Parameters I: The Myth Of Liberal Democracy

for string quartet

David Pocknee

Parameters I: The Myth Of Liberal Democracyfor string quartet

duration: 20-30minutesDavid Pocknee

i

Parameter MappingIn parameter mapping a player will listen to the range and values of another performer’s parameters and map those onto one of their own parameters. This relationship is represented in each box by a series of symbols showing the ranges and values of parameters to be mapped to or from.

The example below on the left shows a typical box that a performer might come across in the piece.

The top line of symbols always indicates who and what the performer has to listen to (in this case, cello dynamics). Two symbols joined by a double-headed arrow indicate that these are the minimum and maximum param-eter values that this player (the cello) will be using.

The lower line of symbols indicates what the performer has to do (in this case modify their pitch). Two symbols joined by a double-headed arrow indicate that these are the minimum and maximum values that can be used in the mapping - the values of the cello’s dynamics should be proportionally scaled to the pitch range given. This relationship could also be represented by the graph below:

AboutThis piece explores ways of listening and reacting to four musical parameters: pitch, dynamics, duration, and timbre.

This is done through the technique of “parameter mapping” (see below).By arranging sets of parameter mappings into recursive loops of 2,3 or 4 players (Movements I, II, and III, respectively), chaotic systems arise in which the material is created by the system itself.

The Set-upThe players should be seated in the shape of a square, with each player placed on one of the corners of the square, facing inwards towards the rest of the group.

The players should be sat as close together as practical.

Each performer should be able to clearly see all the other players and their instruments.

The audience should be seated around the players, close enough for the performance to be intimate, but not so much that the audience becomes a distraction for the performers.

Parameter MappingKey terms:A parameter is the pitch, dynamics, duration or timbre of an instru-ment.parameter value is the level of the paramater. e.g. the value of the parameter 'dynamics' is .parameter range is the total ambitus of values encompassed. e.g. a parameter range of the parameter 'dynamics' could stretch from to .parameter mapping is the process of translating the range and values of one parameter onto the range and values of another (see right).

Vcl

The player must imagine there is a 1:1 correspondence between dynamics and pitch - that is equal to middle C and is equal to the G a �fth above, and every dynamic and pitch in between is an extrapolation of this relationship.

“”The greatest myth of modern, democatic society is the illusion of choice.”-F. Droppe

cello

dyn

amic

s he

ard

pitches played

Vln I

Vln II

Vla

Vcl

Audience

AudienceAudience

Audience

Diagram of the set-up

ii

DurationThe duration of a note is based on the amount of the bow used before either chang-ing the bowing direction, or re-attacking the string from the same direction.

In the score, the bow is split up into eighths. The notation speci�es how much and which part of the bow can be used in each box.

There are two types of bowing; The �rst type is indicated by an unbroken line surrounding each box, indicating that at the end of each bow-stroke the direction of bowing should be changed.

The second type is indicated by a box made of dashed lines and symbolizes that the performer should always bow in the same direction. This direction is indicated by conventional bowing sym-bols above the box:

08

18

28

38

48

58

68

78

88

DynamicsThe dynamics used in this piece are: = as soft as possible while creating an unbroken tone.

= as hard as possible, without creating a scraping sound.

These instructions refer to bowing pressure, NOT the audible nature of the sound, with representing the maximum bow pressure possible, without a scraping sound occur-ing, and representing the minimum bow pressure at which a continuous tone can be sustained. This distinction is made due to the variable nature of dynamics when bowing at di�erent string positions.Performers mapping their parameters from dynamics should be careful to compensate for the use of mutes in Movement II.

Parameter RangesIn this piece the following ranges are used:

PitchMost of the piece uses pitch ranges in which the limits of each range are given in equal-tempered tuning with 12 notes to the octave. However, in the last two boxes of the piece, the following equal-tempered quarter-tone notation is used: = a quarter-tone higher = a quarter-tone lower

TimbreXST = Extreme Sul Tasto - as close to the �ngers of the �ngering-hand as feasible/possibleST = Sul Tastoord = OrdinarioSP = Sul PonticelloXSP = Extreme Sul Ponticello - as close to the bridge as feasible/possible

The graph on the previous page simpli�es the relationship between dynamics and pitch by helpfully quantizing the dynamic range into 8 values of dynamics and the pitch range into equal-tempered tuning. However, in the actual piece, no such quantization should occur, with in�nitessimally small changes in one parameter invoking similarly scaled changes in another. The piece will involve players reacting to and performing changes that are far smaller than equal-tempered tuning or even the most precise dynamic markings.

