My high-school piano teacher was reluctant to coach me on anything written in the 20th century. It all seemed just too decadent and non-sensical to her church-musician ears, except maybe Bela Bartok, who had the excuse of ‘ethnic’ explorations.

A few years later, I was learning Arnold Schoenberg’s “Six Little Pieces” for piano. Schoenberg was modern, I was told, and to many of my musical teachers and mentors, it was thought he represented an ending: the end of beauty and achievement in the Western tradition. It would be ugly from here on.

As I studied this music, I came to some conclusions of my own. These pieces barely made sense without reference to previous centuries of European musical tradition. Indeed, what was remarkable to me was not how different they were from what had come before, but how similar.

In what ways?

• The meter was 3/4, the same as the Bach minuets I had learned as a I child.
• The rhythms used quarter, eighth and sixteenth notes. No extremes here.
• Who was to play the music? A neatly-dressed, serious-minded and well-trained pianist.
• For whom? An audience seated in the dark, quiet and appreciative — if a little alienated.
• The instrument was the piano, the same instrument that dominated European music in the 19th Century.
• How was the piano played? Fingers on the keyboard, just like Beethoven.

So what was different? The harmony and the shapes of the melodic lines.

Schoenberg was an incrementalist, not a revolutionary, and much of the music he wrote was a natural progression, an expected permutation — perhaps long overdue — and not a radical departure or complete reinvention.

Why is this sense of ordinariness still important to me?

It reminds me that the details we pay attention to determine our sense of innovation.

The musical establishment was focused on the particulars of harmony and melodic shape, and any experimentation with those core elements was a radical act. For me, considering the sweep of global music in the 20th century, and anticipating the 21st, these experiments seemed relatively unremarkable.

I always return to this perspective when thinking about how a project relates to tradition: which parts are best left as they would be assumed and expected to be, and which parts could be essentially and profoundly different? And when I’m working with or for someone else who might be more traditional: which aspects are defensibly different, and which aren’t worth fighting for?

It reminds me of the interplay between familiarity and confusion: give an audience just enough of what they know to understand the context, and just enough innovation to surprise and delight.