MUSICOLOGISTS have long struggled to find underlying structures in human
music. The ancient Greeks dreamt of a rigorous mathematical science of melody
that would emphasise the rationality of human culture, and also reveal its
diversity. Sadly, progress towards this ideal has been slow. But in 1975,
Denys Parsons, a scientist then at the British Library, achieved a significant
breakthrough. He devised a way of describing a melody simply by its ‘pitch
profile’ – the pattern formed by the sequence of steps between each note
in turn. Our research, building on Parsons’ work, suggests that this pattern
can distinguish forms of music from different cultures.
Parsons’ Directory of Tunes and Musical Themes contains the pitch profiles,
recorded as ‘up’ (a rise in pitch), ‘down’ (a descent in pitch) or ‘repeat’
(no change in pitch), of more than 10 000 classical themes and nearly 4000
popular tunes. He then grouped those melodies with common profiles, enabling
a reader to find quickly the title, composer or source of the particular
tune in mind.
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His classification revealed something unexpected. In a sample of more
than 7000 classical themes, he found an intriguing pattern: in the melodies
in his sample, the most common initial profile is ‘up-up’ – that is, the
preferred pitch profile is a rising interval from the first to the second
note, and from the second note to the third. The next most popular is ‘up-down’;
the least popular is ‘down-repeat’.
Parsons enlarged his sample to include a further 3005 classical melodies
and 3763 popular songs. For each sample he ranked the nine possible pitch
profiles, for the first three notes, in order of frequency. With the opening
note marked with an asterisk, the order was: *UU, *UD, *DU, *DD, *RR, *RU,
*UR, *RD, *DR Parsons announced his discovery in the New ÐÓ°ÉÔ´´ on 24
March 1977, and wondered what musicologists would make of it. Until recently,
the answer would have been ‘very little’. Although his directory has received
some measure of acceptance, no one has seriously responded to the issues
he raised. My colleagues and I at the University of New South Wales have
accepted the challenge, and have come up with some interesting results.
We first verified his findings on a much larger sample of Handel’s work.
Our analysis shows the marked preference for ‘up’ at the first interval,
between the first and second notes of Handel’s melodies. It also seems to
suggest the lack of any marked preferences for either ‘up’ or ‘down’ thereafter,
although both are consistently preferred to ‘repeat’. We analysed Parsons’
sample of the works of other major composers, such as Mozart and Beethoven,
with similar results.
Yet while these studies confirm Parsons’ original observations, there
appears to be a good deal of personal variation in the preferences of different
composers. This suggests the possibility of using this approach to identify
and quantify precise characteristics in a composer’s own melodic preferences
– something which Parsons has begun to explore. Science might then at last
obtain an objective measure of what the ancient Greek theorists called ‘ethos’
– the social or individual character recognised in typical patterns of pitchor
rhythm.
In its present form at least, Parsons’ law holds mainly for the first,
and sometimes the second, intervals of European melody. The initial direction
of the melody, the step from the first note to the second, is statistically
the most significant. Parsons has recently found that his test, if extended
to the third interval, also reveals a marked preference or the ‘up’ profiles,
particularly *UUU, but other workers have yet to confirm the generality
of this finding.
Even so, his original discovery is intriguing. Why the marked significance
of the first note in a melody? My colleague, Jenny Nevile, has suggested
that it may be connected with the way we perceive sounds. Musicologists
have long known that if you remove the initial articulation of a vocal or
instrumental, so that listener hears only the after-sound, they find it
very difficult, sometimes impossible, to distinguish one voice or instrument
from another. In other words, the recognisable timbre of different voices
and instruments is mainly conveyed in the initial speaking, the opening
of the sounds. I suspect that both Parsons’ finding and this aural significance
of the first note are part of the same phenomenon: the role of the initial
sounding, in the direction of its pitch as well as timbre, in enabling us
to identify a tune.
Stimulated by these speculations, we wondered whether Parsons’ law held
across history, and across cultures. It could be applied to the most primitive
form of musical notation developed in modern Europe – the neumes. These
signs arose late in the first millennium, as an aide-memoire for the singing
of liturgical chants. The neumes record only the general direction of a
melody, but this is the very feature needed for Parsons’ test.
Our analysis of the sacred chants in a modern collection, the Liber
Usualis, provides dramatic confirmation of Parsons’ law (see Figure 1).
For the first two intervals of the chant, the frequency of ‘up-up’ is almost
as high as that for modern melody. This suggests that Parsons’ test has
revealed not merely an accidental feature of modern melody, but a fundamental
tendency of European intonation. We think that this is one of the most important
discoveries ever made in the science of melody.
We tried to confirm this finding by looking at 29 melodies preserved
in ancient Greek notation – but this sadly limited sample is too small to
provide statistically significant data. Yet from what we have, it looks
as though the melodies of the ancient Greeks have more in common with medieval
chant than they do with modern melody. Further research might shed some
light on the much debated origin of Christian chant. The prevailing view
today is that Christian chant is largely Jewish in origin, rather than Greek.
