Set Theory

Step-by-Step – Workbook Example 5

1. Segment the piece into groups of notes called sets. They can be grouped by such categories as pitch, rhythm, phrasing, register, timbre, etc

(Bb,A,C,B)

2. Put the set in Normal Order.

· Pitches must appear in ascending order

· Interval framing the set must be the smallest possible.

·

(9,10,11,0)

3. Breaking a tie.

NO TIE

4. Put set in Prime Form.

To get the 9 to 0 either add 3 or subtract 9

	9	10	11	0
-9 or +3	0	1	2	3

5. Determine the Vector.

	0	1	2	3
-1		0	1	2
-2			0	1
-3				0

6. Count up Interval Classes to determine interval content. The six interval classes are:

Interval Class 1—1or 11 (m2/M7)

Interval Class 2—2 0r 10 (M2/m7

Interval Class 3—3 or 9 (m3/M6)

Interval Class 4—4 or 8 (M3/m6)

Interval Class 5—5 or 7 (P4/P5)

Interval Class 6—6 (TT)

1(11)	2(10)	3(9)	4(8)	5(7)	6
3	2	1	0	0	0

This Vector is: [3 2 1 0 0 0]

7. Look up the Set Class number

4 – 1

Hanson Analysis – All the intervals above A, then Bb, then, B.

A – Bb = m2 – d ; A – B = M2 – s ; A – C = m3 – n

Bb – B = m2 – d ; Bb – C = M2 – s

B – C = m2 – d

Answer: n,s²d³ a very dissonant chord!!!