27208edt: Difference between revisions

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27208edt provides an ''extremely good approximation'' to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the [[5/1|5th harmonic]] tuned 0.045% sharp (approximately 1/2231 of a step), and the [[7/1|7th harmonic]] tuned 0.0073% sharp (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]].

27208edt provides an ''extremely'' good approximation to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the [[5/1|5th harmonic]] tuned 0.045% sharp (approximately 1/2231 of a step), and the [[7/1|7th harmonic]] tuned 0.0073% sharp (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]]. Though the 8th harmonic is tuned only 1% flat, tripling the tuning to [[51499edo]] increases the error several hundredfold on the 3rd, 5th, and 7th harmonics; even so, this makes 51499edo a relatively good EDO for 7-limit, with errors comparable to those of [[18355edo]].

~~Nevertheless,~~ 27208edt also has good approximations to the 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.13.23 subgroup.

27208edt also has good approximations to the 8th, 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.8.13.23 subgroup.

=== Prime harmonics ===

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 {{ED intro}}
-edt provides an ''extremely good approximation'' to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the [[5/1|5th harmonic]] tuned 0.045% sharp (approximately 1/2231 of a step), and the [[7/1|7th harmonic]] tuned 0.0073% sharp (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]].
+edt provides an ''extremely'' good approximation to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the [[5/1|5th harmonic]] tuned 0.045% sharp (approximately 1/2231 of a step), and the [[7/1|7th harmonic]] tuned 0.0073% sharp (approximately 1/13733 of a step). Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the octave, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]]. Though the 8th harmonic is tuned only 1% flat, tripling the tuning to [[51499edo]] increases the error several hundredfold on the 3rd, 5th, and 7th harmonics; even so, this makes 51499edo a relatively good EDO for 7-limit, with errors comparable to those of [[18355edo]].
-Nevertheless, 27208edt also has good approximations to the 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.13.23 subgroup.
+edt also has good approximations to the 8th, 13th and 23rd harmonics, making it an excellent tuning in the 3.5.7.8.13.23 subgroup.
 === Prime harmonics ===
-{{Harmonics in equal|27208|3|1|intervals=prime}}
+{{Harmonics in equal|27208|3|1|}}