Telicity: Difference between revisions

Given that different EDOs can temper out different commas to achieve the same type of telicity – for example, [[12edo]] tempers out the [[Pythagorean comma]] to achieve 3-2 telicity, while [[53edo]] tempers out Mercator's comma to achieve 3-2 telicity – it can thus be argued that sequences of different EDOs demonstrating one or more types of telicity can be compiled.  For instance, the first nine EDOs to demonstrate 3-2 telicity specifically form the sequence of {{EDOs| 1, 2, 5, 12, 24, 53, 106, 159, 306}}.  In addition, one can compare multiple such telicity sequences, and see how frequently the various prime chains connect to one another across various EDOs, revealing which portions of the harmonic lattice are best utilized by any given EDO.  Furthermore, this also enables one to examine the properties of the various prime chains themselves and provides cause to look for unexpectedly useful commas that, as of yet, are still unknown.  As if all this weren't enough, telicity also useful in notation systems for establishing good positions for the "resets" in JI harmonic lattice representation that inevitably come about due to EDOs being closed systems in terms of their own harmonic lattices.  All this makes telicity a viable endgame for the application of [[Consistent #Consistency to distance d|consistency to distance ''d'']], with which the concept of telicity is closely related.

[[Category:EDO theory pages]]

[[Category:Terms]]