Sensipent: Difference between revisions

If we take a look at the 5-limit version of sensi called [[sensipent]], we find a high-accuracy extension that specifically only requires prime 31, interpreting the generator accurately as [[~]][[40/31]][[~]][[31/24]] (by splitting [[16/15]] into [[~]][[32/31]][[~]][[31/30]]). This can be left as is, or one can extend to other slightly less accurate primes; the main two strategies for doing so are called [[sendai]], focusing on accuracy and adding primes 23 and 29, and [[sensible]], which adds primes 11, 17 and 23 and focuses on adding more primes, in both cases doing so while avoiding the less accurate [[~]][[9/7]] and [[~]][[13/10]] interpretations of the sensi generator. They merge meaningfully (though ''not'' uniquely) in [[65edo]], which can be seen by that [[65edo]] is an amazing no-7's no-13's [[31-limit]] temperament, where we've gained prime 19 through a possible extension of either sendai or sensible. Furthermore, [[65edo]] can also be used as a tuning of 7-limit sensi through the 65d [[val]] (which corresponds to 65edo roughly supporting [[garibaldi]]), though note that if one tries to use its patent but very sharp [[~]][[13/8|13]] (which makes the most sense if one accepts the 65d val) then [[13/10]] is mapped distinctly and sharp of the [[~]][[9/7]] sensi generator.

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