38ed7/3: Difference between revisions

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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 and 31.

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.

~~{{Harmonics~~ in ~~equal|38|~~7|3~~|prec=2|columns=15|intervals=prime}}~~

38ed7/3 possesses a shimmering octave at 31 steps in, therefore making this a potential octave stretch 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~~ in ~~equal|38|7|3|prec=2|columns=15|intervals=odd}}~~

== Intervals ==

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|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

}}

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 {{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 and 31.
+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.
-{{Harmonics in equal|38|7|3|prec=2|columns=15|intervals=prime}}
+ed7/3 possesses a shimmering octave at 31 steps in, therefore making this a potential octave stretch 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 in equal|38|7|3|prec=2|columns=15|intervals=odd}}
 == Intervals ==
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 |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
+}}