Where Do You Put the Notes?
Tempering
  
  • Twelve 5ths > 7 octaves
    (1.512=129.75) > (27=128)
     
  • Mean Tempering Favors Fifths
    adjust semitones to make most Fifths perfect but
    leaves annoying "Wolf Fifths" which can be avoided for any one piece by specialized tuning

     
  • Even Tempering Favors Octaves
    adjusts semitones to make octaves work and
    abandons consonance of the perfect fifths

     

The Problem of Specialized Tuning