23e Lesson - Serialism and Tone Rows

Class discussion

Serialism and Tone Tows

Any type of music when the composer decides to take music out of subjectivity. They turn a melody in a series. We are serializing the intervalic relationship within our melody.

Serialism does not = 12 tone music.

Branches of Serial Music:

1. 12 tone music
   • takes all 12 pitches and makes sure they are all of equal importance
   • you cannot use one a second time until all other 11 pitches are repeated
   • a tone row: a set of 12 pitches with fixed intervalic relationships

You have a musical idea that the piece is based off of. How many versions of one form are there?

Take the prime form (013).

• T0 = [0,1,3]
• T1 = [1,2,4]
• T2 = [2,3,5]
• T3 = [3,4,6]
• T4 = [4,5,7]
• T5 = [5,6,8]
• T6 = [6,7,9]
• T7 = [2,3,5]

The inversion is T0I = [9,e,0]

• T0I[0,1,3] = [9,e,0]
• T1I[0,1,3] = [t,0,1]
• T2I[0,1,3] = [e,1,2]
• T3I[0,1,3] = [0,2,3]
• T4I[0,1,3] = [1,3,4]
• T5I[0,1,3] = [2,4,5]
• T6I[0,1,3] = [3,5,6]
• T7I[0,1,3] = [4,6,7]
• T8I[0,1,3] = [5,7,8]
• T9I[0,1,3] = [6,8,9]
• TtI[0,1,3] = [7,9,t]
• TeI[0,1,3] = [8,t,e]

We have 24 possible PC sets, with 12 transposed PC sets, and 12 transposed and inverted PC sets.

Common PC: a shared number between the left side of the T PC set and the right side of the TI PC set.

What if we had all 12 pitch classes? The normal form both inverted and not would be [0,1,2,3,4,5,6,7,8,9,t,e]. But out of normal form, find the different options for starting points while maintaining all the same intervalic relationships between pitch classes. So when we find the different variations of a 12-pitch PC set, we have to do it out of normal form. We use the set of pitch classes in the order they appear in a piece of music. EX: (0,2,4,6,8,t,1,3,5,7,9,e)

The name for a PC set that includes all 12 tones is a tone row. To organize these pitches and their various transpositions and inversions, we have to build a tone row matrix.

• a tone row matrix is a grid that lists all of our pitches and their intervalic relationships, representing all possible tone rows.
• a tone row matrix can be built using numbers or letter names to represent pitch classes.

Tone Row Matrix

You can take your tone row and transfer it to numbers. We can use the row above, (0,2,4,6,8,t,1,3,5,7,9,e). The letter equivilant is (C,D,E,F#,G#,A#,C#,D#,F,G,B).

Building a tone row matrix involves comparing intervals to fill in a grid based on a tone row in a piece of serial music. Matrix row names:

• prime (P with subscript of the number you started on)
• inversion (I w/ subscript)
• retrograde (R w/ subscript from the prime row, reads prime backwards)

The middle diagonal in a tone row from top left to bottom right is the same letter/number.

• retrograde inversion (RI w/ subscript from the inversion row, reads inversion backwards)

Fixed zero in a tone row matrix lets you know what the pitches are, and movable zero lets you know how it functions. If you’re using the tone row matrix, we already know what the fuction is. So we use fixed zero to get the pitches. If we have movable zero, realign it to zero to get pitch classes that match letter names around C.