26ed5: Difference between revisions

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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.

[[~~29ed6~~]] is a ~~compressed version of 26ed5, compressing~~ 5/1 ~~by roughly 6 cents~~, but ~~it is not enough to bring many primes into line~~. ~~Further compression than that is required~~.

A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23. 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 and 23 are genuinely solid approximations.

[[Octave stretch|~~Stretching~~]] ~~rather than compressing the equave is also an option. It~~ will ~~change a lot of~~ [[~~val~~]]s, so ~~the tuning may~~ not ~~longer be fully recognisable as 26ed5, however the right amount of~~ stretching ~~will improve primes~~.

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.

=== Composite subgroups ===

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 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.
-[[29ed6]] is a compressed version of 26ed5, compressing 5/1 by roughly 6 cents, but it is not enough to bring many primes into line. Further compression than that is required.
+A good compressed tuning of 26ed5 is [[46ed17]], which transforms 26ed5 from a 5.41 tuning to a 3.5.11.17.23. 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 and 23 are genuinely solid approximations.
-[[Octave stretch|Stretching]] rather than compressing the equave is also an option. It will change a lot of [[val]]s, so the tuning may not longer be fully recognisable as 26ed5, however the right amount of stretching will improve primes.
+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.
 === Composite subgroups ===