159edo: Difference between revisions

'''159edo''' is the '''159 equal division of the octave''' into equal parts of 7.547 [[cent|cents]] each.  

As the step size of 159edo is simultaneously above the average peak [http://musictheory.zentral.zone/huntsystem2.html#2 JND] of human pitch perception and small enough to be well within the margin of error between Just 5-limit intervals and their [[12edo]] counterparts, 159edo offers a decent balance between allowing the possibility of seamless modulation to keys that are not in the same series of fifths, and not having so many steps as to have individual steps blend completely into one another.  Furthermore, the septimal kleisma, [[225/224]], maps to a single step in 159edo- a third the size of the tempered version of [[81/80]]- which allows not only for the septimal kleisma to be easily accounted for in notation systems, but also for easy distinctions between certain fairly important intervals such as [[25/16]] and [[14/9]] that are tempered out in other EDOs.  As a bonus, 159edo is [[consistent]] up to the 17 odd-limit- though it proves to be inconsistent in the 19-limit.