Dual-fifth tuning: Difference between revisions

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 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.
+=== Stretched or compressed edos ===
+[[Octave stretching]] or [[octave shrinking]] can be used to equally share the error between an edo's best and worst fifths (i.e. bring them both to exactly 50% [[relative error]]).
+Here is the amount of error the sharp and flat fifth will both exhibit in some possible dual-fifth edos after they have been stretched/compressed in this way:
+* [[16edo]]: 37.50{{c}}
+* [[18edo]]: 33.33{{c}}
+* [[20edo]]: 30.00{{c}}
+* [[23edo]]: 26.09{{c}}
+* [[25edo]]: 24.00{{c}}
+* [[28edo]]: 21.43{{c}}
+* [[30edo]]: 20.00{{c}}
+* [[32edo]]: 18.75{{c}}
+* [[33edo]]: 18.18{{c}}
+* [[35edo]]: 17.14{{c}}
+* [[37edo]]: 16.22{{c}}
+* [[40edo]]: 15.00{{c}}
+* [[42edo]]: 14.29{{c}}
+* [[47edo]]: 12.77{{c}}
+* [[49edo]]: 12.25{{c}}
+* [[52edo]]: 11.54{{c}}
+* [[54edo]]: 11.11{{c}}
+* [[57edo]]: 10.53{{c}}
+* [[59edo]]: 10.17{{c}}
+* [[64edo]]: 9.38{{c}}
+* [[66edo]]: 9.09{{c}}
+* [[69edo]]: 8.70{{c}}
+* [[71edo]]: 8.45{{c}}
+You can calculate this for any edo by subtracting the smaller fifth from the bigger fifth, then dividing the result by two (i.e., by dividing the size of one edo-step by two).
 == Dual-fifth temperaments ==