Integrated Music Theory 2020-21

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24d Lesson - Serialism and Tone Rows

Class discussion

What is serialism?

  • Using set rules/creating your own rules to follow in order to systematically compose a piece of music

Using the transposition/inversion system we’ve used so far, it becomes clear that there are 24 total vesion of any default pitch class set. How do we represent this information in a streamlined, easily interpreted format?

  • Put it in a matrix! See examples in the textbook.
  • Matrices can have any number of pitches in their pitch class sets, but we will deal most with 12-tone music, where a matrix is made up of a tone row with all 12 pitches

12-tone music

  • Prime (P): a tone row or any of its transpositions
  • Retrograde (R): any prime row played in reverse order
  • Inversion (I): the inversion of the original prime tone row and all its inversions
  • Retrograde Inversion (RI): any inverted row played in reverse order
    • When you make a matrix, these four groups will be easily labeled and organized! It ends up looking like a big square.

Developing a matrix

  • When we construct a matrix, we write the original row across the top (horizontally) and its inversion down the side (vertically). This only works when your row begins with 0 (since 0’s inversion is 0), so if you start your row with a first number other than 0, zero it out and use that one for your top row instead
  • Once you have these two, you can transpose for each horizontal line going off of the first digits provided in the inversion/first veritcal column. The lines represent transpositions, and the columns are inversions
  • You can check yourself by making sure that you have 0’s in a diagonal across the middle from the upper left corner to the bottom right corner
  • The subscript numbers will always match for P/R and I/RI. Retrograde and retrograde inversion labels must match the prime and inversion labels so that we know what they are a retrograde of. So, R and RI rows will have subscripts that don’t match the number they start with.

The primary purpose for a tone row matrix is to use it as a point of reference to analyze 12-tone music. It gives us a list of all the possible rows a composer might use in their piece.

You can have a tone row with less than 12 tones, but our matrix method only works with a full 12-tone row. So don’t use it for hexachords and stuff