A Sonata as Teacher

Music makes things in our minds, but afterward most of them fade away. What remains? In one old story about Mozart, the wonder child hears a lengthy contrapuntal mass and then writes down the entire score. I do not believe such tales, for history documents so few of them that they seem to be mere legend, though by that argument Mozart also would seem to be legend. Most people do not even remember the themes of an evening's concert. Yet, when the tunes are played again, they are recognized. So...

 Human Propensity for Making More Complicated Things Out o...

A child stacks and packs all kinds of blocks and boxes, lines them up, and knocks them down. What is that all about? Clearly, the child is learning about space! But how on earth does one learn about time? Can one time fit inside another? Can two of them go side by side? In music, we find out! It is often said that mathematicians are unusually involved in music, but that musicians are not involved in mathematics. Perhaps both mathematicians and musicians like to make simple things more complic...

 Why Do We Like Certain Tunes or Understand Certain Senten...

Contrast two answers to the question, Why do we like certain tunes? Because they have certain structural features.Because they resemble other tunes we like.   The first answer has to do with the laws and rules that make tunes pleasant. In language, we know some laws for sentences; that is, we know the forms sentences must have to be syntactically acceptable, if not the things they must have to make them sensible or even pleasant to the ear. As to melody, it seems that we only know some...