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The term notation refers to any codied or organized system of scripted

characters or

visually perceived communication that represents or implies meaning and is

capable of

eectively transmitting information from one party to another.

Systems of notation designed specically to represent musical performance are

found

around the world and date back at least 2,!! years with each system varying

considerably based upon musical and cultural values and societal progress. The

single

commonality in all musical notational systems is that there is no known society

to have

created one without rst developing a method of linguistic notation

" it is no surprise then

that the pictographic elements, orientation, form, and comprehension in musical

systems

of notation typically resemble the literary systems of their respective societies

and

geographic locations. Though some musical societies, namely #frican and $ative

#merican cultures, have eectively e%isted without written systems of notation,

contrary

cultural values made a method of writing down music essential and inevitable.

#s suggested by the linguistic parallel, musical notation functions rst and

foremost

as a method of communication" it allows the composer or creator to indirectly

transfer

directions to the performers in lieu of oral transmission. &n the form of a score,

musical

notation also allows the musicians to better communicate with each other and

the

conductor 'if necessary( during a performance. e. $otation also functions to

e%pand the

repertoire of performers by either assisting in the process of memorization or in



eliminating the need to memorize altogether. )inally, notation allows for the

preservation

of music for future performances or study and dissolves the necessity of the

intergenerational rote teaching that would otherwise be necessary to allow the

same music to

be accurately performed for any great period of time.

The degree to which any musical notation is specic varies depending on cultural

usage and musical aesthetics. *any of the rst systems of notation, such as the

use of

ekphonetic or neumatic symbols, aorded only appro%imate directions yet still

allowed

for relatively consistent musical performances.2

+ater systems provided general

instruction to the learned and knowledgeable performer, like the aro-ue system

of

gured bass, or allowed the performer to interpret the nonuse of musical

direction to

intuitively make musical decisions as appropriate within the style 'e.g. dynamics,

phrasing, rubato, etc.(. &f there is an observable trend in the degree of notational

specicity from the beginning of musical notation to the present day, it is the

evolution

and accumulation of notational symbols that has allowed the composer to notate

increasingly precise musical directions and to maintain nite control of the

musical

product.

Though concepts in musical notation rst appeared in #sian societies and in

cantillized te%ts of /reek, 0oman, and 1ebrew origins, it is the development and

evolution of the musical notation of estern 3urope that most greatly in4uenced

graphic

music.

The documented musical activities of medieval estern 3urope reside primarily

in

sacred use. The eorts to standardize the 0oman 5atholic *ass and liturgical

practices



by 5harlemagne are considered to be at least partly responsible for the attempts

to notate

chant and sacred music, which had originally been learned by rote. The earliest

known

e%ample dates from about 67! by #urelian of 089me, though it has been

suggested that

collections of notated chants may have been kept in 5harlemagne:s library

several years

earlier.

Two distinct methods of chant notation were rst employed. ;ratorical neumes

were

written above chant te%ts and provided the singer with a basic rising or fallingshape of

pitch on which the te%t was to be sung. # system of twentyone dierent

neumatic

symbols eventually aorded a more comple% vocabulary of pitch contour. # later,

diastematic method placed neumes in relation to an imaginary line of denable

pitch" the

distance of the neumes from the %ed point of reference represented anappro%imate

value of pitch and oered a system that more aptly dened musical content.

)rom this point, innovation in musical notation entered a period of perpetual

evolution as re-uired by musical demands and an increased interest in

specicity,

ob<ectivity, and consistency in performance. y the end of the tenth century, the

imaginary line of the diastematic system became a real one in the score, andmore lines

were eventually added by /uido =:#rezzo and others to create our present

musical sta

of %ed pitch. $eumes became noteheads designating specic pitches on the

sta and

later became responsible for conveying specic rhythm. y the aro-ue era,

articulation, dynamic, and phrase markings became notated as composerswished to



e%press greater musical direction and leave less interpretive consideration to the

performer:s training or intuition.

Though notational innovations slowed and crystallized into an eectively

standardized notational system by the nineteenth century, postromanticcomposers again

began to make ad<ustments in notational practice as necessary to convey the

meaning of

the works, and their individual advancements collectively contributed to the air

of

e%perimentation that permitted further and more drastic departures from

traditional

notation. /ustav *ahler:s music is littered with substantial amounts of written

directions

to the performers and conductor, and though not notation per se, *ahler:s words

were

necessary to convey musical meaning that no notation in use was able to aord.

