293edo: Difference between revisions

== Theory ==

293edo does not approximate prime harmonics well all the way into the 41st, unless 30% errors are considered "well", in which case it equally represents all of them. The first harmonic that it approximates within 1 standard deviation of one step is 43rd, which is 10% flat compared to the just intonated interval. Nonetheless, it is [[consistent]] in the 5-limit.  

When it comes to the intervals that are not octave-reduced prime harmonics, some which are well-approximated are [[6/5]], [[11/7]], [[17/11]], [[19/17]], [[24/23]], [[25/17]], [[25/19]], and respectively their octave inversions. [[21/16]], which is a composite octave-reduced harmonic, is also well represented. These numbers are related to poor approximation of prime harmonics by cancelling out of the errors. For example, 19th and 17th harmoincs have +36 and +37 error respectively, which together cancels out to 1.

! Associated<br>Ratio

! Temperaments

|-

| 1

| 52/45

| [[Symmetry454]]

|}

[[Category:Prime EDO]]

[[Category:Listen]]