But would scholars revise their opinions if it were discovered that the
oldest examples of traditional or pre-Christian Jewish chant do not share
the preferred pitch profile of ‘up-up’?
Parsons’ research raised other important issues: the relationship of
Western music with the music of other cultures, and even the origins of
human music in the natural world. The further we move from the artificial
world of modern musical notation, the nearer we approach the music of nature
in which it is often impossible to say where exactly a melody begins or
ends, or whether it is moving in discernible ‘intervals’ or even if a cry
or vocalisation is a melody at all. Parsons’ test might not fit all such
situations, but we can validly apply it to the songs of birds that sing
in clearly defined intervals, such as the cuckoo with its insistent ‘up-down’
call.
We have begun to explore the universality of Parsons’ law in human cultures,
by studying the melodies of non-European cultures, or those of western subcultures
that have retained some independence from the mainstream. We find that Parsons’
test does reveal profound differences. Take, for example, the preferred
pitch profiles of Scottish Gaelic songs, derived from three collections
made at different times by three independent researchers (see Figure 2).
Two of these collections show the marked European preference for the initial
rising contour, but the distribution of frequencies for other intervals
is radically different from Parsons’ European norm (see Figure 3). Similarly,
an extensive and reliable collection of Romanian folk music yields an exceptionally
high level of the initial rising profile, together with a marked preference
for the profiles such as ‘repeat-up’ and ‘up-repeat’ which are very low
in Parsons’ European scale.
We need one final test to demonstrate the reliability of Parsons’ law:
can his test produce non-European pitch profiles which are consistently
different from the European norm? Without this test, it might be possible
to argue that Parsons’ findings are culture-dependent – like some intelligence
tests that might be reliable for the society that invented them but unreliable
for other social groups.
We chose to compare the pitch profiles of the songs collected by Frances
Densmore from the remnants of four North American Indian tribes, during
the first third of this century. From her observations we derived Figure
4, which leaves no doubt that Parsons’ test can meet this final criterion
of a general comparative method. It reveals that the traditional melodies
in this part of the world favoured initial pitch contours radically different
from those that have prevailed in Europe. The initial contour of ‘up-up’
is one of the least common in American Indian songs, whereas the pattern
of ‘repeat-repeat’ – fifth in the European list of preferences – is far
and away the most preferred, being found in almost two thirds of the Menominee
songs.
A similar pattern of preferences emerges from a recent collection of
84 Peyote songs, melodies coming not from a tribal society but a religious
cult that has developed among various surviving groups of North American
Indians. Our evidence suggests that the singers of this new cult preserve
the characteristic melodic contour of their tribal ancestors.
Songs of the Australian Aborigines show an even higher level of the
‘repeat-repeat’ contour in our analysis of 218 songs of the Pintupi of central
Australia (see Figure 5). But what is the true significance of these comparisons?
Are they reliable indices of genuine cultural differences?
To be sure, researchers will need to evaluate Parsons’ test further,
and possibly introduce some refinements. But his discovery suggests many
exciting possibilities. It could provide a simple way of plotting the distribution
of ‘horizontal’ melodies, those with a more or less stable pitch, popular
among the native people of North America, Australia and elsewhere – as shown,
for example, by fragments from an ancient song of Hawaii and one in the
Babylonian liturgy.
These are quite different from another archaic and widespread kind,
which the late Curt Sachs called, in his book The Wellsprings of Music,
‘tumbling strains’. This sort of singing takes the form of a leap to a high
note followed by descent to a lower level. The examples that follow are
from music by the Zuni of New Mexico, Australian Aborigines, and the Watusi
of Africa.
Parsons’ data show no significant preference for either form in the
beginnings of European melodies, but the preponderance of horizontal tunes
is strongly marked in the music of North American Indians, and some Hispanic,
Celtic and Gaelic songs. The non-Gaelic songs of Britain show the reverse
situation, with the ‘down-down’ more common that ‘repeat-repeat’. This could
be a significant discriminator in ethno-musicological and bioacoustic classification.
For instance, in two small samples of Irish songs, the ‘repeat-repeat’ profile
was the one most preferred by Gaelic Irish singers, but was among the least
preferred by Anglo-Irish singers. In the classical music of Japan and Korea,
the most common pitch profile seems to be ‘up-down’, a preference we have
not yet found anywhere else. So the comparative study of pitch profiles
could provide a way of mapping the geography of human song, and perhaps
the song of other animals too.
Dr Graham Pont is senior lecturer in the Centre for Liberal and General
Studies at the University of New South Wales. His co-workers in the research
reported here are Jenny Nevile, a doctoral student in the Department of
Music, and Dr Nigel Nettheim, a research fellow supported by the Australian
Research Council. This research was funded by the University of New South
Wales.
Further reading: Denys Parsons, The Directory of Tunes and Musical Themes,
published by Spencer Brown, Cambridge, 1975. Curt Sachs, edited by Jaap
Kunst, The Wellsprings of Music, Martinus Nijhoff, The Hague, 1962.