;ther

earlytwentieth century composers amended e%isting notations to t their needs>

1enry

5owell:s piano music used thick vertical bars that encompassed the range of the

sta to

represent tone clusters" =arius *ilhaud:s +es 5ho8phores '?@?A( eliminated the

redundant lines of the sta and used <ust one line to notate unpitched percussion

instruments7

" #rnold SchBenberg used Cshaped noteheads to denote his use of

Sprechstimme" and the use of -uartertones or microtones by many composershas been

eectively indicated with variations on the traditionallyused sharp and 4at

symbols.

The most profound adaptation of traditional notational symbols was invented by

1enry 5owell in his $ew *usical 0esources '?@!(, a treatise initially conceived

in his

study with 5harles Seeger about a decade earlier Dto rationalize his manner ofplaying the



piano.E F

+ooking to eliminate the Dclumsy e%pedientE of notating asymmetric divisions

of the beat with a numerical notation dictating ratio 'e.g. DE over a triplet(,

5owelldivised a system of distinct notehead shapes to represent various metric

proportions. y

replacing the previous system of notation with noteheads that concisely specify

triplets,

-uintuplets, septuplets, etc., some of the clutter and e%tra notations of a score

could be

eliminated. The following e%amples show the series that 5owell devised and an

e%ample

of the notation in application>



1erbert rGn pioneered the use of computers in graphically notated music scores

in

the midsi%ties, and Stalks and Trees and =rops and 5louds '?@AH( for

percussion, the

nal piece in a trio of solo percussion works of the same year, represents one of

the rst

pieces created by a computer plotter. &n the work, thirteen dierent instruments

or groups of like instruments are chosen by the performer and are each

represented by a

dierent shape of notehead. Sounds are notated spatially in relation to two time

a%es,

with the lower containing dry sounds and the upper, resonant and ringing

sounds. The

DstalksE and DdropsE of the title are notated by noteheads connected to vertical

lines

emerging from the lower and upper time a%es, respectively, and signify single

attacks.

The DtreesE and DcloudsE are single structures of continuous attacks comprised

of

noteheads that converge at a single point on either a%is. The vertical distancefrom each

a%is determines the dynamic intensity of each sound, and the size of each

notehead

determines the timbral intensity or fullness of each sound I a degree of timbral

specicity

that appears to be uni-ue to rGn:s music and notation. The composer:s method

of

notation is one that provides the performer with precise and detailed direction as

to the

performance of each sound in an e%tremely eJcient manner. Though the

dynamic and

timbral intensities are relative and sub<ect to the performer:s choice of

instruments,

implements, and personal preferences, the score can be regarded as being

highly specic

yet simultaneously sub<ective.



+inear form is perhaps the most common method of form. &t is much like the

method of reading traditional notation and probably used so fre-uently because

of its

nearly universal use in reading and comprehending most forms of written

language. &t

was particularly used in the early stages of the graphic notation trend and

especially in

the works of rown, 5age, and )eldman. Knlike in traditional notation, linear form

in

graphic notation does not typically adhere to a pulse. 5hronological progression

in

accordance with a time line is common, as in rGn:s Stalks and Trees and =rops

and

5louds,

2( Spatial or linear methods of notating rhythm are perhaps the most common in

graphically notated works. $otes or symbols are read and performed in relation

to their

position on the page. This system is often used with a time line, as in rGn:s

Stalks and

Trees and =rops and 5louds.

# spatial rhythmic notation

aords the composer varying levels of control over rhythm" using time lines

allows the



composer to place notes outside of a strict rhythmic framework while still

maintaining F!

uncompromising control, while other models permit the composer to establish

consistent

and determinate rhythmic relationships yet allow the performer interpretive

choice in the

e%act duration or placement of each sound.

F( )ree rhythm, that is, an absence of rhythmic direction, is found in most of the

abstract graphic forms but can also be present in combination within other

systems of

rhythmic notation. &n rGn:s Stalks and Trees and =rops and 5louds, the DtreeE

and F?

DcloudE structures are meant to be heard as continuous events of sound" being

that they

are performed by percussion instruments that are unable to truly sustain sound,

it is

necessary for the performer to continually strike the instruments to create this

illusion.

