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
Vln II
STXSP
08
78
18
88
Vln II
ST XSP
08
34
Vln I
Vln II Vln II
18
78
Vln II
18
78
STXSP
Vln I
18
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
88
12
88
08
58
08
12
08
58
08
34
SP XST
SP XST
ST XSP
ST XSPST XSP
SP XST
ST XSP
14
88Vla Vla SPXST Vla SPXST
Vln I SP XST
Vcl XSP STVcl
Vla Vla
Vln II
14
88Vln I 3
888Vln I
Vla
SP XST
Vla
Vln I SP XSTVln I
Vcl08
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
’
’
’
’
4step
1 1/4CUE
Vcl
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
’
’
’
’
’
’
’
’
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