Part of a piano keyboard
Diophantine approximations with denominator n to the logarithms of the six "pleasant" musical intervals r_1=2/1 (octave), r_2=3/2 (fifth), r_3=4/3 (fourth), r_4=5/4 (major third), r_5=6/5 (minor third), and r_6=9/8 (whole tone), and the quality of the nth approximation (lower diagram).