Though the beginning and ending of these structures are strictly specied, aswell as the

specic timing of entrances of the instruments that may make up the events,

both the

number and rhythmic placement of the pulses contained in each tree is

indeterminate,

which aords the performer a considerable amount of freedom in shaping the

te%tural

content of the structures.

0oman 1aubenstock0amati:s Lreise for Sprechstimme and Mercussion consists

of

two similarlysized circles, one containing various abstract shapes and the other



fragments of newsprint, numbers, and even snippets of crossword puzzles. $o

directions

are given other than the instrumentation. &t is not even dictated which of the

circles each

performer is to play, or if they should realize both" however, a circle of shapes

identical

to the one on the left below is also used in 1aubenstock0amati:s =uo '?@H2( for

guitar

and percussion and a similar graphic is used in his atterie '?@A@( for solo

percussion, so

it seems implicit that the percussionist is meant to perform the circle on the left

of the

page and the vocalist the te%ted circle on the right.

2( Merformerselected form allows the performer to choose from specied

substance

that will be included or e%cluded from performance. Larlheinz Stockhausen:s $r.@

Nyklus '?@F@( for solo percussion includes graphic structures that provide this

kind of

option. &n the following e%ample, the performer plays the sta system in the

middle of 77

the page and chooses only one of the bo%es on each side of it to perform,

omitting the

other entirely from the performance. The resulting music is thus one in which the



performer has a degree of compositional input, yet the composer still maintains

a large

amount of creative control.

7( proportional dynamics allow any instrument

to e%plore more eectively its dynamic range and capabilities than traditional

notation

allows. y the mid?@A!:s, this method was so common, it became implied 'or at

least

suggested( that noteheads of varying shapes represented dynamic intensity, and

the

techni-ue continues to be employed in music today. &t may be found in

Stockhausen:s

Nyklus and in numerous other works

( =iastematic dynamics are those that are proportionate to a reference point

and may

be likened to the diastematic method of notating pitch. Though not as common

as the

previous method of notating dynamics, this style is e-ually eective. rGn:s

Stalks and

Trees and =rops and 5louds demonstrates this style with the distance of eachnotehead



from the time a%es representing relative intensity. 5age:s 2H: ?!.FF7E for a

Mercussionist '?@FA( features a similar but dierent method in which each sta

line

'designating dierent families of instruments> *etal, ood, Skin, #u%illiary(represents a supposed mezzoforte dynamic" dots 'single sounds( or lines

'crescendi and

decrescendi( above or below each line specify dynamics that are proportionately

louder

or softer. &n some scores, a marked reference point is not always present, as an

ob<ect:s

physical location on the page can also suJce.

&t is easily observed that the period from ?@F!?@H! represents the era in which

graphic notation was most signicantly and widely used. oth the large number

of

works from this time which contain nontraditional notation as a central concept

and the

development of graphic notation by composers of all nationalities and aesthetic

orientations characterizes this trend as a greatly signicant aspect of musical

history. &t is



worth pondering then the causes of such a trend. Though it would be impossible

to

assign a single motivation, there are a number of philosophies that are likely to

have

contributed.

# nal possible in4uence is the e%periments in percussion music in the ?@! and

7!:s

and the continued e%ploration of percussion in the music ensuing after orld ar

&&.

5omposers, especially Oohn 5age, who was responsible for much of the

percussion music

of the time, must have realized the sonic ambiguity in composing for any type of

percussion instruments. )or e%ample, any two 4utes will be of the same size and

shape

and will produce very comparable sounds" thus music specied for D4ute,E in

most cases,

will sound very similar from one performance to the ne%t. #ny two performances

of music specied for Dgong,E however, will most likely sound vastly dierent. #

gong

may range in size from <ust a few inches to several feet in diameter" it may have

a tonal

pitch, a wide range of harmonics, or even an upward or downward glissando

eect" it

may come in one of dozens of dierent varities from around the world" each with

a

uni-ue sound and timbre. The variety of sounds that a gong may produces is

further

compounded by the huge variety of available mallets, sticks, and implements,

each

capable of making a markedly dierent sound when used even on the same

instrument.

&n short, a composer scoring for Dgong,E or, for that matter, Dbass drum,E

Dcymbals,E

Dtriangle,E etc., cannot aptly dene the e%act sound of the instrument no matter

how



specic sPhe attempts to be. &t is perhaps possible then that the naturally and

unavoidably

indeterminate -uality of scoring for percussion translated to a more sub<ective

and even

aleotoric approach to musical performance in general and one that allowed the

performer

a broader sonic spectrum I even for nonpecussive instruments.