When playing a box, only the parameter which the box speci�es to change, should alter. All other parameters should stay at the same values as they were at the end of the last box they played.

If there is more then one set of parameter mapping in a box, all mapping indicated must be done simultaneously.

With each type of bowing the shortest bow-stroke possible is a tremolo as fast as possible and using as little of the bow as possible. The longest bow-stroke possible would be one which encompasses the entirety of the range of the bow given.

The length of each bow-stroke should always take the extreme of the range closest to the frog (base) of the bow as the point of departure or termination for the stroke. The length of the srtoke is then measured in relation to this point, whether it is at the beginning or end of a stroke.

iii

The ScoreThe score is arranged as a series of blocks, grouped together in phrases.Each block contains information about how each player should map the parameter range and values of another player onto their own parameters.

TimingIn the middle of the top of each box is a fraction, indicating how much longer or shorter that box should last in relation to the previous box. e.g. if the fraction is “2/3” that box should be 2/3rds of the length of the previous box. This fraction should only be taken in reference to the actual length of the box directly previous. If the previous box lasted longer or shorter than anticipated, then the length of the following box should be adjusted pro-portionally (i.e. lengthened or shortened).The length of the box should be subjectively determined by the performer who cues the following box. The length of the box should not be measured using a stopwatch, other temporal measuring device, or any sort of counting, but should spring out of the performer's intuitive sense of time during the performance of the piece.

CueingThe top left corner of the box shows which performer is to cue the start of the box. All performers start and end each box simultaneously.The indicated performer is in charge of judging the length of the previous box and cueing the start of the indicated box.

Each cueing indication either gives the name of another performer, who is the performer to cue that box, or the instruction “CUE” which indicates to a player that they are in charge of cueing that box. All players should look ahead to the next box when playing, to ensure that they are cognizant of which boxes they should be monitoring the length of, and which ones they should be cueing.

Where a box occurs at the beginning of a phrase, the cueing performer should cue the end of the last box of the previous phrase, wait the correct amount of silence (see right) before cueing their box.

Continuous/SteppedIn the bottom centre of the box is an indication of how the parameters inside should be mapped.“continuous” = the performer's parameter values should be constantly and �uidly changing, reacting immediately to the changes in other players. “stepped” = the performer only changes the value of any parameter inside the box upon beginning a bow-stroke, and these values are static for the entirety of the stroke, creating a stepped, quantized e�ect.

Rest BarsBars which feature a �ve-lined sta� with a rest, indicate that the performer should not play in this box. When they begin playing again, they should start that box with exactly the same parameter values as they had at the last box that they played in.

PhrasesBoxes are grouped together into “phrases” of 2-4 boxes. This is indicated through the use of phrase markings and a thick horizontal line which joins the boxes together. Boxes grouped like this should be played attacca with no silence between them.

At the end of a phrase, an apostrophe above the boxes indicates a short rest (approximately 1/6th of the length of the previous box. A longer length of silence should be inserted between movements (approximately the length of the previous box).

3/4

CUE

continuous

Starting The PieceThe �rst box of the piece is slightly di�erent to those that follow, in that no parameter mapping takes place. This box sets the initial conditions for all that follows.

All players should start simultaneously and sustain the sound speci�ed (full bow-strokes, middle G#, mezzo-forte, ordinario) until they receive a cue from the cello to start the second box. The piece then proceeds as described above.

dp23 August 2012

Movement I

Violin II:

Violoncello:

Viola:

Violin I:

Parameters I: The Myth Of Liberal Democracy

(Version 2)August 2012

for String Quartet

(2010 - 2012)

David Pocknee

’

’

’

