26ed5: Difference between revisions

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~~{{Stub}}~~

== Theory ==

=== Subgroup interpretation ===

26ed5 is a weak tuning for [[prime limit]] tuning. It can instead be used as a strong tuning for the obscure [[subgroup]] '''5.6.12.22.32.34.41.44.46.49.53.56.59.63.67'''.

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* Only 6 and the primes: '''5.6.41.59.67'''

~~Many of 26ed5’s 'near-miss' [[prime]]s are tuned sharp, so~~ 26ed5 ~~can be made to work more normally by [[Octave stretch|compressing]] 26ed5’s [[equave]], making [[5/1]] slightly flat but still okay and the other primes more in-tune~~.

Fractional subgroups might also be an option for 26ed5.

=== ~~Harmonics~~ ===

=== Equave stretch ===

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 5 cents, but even it is not enough to bring many primes into line. Further compression than that is required.

[[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.

=== Tables of harmonics ===

{{Harmonics in equal

| steps = 26

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== Intervals ==

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-{{Stub}}
 {{Infobox ET}}
 {{ED intro}}
 == Theory ==
+=== Subgroup interpretation ===
 ed5 is a weak tuning for [[prime limit]] tuning. It can instead be used as a strong tuning for the obscure [[subgroup]] '''5.6.12.22.32.34.41.44.46.49.53.56.59.63.67'''.
@@ Line 12: / Line 13: @@
 * Only 6 and the primes: '''5.6.41.59.67'''
-Many of 26ed5’s 'near-miss' [[prime]]s are tuned sharp, so 26ed5 can be made to work more normally by [[Octave stretch|compressing]] 26ed5’s [[equave]], making [[5/1]] slightly flat but still okay and the other primes more in-tune.
+Fractional subgroups might also be an option for 26ed5.
-=== Harmonics ===
+=== Equave stretch ===
+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 5 cents, but even it is not enough to bring many primes into line. Further compression than that is required.
+[[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.
+=== Tables of harmonics ===
 {{Harmonics in equal
 | steps = 26
@@ Line 72: / Line 80: @@
 == Intervals ==
 {{Interval table}}
+{{todo|expand}}