- Atonal: Music without a tonal center or key.
- Modernism: scale down pattern
- Consists of 12 Tone Row and/or Pitch Class Set
- Schoenberg was to first to compose this type of music with Webern and Berg following his footsteps.
- Began around 1908
Example of Pitch Class Set on p. 492 m. 11 violin I
Step 1: F(0) Ab(3) G(2) →Unordered pitches
Step 2: F(0) G(2) Ab(3)→Best Normal Order(BNO)
G(0) Ab(1) F(10)
Ab(0) F(9) G(11)
Step 3: BNO (0 2 3)
Step 4: 3 F(0) G(2) Ab(3)
1 Eb
0 D
Reterograde Inversion (RI)
Step 5: Prime Form(PF) [0 1 3]
Step 1: P(0) Ab G F F# E C D Bb A B Eb C# →Original Tone Row
Step 2: P(1) A Ab F# G F C# Eb B Bb C E D →Find the Matrix
P(3) B Bb Ab A G Eb F C# C D F# E
P(2) Bb A G Ab F# D E C B C# F Eb
P(4) C B A Bb Ab E F# D C# Eb G F
P(8) E Eb C# D C Ab Bb F# F G B A
P(6) D C# B C Bb F# Ab E Eb F A G
P(10) F# F Eb E D Bb C Ab G A C# B
P(11) G F# E F Eb B C# A Ab Bb D C
P(9) F E D Eb C# A B G F# Ab C Bb
P(5) C# C Bb B A F G Eb D E Ab F#
P(7) Eb D C C# B G A F E F# Bb Ab →Ab diagonally top left
RI0 RI11 RI9 RI10 RI8 RI4 RI6 RI2 RI1 RI3 RI7 RI5 → Retrograde Interversion