’

continuous

Vla

continuous

Vla

continuous

5-9 bowsVla

CUE

continuous

CUE

continuous

1

continuous

1Vln I

continuous

1Vln I

continuous

1Vln I

continuous

x 1Vln II

continuous

1Vln II

continuous

1Vln II

continuous

1Vln II

CUE

continuous

1

continuous

1Vla

continuous

1Vla

continuous

1Vla

CUE

continuous

1

continuous

1Vcl

continuous

1Vcl

continuous

1Vcl

CUE

continuous

1

08

88

ordIV

08

88

ordIV

08

88

08

88

ordIII

08

88

ordI

XSP XSTVcl

Vln I

Vcl

Vln II

Vla08

88

XSTXSP

Vln II

XSTXSP

08

88

Vln I

08

88

Vcl

08

88

Vln I

XSTXSP

08

88

XSP XSTVla

XSP XSTVln II

XSP XSTVln I

Vla

Vln II

Vcl

XSTXSP

08

88

08

88

Vla

’

’

’

’

2

continuous

2/3CUE

Vln I

continuous

2/3

Vln I

step

2/3

Vln I

step

1/3

Vln II

continuous

3/4

Vln II

step

3/4

Vln II

step

3/4

continuous

3/4CUE

step

1CUE

Vla

continuous

1

Vla

continuous

1

Vla

step

1

step

1 1/4CUE

Vcl

continuous

1 1/4

Vcl

continuous

1 1/4

Vcl

step

1 1/4

Vln II Vln II

Vcl

Vla

18

88

Vln II

18

88

14

88

ST XSP

A

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STXSP

08

78

18

88

Vln II

ST XSP

08

34

Vln I

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18

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Vln II

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STXSP

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88Vla 1

488Vla

08

78Vcl

STXSP

SP XST SPXST

SPXST SP XST

Vln I

Vcl

Vln I

08

78

Vln I

08

78

ST XSP

Vla XST SP Vla XSTSP

08

34

Vln I STXSP

Vcl Vcl

Vla

Vln I18

78Vln I

18

78Vcl

ST XSP

Vcl SPXST Vcl SPXST

Vla Vla

’

’

’

’

3

step

1 1/3CUE

Vln I

step

1 1/3

Vln I

continuous

1 1/3

Vln I

step

1 1/3

step

4/5CUE

Vln I

step

4/5

Vln I

continuous

4/5

Vln I

step

4/5

Vln II

step

2/3

Vln II

continuous

2/3

Vln II

step

2/3

step

2/3CUE

step

2/3CUE

Vla

step

2/3

Vla

continuous

2/3

Vla

step

2/3

B

Vln I

Vla

Vln IVln I

14

88

14

88

38

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12

88

08

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08

12

08

58

08

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SP XST

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88Vln I 3

888Vln I

Vla

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Vln I SP XSTVln I

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34

Vln II08

58 Vln II

08

58

Vcl

Vln IIVln II

Vcl Vcl

Vln II XSP ST

Vcl XSP ST Vcl08

12

Vln II XSP ST Vln II

12

88

’

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’

’

4step

1 1/4CUE

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step

1 1/4

Vcl

continuous

1 1/4

Vcl

step

1 1/4

step

2/3CUE

Vln I

step

2/3

Vln I

continuous

2/3

Vln I

step

2/3

Vln II

step

3/4

Vln II

continuous

3/4

Vln II

step

3/4

step

3/4CUE

step

1 1/2CUE

Vla

step

1 1/2

Vla

continuous

1 1/2

Vla

step

1 1/2

C

12

88

08

12

38

78

38

78

Vcl SPXST Vcl ordXST

Vla ordXSP

18

58

18

58

SPXST

XSP ST

ord XST

ord XSP

ord XST

ord XSP ord XSP

ord XST

Vln II

Vcl

Vln II ordXSP Vln II ord XSP

Vla ST XSP

Vln II08

12

Vla

14

34

14

34

Vcl

Vln I

38

78 3

878Vcl Vcl VclVcl

14

34Vln I

14

34Vln II

Vln I12

88 Vln I

Vln II

Vln I Vln I Vln I ord XST Vln I XST ord

Vln II

Vla18

58Vla

Vln II

Vla18

58Vla Vla

’

’

’

’

