1. Tonic, mediant and dominant together form the tonic triad.

2. Focused on the asymptotic behaviour of mediant for fourth order Lagrange's mean value theorem and obtained the main results as followed (The equation is abbreviated).

3. The present invention has all pitch of treble, mediant and bass, and thus rich expressive force.

4. The mediant is the third degree of the scale and is midway between the tonic and the dominant. Tonic, mediant and dominant together form the tonic triad.

5. Starting from the tonic or key-note, the scale degrees in ascending order are: tonic, supertonic , mediant, subdominant, dominant, submediant, leading tone or leading note, tonic.

6. The right rectangle formula was generalized, the asymptotic behaviour of mediant for the right rectangle formula and the generalized right rectangle formula were given.

7. In the second chapter, I propose semi-parametric estimate to get median regression models with the measured error margin and use it to estimate the mediant of survival data.

8. Starting from the tonic or key-note, the scale degrees in descending order are: tonic, leading tone or leading note, submediant , dominant, subdominant, mediant, supertonic, tonic.

9. Give a class of differential intermediate value theorem, and obtain the asymptotic behavior of mediant for the theorem.