=espite the possible problems in composing with graphic notation, there are a

multitude of benets that arise in its use. *ost signicantly, the sub<ectivity of

graphic

notation often separates innite sound possibilities from nite notational

possibilities.

Mut another way, it e%pands the sonic, musical, and e%tramusical capabilities of

both the

performer and the instrument in a way in which traditional notation 'even with

detailed

instruction from the composer( cannot possibly eectively duplicate, and it

allows the

composer and performer to e%plore a musical spectrum that had been greatly

limited by

the ideals associated with traditionallynotated music. Similarly, graphic notation

allows

for much greater artistic e%pression and liberates the performer from the

constraints of

established performance practice, and, for the rst time, it permits the performer

to ask

-uestions and then provide the answers. /raphic notation thus allows the

performer to

embrace creativity, e%pression, and artistry to a much greater e%tent than music

previously aforded. +astly, these factors provide a more sub<ective and open

listening

e%perience for the astute audience member, an e%perience that may be

perceived A2



according to personal e%periences and aesthetics instead of one implicitly

suggested by

the composer.

+:1istoire du Soldat is a fteenmovement chamber

work for clarinet, bassoon, cornet, trombone, violin, contra bass, percussion,

narrator,

two speakers, and a dancer. &t was composed as a theatre piece that would be

ine%pensive to perform and could be taken on tour. This economic motive,

important especially due to orld ar &, may have been what inspired Stravinsky

to

compose for a multiple percussion setup" it would have been more convenient

and

less e%pensive to use only one percussionist. &n eect, the sole percussionist was

re-uired to take on the role of an entire percussion section.

#nother in4uence on Stravinsky:s decision to use only one percussionist was

<azz. The percussion setup was Stravinsky:s creation, but the sound he was

attempting to emulate was aected by the <azz drum set.

The percussion instrumentation of +:1istoire du Soldat consists of two snare

drums without snares, a bass drum, a eld drum with and without snares,

suspended

cymbal, tambourine, and triangle.

The score

contains Stravinsky:s suggestions to the percussionist, including a setup

diagram.

The recommended setup ')igure 2.?( is in the shape of a diamond, allowing the



drums to be as close together as possible. # compact setup was essential in

allowing

the performer to accurately maneuver around the instruments.

The term #u milleu below the bass

drum sta instructs the performer to play these notes on the middle of the

drumhead

while #u bord, which is indicated ne%t to an additional line above the sta,dictates

that the performer play on the edge of the drumhead. The purpose of this

additional

line is to dierentiate the notes played on the edge from those played in the

center.

These instructions allow the performer to obtain two dierent sounds from one

drum.

&n many ways, The Ling of =enmark is an antipercussion piece. &t is to be

played very softly using only the hand and ngers I no sticks or

mallets...3ven though a tempo runs throughout, no rhythmic coherence



emerges. Sounds simply 4oat out, detached and weightless. ;ne instrument

has no more sonic gravity than another does...They are sounds in many

dierent loudnesses, but they are being heard from dierent distances. The

gong is really forte but is heard from the distance of fty yards. &t sounds as softas the little bell si% inches from your ear. *irages of distance appear and

evaporate again into music. &t is like rain or the sound of rain. These illusions

come from )eldman:s love of the pulsating but rhythmically directionless

canvases of *ark 0othko and other #merican #bstract 3%pressionists.

The score presents multiple problems to the performer> he must interpret the

grid

and its conse-uences on rhythm and time, translate the symbols contained in

the grid,

and devise an appropriate setup. &n order to interpret the notation illustrated in

)igure 7.?, the performer must refer to the performance notes provided at the

beginning of the score.



The rst problem the performer must solve is the interpretation of the grid.

#lthough the tempo of the piece is strictly structured through the grid, the actual

rhythms to be played are determined by the performer. 3ach bo% in the score

represents a metronome beat at a marking between AA and @2. The second

instruction

in the performance notes indicates that within the boundaries of each bo% the

performer has freedom to determine the se-uence of sounds and rhythm.

)eldman did not include an instrumentation list or a suggested setup in the

performance notes, so it is up to the discretion of the performer to choose the

instruments that will provide the registers of sounds. Throughout the score the

performer will nd instances of specically notated instrument groups, which will

help her in the determination of the complete setup.



