UFPr Arts Department
Electronic Musicological Review
Vol. 6 / March 2001
EMR
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5. Nationally Specific Features of Melodies
The integral regularities that carry information of national belonging are
discussed in this section. The term "integral" means that these
regularities manifest themselves in the sample as a whole, but for any specific
melody their manifestation may not be so evident.
On average, Russian melodies are less recitative than French or American
Some special experiments have shown that
these differences are significant in the sense that they exceed substantially
the admissible spread due to random factors. The value of this spread can be
estimated from experimental data obtained from other samples. For the sample of
Soviet songs (216 melodies, N=16905) the recitativity factor (
) is equal to 0.144, for the sample of "Day of
Victory" songs (songs about the Second World War, 58 melodies, N=5126)
=0.169, for
samples of the Russian and French folk songs twice decreased randomly the
recitativity factors are
=0.147 and
=0.22, respectively. It can
be easily seen that the range of 0.14 – 0.17 is characteristic just for
the Russian songs and their variations are determined by the genre and thematic
differences, size of the sample, and some other factors.s
A significant difference is also observed for the mean lengths of maximum
recitative chains:
The effect of asymmetry of
the pitch line displayed in Russian songs to a larger extent than that in the
French or American is thus expressed:
This means that, on average, Russian melodies are characterized by a steeper
jump-like rise and by a smoother gamma-like drop of the pitch line. The
relative fraction of large jumps with values
in the Russian samples is
2–3 times larger than that in the French and American samples. For
example,
(the upwards octave) is
equal to 28 (for
), 22
and 10 (
); similarly,
is equal to 29
(for
), 19 (
) , and 12 (
). When comparing
these values one should take into account the difference in numbers of
melodies. These specific features impart to Russian melodies their distinctive
emotional color.
Among other features, we note the following. Absolutely symmetric
saw-like melodic lines are atypical of Russian melodies, admissible for
American and ordinary for French melodies as is seen from examples shown in
Table 4 below:
Table 4
| Chain ±
|
|
|
|
| (1– +1+
–) (1– +1+ –)
|
16
|
4
|
0
|
| (2+
–2– +) (2+ –2– +)
|
8
|
4
|
0
|
| (2–
–2++) (2– –2+ +)
|
11
|
2
|
0
|
| (3–
–3+ +) (3– –3+ +)
|
6
|
0
|
0
|
Repeating elements of the inner structure in Russian melodies are
more variative than in French and American melodies. An alternate
meter is rather typical for Russian melodies (occurred in approximately 20%
of cases), is less characteristic for French (11.4%) and practically absent in
American melodies. Significant differences between samples are also observed
both in the initial and final stages of the melody. For example, elements
3– – and 4 + – occur at the final stages of
melodies in the Russian sample (15 and 17 cases).
An important characteristic of each melody is the maximum repetition length
(in terms of IS
–representation). A large value of
suggests both little
variation of individual structural elements of the melody and the simplicity of
its composition (very often the melody is composed by the scheme XX
where X is the repeated fragment of the length
).
As an indicator of the sample "saturation" by long repetitions we
selected the following: the ratio between the number of melodies containing
repetitions with the length of no less than 15 elements to the total number of
melodies in the sample. The proportion of melodies with such long repetitions
is 11% for the Russian sample, 17.5%, for the French sample, and 20% for the
American sample.
6. Nationally Specific Intonation Fragments
As a first step, we average the chains forming complements
,
, and
, i.e. the unique
l–grams represented only in one of the samples (
,
, or
). Secondly, we consider the
chains from the intersection 
having the
"contrast" property, i.e. l-grams represented mainly in one of
the samples but admissible in the other samples.. According to their
predominance in
,
, or
, these chains are divided
into subsets
,
and
.
When forming complements we confined ourselves to the values l=3 and
4, since the complements of the first and second orders are nearly empty
and the complements of the 
and
higher orders consist already of l–grams with frequency
. Chains with
and
but presented in one melody
are eliminated from
and
. When electing the contrast
chains two constraints were applied:
1)
;
2) the relative occurrence frequency in the sample, where it dominates,
should exceed the sum of its relative frequencies in the two other samples.
Taking into account these limitations, the subsets
(l=3) include
44 chains for
, 84 for
, and 106 for
. The
3–grams selected identify unambiguously 56% of all the
melodies in
, 70% in
, and 76% in
. Sets
are larger:
and
(chains). The learning
samples are overlapped by the unique 4-grams as follows: 84% (for
), 86% (
), and 97% (
). Some examples of chains from
and
for different samples with
the indication of their occurrence frequencies in (
) and
the number of melodies in which they were found (
) are
given in Table 5 below.