5

CUE

continuous

3/4

continuous

3/4Vln I

step

3/4Vln I

step

3/4Vln I

CUE

continuous

1 1/4

step

1 1/4Vln I

continuous

1 1/2Vla

step

1 1/2Vla

step

1 1/2Vla

CUE

continuous

1 1/2

step

4/5CUE

Vcl

step

4/5

Vcl

continuous

4/5

Vcl

step

4/5 Vln I

continuous

1 1/4

Vln I

step

1 1/4

D

Vln II Vla SPST Vcl SPST

ordXST

14

34

14

34Vln I

SP ST

Vcl

18

58

18

58

Vla SPST

18

58Vln I

SP ST

SPST

XSTord

18

58Vln I

38

78Vcl

38

78Vla

38

78

Vln II

38

78

Vln II

Vln I

VclVln II

Vla

12

88

Vcl

Vla12

88

6

’

’

’

’

continuous

x 1Vln II

continuous

1Vln II

continuous

1Vln II

step

1Vln II

CUE

step

1

Vcl

step

1 1/2

Vcl

continuous

1 1/2

step

1CUE

Vla

step

1

Vla

continuous

1

Vla

step

1

CUE

continuous

2/3

continuous

2/3Vln I

step

2/3Vln I

step

2/3Vln I

continuous

1 1/2Vcl

CUE

continuous

1 1/2

E

08

12

08

38

Vln I

Vcl 08

12 Vln II

08

38 Vla

08

38

XSPSP

Vln II XSP SP

Vcl XST ST

Vcl XST ST

Vla XSPSP

Vln I

08

38

Vln I

Vln I

Vln II

Vln I

XSPSP

XSTST

Vla

XSTST58

88

Vcl58

88

Vln II

’

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’

’

’

’

’

’

7

CUE

continuous

1 1/4

continuous

1 1/4Vln I

step

1 1/4Vln I

step

1 1/4Vln IVcl

continuous

1 1/3

Vcl

step

1 1/3

continuous

1 1/3Vcl

CUE

continuous

1 1/3

continuous

x 1Vln II

continuous

4/5Vln II

continuous

1 1/3Vcl

continuous

1 1/3Vcl

step

1 1/3Vcl

continuous

4/5Vln II

step

4/5Vln II

CUE

step

4/5

CUE

continuous

1 1/3

F G H

XSTST

Vla STXST

12

78

Vla

Vln IIVln II12

78

Vcl XSP SP

Vln I

XSPSP

Vla XSPSP Vln II XSP SP

Vln I

XSPSP

Vcl

XSTST

Vln I

SPXSP

Vln II XSTST

14

34

14

34Vcl

Vla

’

’

’

’

8

continuous

3/4Vln I

continuous

1Vln II

continuous

1Vla

step

1Vln II

step

1Vla

continuous

3/4Vln I

Vln I

continuous

3/4

Vln II

continuous

1

Vla

continuous

1

Vln II:

Vcl:

Vla:

Vln I:

1 2/3Vla

continuous

1 2/3Vla

continuous

1CUE

continuous

1CUE

step

3/4CUE

continuous

1 2/3Vla

CUE

continuous

1 2/3

Vcl

Vln II

Vla

Movement II

58

Vln II

ord MSP

ord MSP

Vln II

ord MSP

Vln II Vcl

ord MSPord MSP

Vln IMSP ord

58

88

Vla MSP ord

ord MSP

12

78

Vla MSP ord

12

78

Vla MSP ord

58

88

88

Vla18

12

Vcl12

78 Vcl Vln I

18

12

12

78

Vln II

Vcl58

88

Vcl

ord MSP

Vla

Vln I08

38

Vln II MSP ord

08

38

with mute

with mute

with mute

with mute

’

’

’

’

’

’

’

’

