Music and Math

12 tone rows and 12th order Langford series

Arnold Schoenberg developed the twelve tone row technique for composing atonal music. He objected to the term atonal, insisting that his music demonstrated a new kind of tonality, not the absence of tonality, but the atonal label stuck.

Tone row compositions are difficult to listen to, but they have an interesting mathematical structure. That’s the topic of my latest post.

Before blogging about Schoenberg, I wrote a short post about Langford series. I just give a teaser and link to a site that does into much more detail.

Have a good week.