20th Century Techniques

Question 1

What is the normal order?

Answer 1

10, 1, 2, 3

Question 2

Pitch class interval

Answer 2

higher pitch # - lower pitch #

if higher pitch # is lower than lower pitch #, add 12

Question 3

What is transpositional symmetry?

Answer 3

Any combination of a set.

Example: {0, 2, 4} ; {2, 0, 4}; {4, 0, 2} are all transpositionally symmetrical

Question 4

What is a “segment”?

Answer 4

A collection of notes in ANY ORDER

Question 5

Locate the prime segment.

Answer 5

S1 line, first six pitches before the double line

Question 6

Locate the inversion of the prime segment.

Answer 6

S2, first six pitches is the inversion of S1.

First two pitches of S1 = up M3

First two pitches of S2= down M3

Question 7

Locate the retrograde of the prime segment.

Answer 7

The last six pitches of the S1 line

matches the first six pitches of the S1 line, but in retrograde (reverse) order.

Question 8

Locate the retrograde inversion.

Answer 8

The last six pitches of the S2 line.

The inversion=the first six pitches of the S2.

The retrograde inversion= the reverse order of the inversion.

Question 9

Transpositions (T) are all versions of the _____ row. There are ____ ways to transpose this row.

Answer 9

prime; 11

There are twelve tones, meaning there are 11 ways to transpose a pitch set.

Question 10

If D and E are the first two pitches of the prime row (P0), which row has D and C as its first two pitches?

Answer 10

The inversion or I0.

D to E = up M2

D to C = down M2

Question 11

If prime row (P0) = {D, E, Eb, C, Gb, A, G, Ab, Bb, B, F, Db}, then

{Db, F, B, Bb, Ab, G, A, Gb, C, Eb, E, D} are the ____ row.

Answer 11

Retrograde

Question 12

__________ are the inverted rows in reverse.

Answer 12

Retrograde inversion

Question 13

If P0 = {D, E, Eb, C, Gb, A, G, Ab, Bb, B, F, Db}, what are the first four pitches of R4?

Answer 13

{F, A, Eb, D}

Transpose the last four pitches of the prime row (Db, F, B, Bb) up 4 (hence R4) half-steps.

Question 14

P0 = {D, E, Eb, C, Gb, A, G, Ab, Bb, B, F, Db}

When segmenting the row into four trichords, there are _____ instances of interval class 1.

Answer 14

Interval class 1 = pitches with 1 chromatic interval difference

Trichords: {D, E, Eb} {C, Gb, A} {G, Ab, Bb} {B, F, Db}

{D, E, Eb} = D to Eb; Eb to E (2)

{C, Gb, A} = Gb to A (1)

{G, Ab, Bb} = G to Ab (1)

{B, F, Db}= none (0)

2+1+1= 4

Question 16

Explain how the trichords are symmetrical:

{B, Bb, D}

{Eb, G, F#}

{Ab, E, F}

{C, C#, A}

Answer 16

P0 = {B, Bb, D, Eb, G, F#, Ab, E, F, C, C#, A} =

Divided into trichords: Normal order or trichords:

{0, 11, 3} {0, 3, 11}

{4, 8, 7} {4, 7, 8}

{9, 5, 6} {5, 6, 9}

{1, 2, 10} {1, 2, 10}

When compared in normal order, the trichords have the same intervallic distance.

Question 17

What is hexachordal combinatoriality?

Answer 17

When six pitches (hexachord) of one row complete the twelve tones with six pitches of another row.

Question 18

What is the best order of filling out a matrix?

Answer 18

1. Prime row/P0
2. The prime row will automatically give you the Retrograde/R0
3. Fill in the inversion of the prime row. This will automatically give you the retrograde inversion of the prime row.

Numbers refer to the number of semitones above the prime row (transposition).