Qtwo highregistered sounds, seven middleregistered sounds, and three low

registered

sounds are all performed within the time parameters of one bo%. hile the

duration

of the bo% is controlled, the performer determines the actual rhythms or

placement of

sounds within that time limit.

1ere, )eldman clearly indicated that the

particular sounds within the

bracket must be played on skin instruments. &n order to e%ecute this passage,

the setQup must include a minimum of three drums of three dierent registers.

&annis Cenakis Msappha is a composition for solo percussion, written for

performance by

Sylvio /ualda at the 3nglish ach )estival on *ay 2, ?@HA. The notation is placed

on a grid, although it diers from )eldman:s system in The Ling of =enmark by

maintaining control over rhythm. The unconventional score to Msappha presents



several challenges, including instrumentation choices and interpretation of the

notation.

The only specication that Cenakis assigned to the instrumentation is a

division into categories of membrane 'peau%(, wood 'bois(, and metal 'metau%(.

These specications are further divided into registers of high, medium, and low.

The

performer, therefore, determines the choice of e%act instruments

)igure A.? illustrates the instrument key found in the score. The left column

in each half of the bo%, labeled D0egistre de hauteurs,E indicates the register of

instruments 'highPmediumPlow( and each register is assigned a letter '#)(. The

middle column in each half is labeled D/radations dans les registres,E

designating the

graduation in the registers. These graduations are subdivisions within each

register

and are labeled numerically. The third column, labeled D5at8gorie de timbre ou

de

mat8riau%,E indicates the timbres or instrument suggestions that are assigned to

each

group. The key demonstrates that Cenakis divided the instrumentation, and thus

the

score, into si% main groups, labeled #).

#ccording to )igure A.?, /roup # consists of three high wooden or membrane

instruments, such as bongos or tom toms. /roup consists of three medium



membrane or wooden instruments. /roup 5 re-uires three low membrane

instruments, such as bass drums or #frican congas. The bottom instrument in

/roup

5, labeled DE, could be a bass drum played with a foot pedal in order to alleviateH!

technical diJculties in the latter half of the piece. /roup = indicates three

medium

metallic instruments. /roup 3 consists of one neutral metallic instrument, and

/roup ) indicates three very high or acute metallic instruments. Cenakis

described

the metallic sounds he desired as Dnot tamtams, but rough metal such as

railway lines

and pieces of iron or steel.

;nce the performer has chosen the instruments and has assigned each to a

label, such as #? or #2, she can begin to interpret the notation. The notation of

Msappha relies on the registers of instruments '#)( that Cenakis created. ithin

the

registers, he used a separate horizontal line to indicate each instrument.

#s illustrated in )igure A.2, the rhythmic notation is unconventional.

5onse-uently, even if the use of single horizontal lines 'instead of a traditional

sta(

is familiar to the performer, the method in which Cenakis notated the rhythms

will

not be. The rhythms are indicated by dots, similar to note heads without stems.

The

horizontal lines represent the specic instruments, and the location of the dots

on

specic lines determines the actual points of sound.

This informs the performer that the rst sound should be the



instrument he has chosen as the middle of the medium woodPmembrane group.

The

rhythms in which the dots are e%ecuted are determined by the intersection of the

vertical lines of the grid with the horizontal lines. The vertical lines mark specicpoints in the passage of time, which is represented by the horizontal lines" this

system

diers from how )eldman used his grid in The Ling of =enmark, where the

performer decided the specic rhythms within the boundaries of the vertical

lines.

# metronome set at ?F7 beats per minute will correspond to the vertical lines of

the

/rid.

The performer may wish to use two drums to represent line of /roup 5 I a

large concert bass drum for a deeper tone in the beginning of the piece, and the

pedal

bass drum to assist with e%ecution in the latter portion

&t seems likely that Cenakis created this notational system simply by

notating his piece e%actly as he conceived it> as an organization of points on a

line

intended to represent time.

Merhaps Cenakis, who intended this composition to be a study in rhythm,

simply wanted to devise the notation to represent rhythm in a basic wayRfree

from

the limitations of traditional notation and subdivisions of musical time. This is

especially evident in the fact that the concept of the piece was to consider time

Das a

continuous horizontal line, on which you place dots that correspond to the

attacks of



percussion.

&n utilizing his graphic system of notation,

Cenakis chose to strip away the familiar and allow the performer to concentrate

purely on the rhythmic construction.

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