Talk:EDO vs ET: Difference between revisions

# '''Re: finding the approximation of JI intervals: EDs round, and ETs map.''' As we just mentioned, EDs have nothing in particular to do with JI; that said, whenever we do want to know what an ED's closest approximation of a JI interval is, we simply ''round'' each interval's pitch (as measured e.g. in cents) to the nearest step count. With ETs, however, we ''map'' each interval's frequency ratio — using its prime composition — to some step count, which is not necessarily nearest by pitch rounding.  

# '''For each integer <math>n</math>, there's only one <math>n</math>-ED2, but there are many <math>n</math>-ETs.''' An <math>n</math>-ED2 is already a fully-specified pitch set, but <math>n</math>-ET is not quite there yet. For starters, there are different <math>n</math>-ETs for each prime limit, while EDs have nothing in particular to do with primes or prime limits. And more interestingly, we have cases such as <math>n</math> = 17 at the 5-limit where we find more than one reasonable equal temperament: we have 17p-ET with map ⟨17 27 39], but we also have 17c-ET with map ⟨17 27 40].

== "Supports" ==