Table 5
| l–gram (±)
|
|
|
|
l–gram (±)
|
|
|
|
| 7+ –1–
+1– +
|
R
|
8
|
6
|
2+ +1–
–1– +4+ –
|
R
|
9
|
8
|
| 1– –4+
+2– +
|
R
|
7
|
5
|
3– +2+
–1– +1– +
|
R
|
8
|
6
|
| 0+ –1+
+2– –
|
F
|
21
|
15
|
0+ +0+ –1+
+2– –
|
F
|
15
|
10
|
| 3+ –3–
+0+ –
|
F
|
8
|
8
|
2+ +0+
–1– +1– +
|
F
|
15
|
9
|
| 0+ –2–
–1– +
|
A
|
7
|
6
|
0+ –0+
–0+ +0+ –
|
A
|
8
|
6
|
| 0+ –0+
–0+ –
|
A
|
6
|
4
|
5– +3+
–0+ +1+ –
|
A
|
6
|
4
|
As to the contrast l–grams, it is worth mentioning that their
maximum length is l=3 and they cover 95% of "their"
samples. Some examples of the contrast l–grams are given in Table 6
below (
–type is determined by
maximum
).
Table 6
| l–gram (±)
|
|
|
|
l–gram (±)
|
|
|
|
| (R): 5+ – 1– +
|
58
|
12
|
5
|
R): 0+ + 5+ –1– +
|
20
|
1
|
0
|
| (F): 3+ + 3– –
|
2
|
40
|
0
|
(F):1– +1– +1+
+
|
2
|
20
|
0
|
| (A): 0+ – 0+
–
|
3
|
9
|
38
|
(A): 0+ +2– –1– +
|
1
|
7
|
18
|
An analysis of chains from
and
supports the regularities
mentioned in the preceding section: the presence of large jumps (by 4-7
degrees) in chains from
, recitative motives in
chains from
with rarely occurring metric
combinations "– –" , saw-like steps one fourth upwards and
downwards in chains from
, rare metric combinations
"+++", etc.
Note that the 4 types of sets of informative l–grams
obtained (
,
,
,
) are quite independent. The
independence of
and
of
and
follows from their
definitions and their substantial difference in the threshold values of
frequencies (
in the first case
and 
in the second case). At the
same time,
and
(similarly,
and
) are
partially dependent since the unique or contrast l–gram can keep
this property at the left-hand or right-hand expansion. However, the chains
obtained in such a way are not dominant. A substantial fraction of sets at
l=4 consists of chains which at l=3 did not yet satisfy the
required conditions, i.e. were neither unique nor contrast chains but at
l=4 acquired this property.
Sets of specific l–grams formed for each sample can be used not
only for the classification of unknown melodies but also for finding the
most typical and atypical representatives in each class.
For example, the melody from
with the maximum number of
chains from
can be naturally called
"typically Russian". At the same time, the melody from
with the maximum number of
elements from
can be called "the most
French among Russian melodies". Since sets
,
,
,
are not closely correlated,
we have some relatively independent possibilities for defining the
"typical representative". The most typical representative
should be considered as the representative, which satisfies the maximum number
of criteria. Figure II shows examples of the most typical
representatives for each sample with the indication of some informative
fragments. Each melody satisfies at least two criteria.
Figure II: Examples of the most typical
representatives for each sample
Conclusion
The problem of differentiation of song melodies by their
"national" belonging with the use of interval-metric characteristics
was considered. An easily interpreted system of quantitative characteristics is
proposed that enables the formulation of the problem in terms of repetitions of
national-specific features intrinsic to samples of the Russian, French, and
American melodies, . The most informative (in terms of classification)
fragments of melodies were found. These are the unique chains of minimum length
represented only in one sample in the maximum possible number of melodies. The
"contrast" chains dominating in one of the samples but admissible in
other samples have lower differentiating properties.
A method of search for informative features in the problem of
differentiation of melodies by their "nationality" is proposed. The
most and least typical representatives of each class were found. The
most typical representatives can be considered as centers of clusterization of
melodies. The presence of such a clusterization displayed in the form of
the unconscious adaptation was studied earlier (Bakhmutova, Gusev, Titkova, 1997).
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