27208edt: Difference between revisions

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~~'''27208edt''' is a tuning system which divides the '''tritave''', [[3/1]], into 27208 equal parts of approximately 0.0699[[¢]] each.~~

27208edt provides an '''~~extremely~~ good approximation~~'''~~ to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the 5th harmonic ~~accurate to~~ 0.045% (approximately 1/2231 of a step), and the 7th harmonic ~~accurate to~~ 0.0073% (approximately 1/13733 of a step).

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]].

Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the ~~ditave~~, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]].

~~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 ==

=== Prime harmonics ===

~~[[Category:Edt]]~~

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-'''27208edt''' is a tuning system which divides the '''tritave''', [[3/1]], into 27208 equal parts of approximately 0.0699[[¢]] each.
+{{Infobox ET}}
+{{ED intro}}
-edt provides an '''extremely good approximation''' to the [[No-twos subgroup temperaments|no-twos]] [[7-limit]], with the 5th harmonic accurate to 0.045% (approximately 1/2231 of a step), and the 7th harmonic accurate to 0.0073% (approximately 1/13733 of a step).
+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]].
-Despite the very good tuning of prime harmonics 3, 5 and 7, 27208edt misses the ditave, [[2/1]], by approximately a third of a step, making it incomparable with its related [[edo]]s, [[17166edo]] and [[17167edo]].
-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 ==
+=== Prime harmonics ===
 {{Harmonics in equal|27208|3|1|intervals=prime}}
-[[Category:Edt]]