Dual-fifth tuning: Difference between revisions
→Stretched or compressed edos: correct maths |
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=== Stretched or compressed edos === | === Stretched or compressed edos === | ||
[[Octave stretching]] or [[octave shrinking]] can be used to equally share the error between an edo's best and | [[Octave stretching]] or [[octave shrinking]] can be used to equally share the error between an edo's best and second-best 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: | 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: | ||
{{Todo|correct maths|inline=1|text=This list gives half the unstretched step size for each edo. The correct values should be half of the step size after stretching, where the 9/4 reached by stacking both fifths is just.}} | |||
'''>25{{c}} error''' | |||
* [[16edo]]: 37.50{{c}} | * [[16edo]]: 37.50{{c}} | ||
* [[18edo]]: 33.33{{c}} | * [[18edo]]: 33.33{{c}} | ||
* [[20edo]]: 30.00{{c}} | * [[20edo]]: 30.00{{c}} | ||
* [[23edo]]: 26.09{{c}} | * [[23edo]]: 26.09{{c}} | ||
'''15-25{{c}} error''' | |||
* [[25edo]]: 24.00{{c}} | * [[25edo]]: 24.00{{c}} | ||
* [[28edo]]: 21.43{{c}} | * [[28edo]]: 21.43{{c}} | ||
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* [[37edo]]: 16.22{{c}} | * [[37edo]]: 16.22{{c}} | ||
* [[40edo]]: 15.00{{c}} | * [[40edo]]: 15.00{{c}} | ||
'''<15{{c}} error''' | |||
* [[42edo]]: 14.29{{c}} | * [[42edo]]: 14.29{{c}} | ||
* [[47edo]]: 12.77{{c}} | * [[47edo]]: 12.77{{c}} | ||