9

continuous

1 1/4Vcl

continuous

1 1/4Vcl

Vla

continuous

4/5

Vla

continuous

4/5

Vln I

continuous

1

Vcl

continuous

2/3

Vcl

continuous

2/3

continuous

1CUE

1 1/4Vcl

CUE

continuous

1 1/4

CUE

continuous

1 1/3

CUE

step

2/3

CUE

step

4/5

continuous

1 1/3Vln II

continuous

1 1/3Vln II

continuous

1Vln I

continuous

4/5Vla

step

1Vln I

continuous

2/3Vcl

1 1/3Vln II

Vln II

Vln II ord STVcl58

88 Vcl

34

88

Vla08

14

Vcl34

88

Vcl18

14

Vln I Vln I

58

88

Vln II

34

88

Vln II

34

88

Vln II

08

14

Vla

ord ST

ord ST

Vla

ord ST

Vla

ord ST

Vln I

Vcl

Vln I

78

88

Vln I

78

88

Vln II

78

88

Vln II78

88

ord STVln I

ord STVln I Vln I

18

14

I J

10

CUE

continuous

1 2/3

continuous

1 2/3Vln I

continuous

1 2/3Vln I

1 2/3Vln I

ord STVla

Vcl

ST SP

Vln I

K

’

’

’

’

’

’

’

’

Movement III

Vln II:

Vcl:

Vla:

Vln I:

continuous

x 1Vln II

continuous

1Vln II

step

1Vln I

step

1Vcl

continuous

1Vln I

step

1Vln I

continuous

1Vcl

continuous

1Vcl

continuous

1Vcl

step

1Vcl

continuous

1Vla

continuous

1Vln II

step

1Vln II

step

1Vla

step

1Vla

continuous

1Vcl Vln II

step

1

Vln II

continuous

1

Vln II

step

1

step

1CUE

CUE

continuous

1

CUE

step

1

CUE

continuous

1

CUE

continuous

1

CUE

continuous

1

CUE

step

1

continuous

1Vln I

step

1Vln I

step

1Vln I

Vln I

11

Vln II

ord SPVcl Vcl ord SP

14

38

Vcl14

38 Vla

14

12

Vln I14

38

ord SP

Vln I

ordSP

Vla

ord SP

Vln I

Vln II

18

38

ord SPVln II

ord SPVln II ord SPVln II

Vcl

12

14

Vla

38

14

Vla18

38

SP ord

Vla12

38 Vla

38

12

Vln I

ord SP

Vln II

ordSP

Vln I

Vcl

14

12

14

12

VcI

ord SPVcl

Vcl14

12

ordXSP

Vla38

12

XSP ord

Vla

Vln I

38

14

XSP ordVln I

Vln II ord XSP Vln II

12

14

Lwithout mute

without mute

without mute

without mute

’

’

’

’

step

3/4CUE

step

1 1/4CUE

step

1 1/2CUE

continuous

1 1/3CUE

Vcl

step

3/4

Vln I

step

1 1/4

Vln I

continuous

1 1/4

Vln I

step

1 1/4

Vln II

step

1 1/3

Vln II

step

1 1/3

Vla

step

1 1/2

Vla

continuous

1 1/2

Vla

step

1 1/2 Vln II

step

1 1/3

Vcl

step

3/4

Vcl

continuous

3/4

1 1/3

12

VcI Vcl ord SP

12

14

Vcl58

38

Vla58

38

Vcl ord XSP Vln II SP XSP

38

12

SP STVla Vla Vla SP ST

Vln I

STSP

Vla14

12 Vln I

SPST

Vln I

38

58

Vln II38

12 Vln II

ordXSP

Vln II

38

58

Vln II

XSP ord

Vln II

12

34

12

34

Vln II

SP XSP

Vln II

Vcl58

12

SPXSP

Vcl SPordVcl

SPXSPVln I

Vcl58

12

Vln I Vln I12

34 Vln I

12

34

ordSP

Vla

12

58

12

58

ord SPVla

ordSP

Vla Vla

M

’

’

’

’

’

’

’

’

step

3/4CUE

Vcl

step

3/4

Vcl

continuous

3/4

Vcl

step

3/4

step

1 1/4CUE

continuous

3/4CUE

Vln I

step

3/4

Vln I

step

3/4

Vla

continuous

1 1/4

Vla

step

1 1/4

Vla

continuous

1 1/4

step

1 1/3CUE

Vla

continuous

1 1/3

Vla

step

1 1/3

Vla

continuous

1 1/3Vln I

continuous

3/4

13

Vln II

12

34

XSP SPVcl

12

34

XSPSPVla

Vla78

58

XSPord

Vcl78

58

Vln I88

34

Vcl78

58

SP XSP

Vcl

ord SP

Vln I Vln I12

34

58

78

XSP SPVla Vla

8va 8va

8va

Vln I

Vcl Vla34

58

ord SP

Vcl

XSP SP

VclVla

Vla

34

88

Vcl Vcl SP XSP

Vln II

SP XSP

SPXSP

34

88

Vla XSP ord

58

78

Vln II

58

34

Vln I ord SP Vln II

XSP ord

Vln II ordXSPVln I12

34

8va

Vln I Vln II88

34

58

78

XSPSPVln I Vln II

N

’

