What is the normal order?

10, 1, 2, 3

Pitch class interval

higher pitch # - lower pitch #

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

What is transpositional symmetry?

Any combination of a set.

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

What is a "segment"?

A collection of notes in ANY ORDER

Locate the prime segment.

S1 line, first six pitches before the double line

Locate the** inversion** of the prime segment.

S2, first six pitches is the inversion of S1.

First two pitches of S1 = up M3

First two pitches of S2= down M3

Locate the **retrograde **of the prime segment.

The last six pitches of the S1 line

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

Locate the **retrograde inversion.**

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.

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

prime; 11

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

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?

The inversion or I0.

D to E = up M2

D to C = down M2

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.

Retrograde

__________ are the inverted rows in reverse.

Retrograde inversion

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

{F, A, Eb, D}

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

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.

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**

Explain how the trichords are symmetrical:

{B, Bb, D}

{Eb, G, F#}

{Ab, E, F}

{C, C#, A}

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. **

What is hexachordal combinatoriality?

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

What is the best order of filling out a matrix?

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).