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MAGAZINE - APRIL 2018

must be interpreted according to the conventions govern-

ing a particular style.

Comparable to the use of “shorthand” signs for ornaments

is the system of placing Arabic numerals beneath a bass

line in keyboard music of the 17th and 18th centuries. A

numeral, or “figure,” signifies a harmonic (i.e., a vertical)

interval; thus, a “6” indicates a note six degrees of the

scale above a given bass note (A above C, for example). It

is in itself an imprecise measurement, specifying neither

whether the interval is major or minor nor in which octave

figures are governed by the same prevailing key signa-

ture as notes on the staff and can, like notes, carry their

own accidentals. They are thus not an independent type

of notation but a hybrid representation of interval/pitch

that works in conjunction with staff notation. Its purpose

is to indicate the harmonies implied by a bass line (even

absence of figuring has a meaning) while at the same time

leaving the player free to choose the precise notes to be

played. The systems of letters and figures used by jazz

musicians have this same imprecision; they are less de-

pendent upon conjunction with staff notation but lack clear

rhythmic significance unless allied to staff notation in at

least a simplified form. They operate by defining a harmo-

ny in relation to the tonic chord (the chord built on the key

note, or tonic) rather than by interval or pitch.

Transition to modern staff notation

In 16th-century manuscripts and, later, in printed music,

the diamond-headed notes became rounded. Ligatures

were used less often in the later 15th century. The princi-

ples of perfection and imperfection gave way to the mod-

ern relationship of 2 to 1 between adjacent note values,

with the dot adding an extra half value to give a 3 to 1

relationship.

Shorter note values were also introduced, and the old,

longer ones became obsolete. Yet, because of a paradox-

ical survival from 15th-century practice, slow music has

tended to be written in short values (e.g., Beethoven’s

slow movements) and fast music in long values.

The bar line as a measure of metre arose first in 15th-cen-

tury tablatures (notation showing playing position rather

than pitch, as for lute). Barring entered staff notation in the

17th century, but regularly spaced barring became a prac-

tice only in the 18th century. Separate tempo indications,

arising first in the 17th century, were verbally expressed;

for example, adagio, largo, presto. The range of these

terms greatly increased during the 18th and 19th centuries,

and the metronome mark, an absolute indication of tempo,

has never superseded them since its arrival in Beethoven’s

day. The bulk of the shorthand devices emerged during

the 17th century, figured bass early in the century, and the

majority of ornamental signs later. Indications for loud

and soft arose early in the century, expressed as words

(forte, mezzo forte, piano) and later as abbreviations (f,

mf, p). Graphic signs for dynamic and attack (staccato dot,

crescendo mark, for example, and also phrase marking)

appeared in the 18th century. A great proliferation of dy-

namic instructions and signs occurred in the late 19th and

early 20th centuries.

Adaptation To Non-European Music

Notations evolve with the musical styles they serve, and

they reflect the underlying aesthetics of their own cultures.

Thus, staff notation is ill-equipped to cope with non-West-

ern scales and tunings, with music to which the idea of the

“note” (a stable, sustained pitch) is foreign, or with music

whose subtlety lies as much in delicate gradations of

volume or timbre as in pitch and rhythm. Ethnomusicol-

ogists have developed a range of supplementary sym-

bols—e.g., for notes of uncertain pitch, glissandi (slides),

slight lengthening of a value, half-voiced notes, and other

sounds. They have also experimented with staves of fewer

or more lines. The Western system of proportional note

values (for example, quarter note = half of a half note)

does not easily cope with fine fluctuations of value; in-

stead, constant changes of metronome tempo mark may be

necessary. Among the most complex uses of staff notation

in ethnomusicology are the transcriptions of Serbo-Croa-

tian and Romanian folk song by Hungarian composer Béla

Bartók. Other transcribers have used graph paper to draw

a curve of pitch against time. Many significant mechanical

methods of transcription have been devised. The two most

notable are the melograph, invented by ethnomusicologist

Charles Seeger, which traces a pitch/time graph immedi-

ately above a volume/time graph, and a device developed

by Dahlbeck, which produces two similar graphs by

means of a ray tube. These methods can reveal a level of

interpretation by the performer that aural transcription into

staff notation fails to bring out.

Other Systems Of Notation

Written notations are to be found in the musical cultures of

the Far East, Southeast Asia, South Asia, the Middle East,

and the West. Early examples survive from Ancient Egypt

and Greece. Notation may be classified into two broad

categories: phonetic symbols—words, syllables, abbrevi-

ations of these, letters, and numbers; and graphic signs—

accentual signs for the rise and fall of the voice (devel-

oping into neumelike “ecphonetic” signs), curves, lines,

dots, and other symbols, perhaps originally depicting hand

signs, and neumes. Symbols in both categories may denote

simple sounds or stand for groups of successive sounds. In

the West they are read in lines from left to right, whereas