26ed5: Difference between revisions

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Pure-octaves 26ed5 is incompatible with [[prime limit]] tuning. Of all primes up to 41, 5 and 41 are the only two it approximates well. Many of 26ed5’s 'near-miss' [[prime]]s are tuned sharp, so 26ed5 can be made to work more normally by [[Octave shrinking|compressing]] 26ed5’s [[equave]], making [[5/1]] slightly flat but still okay and the other primes more in-tune.

A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23.43 tuning. The 3/1 in 46ed17 isn’t that good, ~~comparable~~ to [[5edo]], but it’s a huge improvement on 26ed5. And the 5, 11, 17, 23 and 43 are genuinely solid approximations. Other tunings which are almost identical to 46ed17, and so provide those same benefits, are [[8ed18/11]] and [[20ed24/7]].

A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23.43 tuning. The 3/1 in 46ed17 isn’t that good, with similar error to [[5edo]], but it’s a huge improvement on 26ed5. And the 5, 11, 17, 23 and 43 are genuinely solid approximations. Other tunings which are almost identical to 46ed17, and so provide those same benefits, are [[8ed18/11]] and [[20ed24/7]].

If one attempts to [[Octave stretch|stretch]] 26ed5 instead of compress, one will not find any tunings that approximate primes well until reaching [[11edo]], so only compression is viable, not stretching.

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 Pure-octaves 26ed5 is incompatible with [[prime limit]] tuning. Of all primes up to 41, 5 and 41 are the only two it approximates well. Many of 26ed5’s 'near-miss' [[prime]]s are tuned sharp, so 26ed5 can be made to work more normally by [[Octave shrinking|compressing]] 26ed5’s [[equave]], making [[5/1]] slightly flat but still okay and the other primes more in-tune.
-A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23.43 tuning. The 3/1 in 46ed17 isn’t that good, comparable to [[5edo]], but it’s a huge improvement on 26ed5. And the 5, 11, 17, 23 and 43 are genuinely solid approximations. Other tunings which are almost identical to 46ed17, and so provide those same benefits, are [[8ed18/11]] and [[20ed24/7]].
+A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23.43 tuning. The 3/1 in 46ed17 isn’t that good, with similar error to [[5edo]], but it’s a huge improvement on 26ed5. And the 5, 11, 17, 23 and 43 are genuinely solid approximations. Other tunings which are almost identical to 46ed17, and so provide those same benefits, are [[8ed18/11]] and [[20ed24/7]].
 If one attempts to [[Octave stretch|stretch]] 26ed5 instead of compress, one will not find any tunings that approximate primes well until reaching [[11edo]], so only compression is viable, not stretching.