34edo: Difference between revisions

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* 34et has a lower relative error than any previous ETs in the 5-limit. The next ET that does better in this subgroup is 53.

* 34et is most prominent in the 2.3.5.13.17 and 2.3.5.11.13.17 subgroups. The next ET that does better in these subgroups is 217 and 87, respectively.

== Tuning by ear ==

In principle, one can approximate 34edo by ear using only 5-limit intervals, using the fact that 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones to within 1.5 cents, and using a pure 5/4 which is less than 2 cents off for the second chain. The overall tuning error, assuming everything is tuned perfectly, will be less than 3.5 cents, or a relative error of less than 10%.

== 34edo and phi ==

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| Superleap

|}

~~== Tuning by ear ==~~

In principle, one can approximate 34edo by ear using only 5-limit intervals, using the fact that 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones to within 1.5 cents, and using a pure 5/4 which is less than 2 cents off for the second chain. The overall tuning error, assuming everything is tuned perfectly, will be less than 3.5 cents, or a relative error of less than 10%.

== Listen ==

@@ Line 637: / Line 637: @@
 * 34et has a lower relative error than any previous ETs in the 5-limit. The next ET that does better in this subgroup is 53.
 * 34et is most prominent in the 2.3.5.13.17 and 2.3.5.11.13.17 subgroups. The next ET that does better in these subgroups is 217 and 87, respectively.
+== Tuning by ear ==
+In principle, one can approximate 34edo by ear using only 5-limit intervals, using the fact that 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones to within 1.5 cents, and using a pure 5/4 which is less than 2 cents off for the second chain. The overall tuning error, assuming everything is tuned perfectly, will be less than 3.5 cents, or a relative error of less than 10%.
 == 34edo and phi ==
@@ Line 852: / Line 855: @@
 | Superleap
 |}
-== Tuning by ear ==
-In principle, one can approximate 34edo by ear using only 5-limit intervals, using the fact that 17edo is very close to a circle of seventeen [[25/24]] chromatic semitones to within 1.5 cents, and using a pure 5/4 which is less than 2 cents off for the second chain. The overall tuning error, assuming everything is tuned perfectly, will be less than 3.5 cents, or a relative error of less than 10%.
 == Listen ==