’

’

’

Vcl

continuous

4/5

Vcl

step

4/5

Vcl

continuous

4/5

Vln I

step

4/5

step

4/5CUE

continuous

1CUE

continuous

4/5CUE

Vln I

continuous

4/5

Vln I

continuous

4/5

Vln II

step

1

Vln II

continuous

1

Vln II

step

1

14

Vln II78

58

8va

Vcl XSP ord

78

88

Vln II

58

78

Vln II Vcl

XSPord

XSPord

XSPord

8va

Vln II

78

88

Vcl XSPord

8va

Vln I

58

78

Vla ord XSP

78

88

Vln I XSPord Vla Vln I88

78 Vla XSP SP

Vla

Vcl

XSP SP

Vcl XSPordVln II88

78 Vln II

Vln I

Vcl78

34

XSPSP

Vln I88

78

Vln I78

58 Vla

8va

Vla

ord XSP34

78

O

step

1 1/2CUE

step

1 1/4CUEVla

continuous

1 1/2

Vla

step

1 1/2 Vln I

continuous

1 1/4

Vln I

step

1 1/4

Vln I

step

1 1/4vVla

continuous

1 1/2

P

15

8va

Vla

8va

XSPord

ord

Vla Vla Vla

78

88

Vln I88

78

78

34

Vln I

8va

Vln I

SP XSP

Vcl78

34

34

78

Vcl XSP Vcl

XSPord

Vcl

Vln II

34

78

Vln II XSP SP Vln II

ord XSP

Vla XSPSP

34

88

78

88

Vla

SP XSP

78

88

Vcl Vcl88

34

XSPSP

Vln II XSPSP

Vln I XSPSP

Vln II88

78 Vln II

XSP SP

Vln I

XSP SP

Vln I8va

’

’

’

’

step

2/3CUE

step

1CUE

Vcl

continuous

2/3

Vcl

continuous

2/3

Vcl

continuous

2/3 Vln II

continuous

1

Vln II

continuous

1

Vln II

continuous

1

16

Vcl

34

88

34

88

Vla

78

88

SP XSP SP XSP

SP XSP78

88

78

88

Vcl

Vla

Vln I XSPSP Vln I

XSP SP

Vln II

XSP SP

Vla Vla

Vln I Vln I Vln IVln I

8va

Vln II88

78 Vln II XSPSP Vcl XSPSP

XSPSP

XSPSP

Vla XSPSP

Vln II

8va

Vln II

Vcl88

78

SP XSP

88

78

88

78

Vcl

Vla

88

34

88

34

Vcl

SP XSP

Vln II

step

1 1/3CUE

step

1 1/2CUE

Vla

continuous

1 1/3

Vla

continuous

1 1/3

Vla

continuous

1 1/3 Vln II

continuous

1 1/2

Vln II

continuous

1 1/2

Vln II

continuous

1 1/2

Q

17

78

88

Vln I

Vln I

XSP SP

Vln I

XSP SP

XSP SP

Vln I

Vln II Vln II XSPSP

78

88

Vln IIXSPSP

Vln I XSPSP

Vln II 88

78

8va

Vcl88

78

78

88

78

88

XSPSP88

78

SP XSP

Vln II

SP XSP

8va

Vla Vla Vla Vla

78

88

78

88

XSPSP88

78

SP XSP

Vcl Vcl

88

78Vln I

Vcl Vcl

Vln I

8va

Vcl VclXSPSP

XSPSP

Vln II

XSPSPVla

Vcl

78

88 XSP SP

Vln I

8va

Vln II Vln II 88

78

XSP SP78

88

Vla Vla Vla 88

78