Dual-fifth tuning: Difference between revisions

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Perhaps a more familiar dual-fifth system to many is [[18edo]]. It is the first system that has intervals that are close enough to 3/2 that they can be regarded as sharp and flat fifth, but also far enough to sound different. Its sharp fifth and flat fifth are almost equally off from just: it has a 733.3¢ sharp fifth 31.4¢ sharp from pure [[3/2]], and a 666.7¢ flat fifth is 35.3¢ flat.

~~Other notable~~ edos which ~~have been studied as~~ dual-fifth ~~include:~~

For a list of edos which could be considered dual-fifth, see [[:Category:Dual-fifth temperaments]].

* [[~~13edo]] (major fifth +36.5¢ from just, minor fifth~~ -~~55.8¢ from just)~~

* [[23edo]] (major fifth ~~+28.5¢ from just, minor fifth -23.7¢ from just)~~

* [[25edo]] ~~(major fifth +18.0¢ from just, minor fifth -30~~.~~0¢ from just)~~

* [[47edo]]

* [[59edo]]

* [[100edo]]

* [[112edo]]

We may, heuristically, define dual-fifth edos as those whose [[relative error]] of the third harmonic is greater than 1/3. In that case 1/3 of all edos will be dual-fifth and the other 2/3 will be plain-fifth.

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 Perhaps a more familiar dual-fifth system to many is [[18edo]]. It is the first system that has intervals that are close enough to 3/2 that they can be regarded as sharp and flat fifth, but also far enough to sound different. Its sharp fifth and flat fifth are almost equally off from just: it has a 733.3¢ sharp fifth 31.4¢ sharp from pure [[3/2]], and a 666.7¢ flat fifth is 35.3¢ flat.
-Other notable edos which have been studied as dual-fifth include:
+For a list of edos which could be considered dual-fifth, see [[:Category:Dual-fifth temperaments]].
-* [[13edo]] (major fifth +36.5¢ from just, minor fifth -55.8¢ from just)
-* [[23edo]] (major fifth +28.5¢ from just, minor fifth -23.7¢ from just)
-* [[25edo]] (major fifth +18.0¢ from just, minor fifth -30.0¢ from just)
-* [[47edo]]
-* [[59edo]]
-* [[100edo]]
-* [[112edo]]
 We may, heuristically, define dual-fifth edos as those whose [[relative error]] of the third harmonic is greater than 1/3. In that case 1/3 of all edos will be dual-fifth and the other 2/3 will be plain-fifth.