{{Harmonics in equal
| steps = 38
| num = 7
| denom = 3
| start = 12
| collapsed = 1
| intervals = prime
}}