The musical interval of a well tempered piano does not agree with the standard instrument scale, specifically, the pitch of the lowest key is about 35 cent lower and of the highest key is also about 35 cent higher than that of the standard scale. Consequently the tuning curve of a piano is S-shaped.
This paper deals with the cause of the S-shaped bent of the tuning curve of a piano. Some industrial applications of our results to tuning of pianoes are also discussed.