(similarly,
). Thus, general regularities
can be summarized as follows. UFPr Arts Department
Electronic Musicological Review
Vol. 6 / March 2001
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4. Properties of IS-characteristics Invariant to the National belonging
This section describes some features of IS-characteristics intrinsic
to all three samples. These features concern primarily the alphabet of
IS-codes and the combination of alphabet elements. The alphabet of
IS-codes can be characterized by frequency characteristics of the first
order calculated for each sample and given in Table 1 in order of frequency of
occurrence. It is convenient to use ranks (ordinal numbers of elements in
orderings) to correlate the first approximation of the same elements in
different orderings. The correlation of relative or absolute frequencies (which
is more explicit) multiplied by normalization factors taking into account
differences in lengths of samples provide a more detailed picture. Therefore,
in the comparison of the Russian with the French sample, the first ordering
frequencies should be multiplied by
(similarly,
). Thus, general regularities
can be summarized as follows.
Table 1: The occurrence frequencies of alphabet elements in samples of Russian (N=9197), French (N=18641) and American (N=7779) melodies (3).
|
N |
Russian songs |
French songs |
American songs |
|||||
|
|
f |
|
f |
|
f |
|||
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
||
| 1 |
1 – + |
1699 |
0 + + |
2787 |
0 + + |
1467 |
||
| 2 |
1 – – |
1531 |
1 – – |
2559 |
1 – – |
927 |
||
| 3 |
0 + + |
1035 |
1 – + |
2454 |
1 + – |
920 |
||
| 4 |
1 + – |
793 |
1 + – |
2100 |
1 – + |
887 |
||
| 5 |
1+ + |
721 |
1 + + |
2027 |
0 + – |
739 |
||
| 6 |
2 – + |
531 |
0 + – |
1531 |
1 + + |
625 |
||
| 7 |
0 + – |
461 |
2 + + |
893 |
2 – + |
507 |
||
| 8 |
2 + + |
453 |
2 – + |
853 |
2 + – |
318 |
||
| 9 |
2 + – |
285 |
2 – – |
703 |
2 – – |
305 |
||
| 10 |
3 + – |
282 |
2 + – |
539 |
2 + + |
290 |
||
| 11 |
2 – – |
259 |
3 + – |
484 |
3 + – |
221 |
||
| 12 |
3 – – |
181 |
3 + + |
319 |
3 + + |
92 |
||
| 13 |
4 + – |
172 |
3 – + |
287 |
3 – + |
82 |
||
| 14 |
3 – + |
144 |
3 – – |
218 |
3 – – |
73 |
||
| 15 |
3 + + |
142 |
4 – – |
151 |
4 – + |
63 |
||
| 16 |
5 + – |
102 |
4 – + |
139 |
4 + – |
46 |
||
| 17 |
4 + + |
85 |
4 + + |
139 |
4 – – |
43 |
||
| 18 |
4 – + |
74 |
4 + – |
125 |
5 + – |
43 |
||
| 19 |
4 – – |
65 |
5 + – |
84 |
5 – + |
32 |
||
| 20 |
5 + + |
45 |
5 + + |
66 |
4 + + |
30 |
||
| 21 |
7 + – |
29 |
5 – + |
42 |
5 + + |
22 |
||
| 22 |
7 + + |
28 |
7 – + |
26 |
7 + – |
12 |
||
| 23 |
5 – + |
21 |
7 + + |
22 |
5 – – |
11 |
||
| 24 |
6 + – |
13 |
6 + + |
21 |
7 + + |
10 |
||
| 25 |
6 + + |
10 |
5 – – |
20 |
6 + + |
3 |
||
| 26 |
7 – + |
10 |
7 + – |
19 |
7 – + |
3 |
||
| 27 |
6 – + |
8 |
7 – – |
13 |
6 – + |
2 |
||
| 28 |
5 – – |
7 |
6 + – |
11 |
6 + – |
2 |
||
| 29 |
8 + + |
4 |
6 – + |
5 |
7 – – |
2 |
||
| 30 |
7 – – |
3 |
8 + – |
2 |
8 + – |
1 |
||
| 31 |
8 + – |
2 |
6 – – |
1 |
9 + – |
1 |
||
| 32 |
6 – – |
1 |
||||||
| 33 |
9 + – |
1 |
||||||
4.1. The power of the alphabet of IS –codes that was actually
observed is about 30 elements. Maximum jumps of pitch observed do not exceed 9
degrees, which is natural for the human voice capabilities. The number of
alphabet elements theoretically possible at
is 38, but at larger values
of
not all the alphabet
elements are realized.
4.2. The most used elements are gamma-like (
=1)
and recitative (=0), the latter corresponding
to the sound repetition at the same pitch. As a rule, frequencies of elements
with
> 1 decrease with the
increase in
. Exceptions are observed
mainly in the lower part of the Table (lower frequency) , and they are more
characteristic for Russian melodies. The element (6 – –), which has
abnormally low occurrence frequency in all orderings, could serve as an
example.
4.3. Among gamma-like elements (
=1), the most
frequent elements in all orderings are (1 – +) and (1 – –)
corresponding to the descending motion of the pitch line (sign
"–" at the
position of the code) for
the "second" interval. Since the pitch line has to be balanced for
the melody as a whole (the sum of upwards jumps has to be much the same as the
sum of downwards jumps), jumps with
> 1 are more frequent in
ascending than in descending motion. The more characteristic jump of such type
is (3 + –), whose frequency is much higher than other jumps for all
orderings. In other words, on average, the increase in pitch is sharper than
its decrease, which indicates the "asymmetric" character of pitch
line peaks. "The change of the direction, various curves of melody lines,
more or less intensity of the motion, are of very important expressive value
and play a primary role for producing a certain character of the melody"
(Mazel, Zukkermann, 1967).
4.4. "Metrics" influences mostly on codes 0 + (0 + + occurs approximately twice more frequently than 0 + – in all orderings), 3+ (3 + – occurs more frequently by a factor 1.5 –2.5 than 3 + +), 5 – ( 5 – + occurs 2 – 3 times more frequently that 5 – –).
4.5. Beginnings and endings of texts, which have individual status, i.e. completed thematically or functionally, carry more information in all the language systems. The analysis of the beginning and endings of IS–codes in melodies illustrates this. The alphabet of elements used in the beginning and at the end of melodies are 2/3 of the initial alphabet of about 20 symbols. Frequencies of such a positional use of symbols are much different from frequencies of their use for the melody as a whole.
The following regularities are of general character. The most frequent
initial element in all samples is 0 + + (20 – 30% of melodies have the
recitative beginning). Other initial elements indicate mainly the ascending
motion of the pitch line with the predominance (especially for Russian
melodies) of the transition from the metrically stronger to the metrically
weaker tone (
="+"). The pitch
jumps with
> 5 are practically
absent. The descending motion with a simultaneous increase in the metrical
accent is absolutely non-typical for the beginning of melodies (frequencies of
elements 1 – –, 2 – –, 3 – –, 4 – – are
small). Final elements predominantly correspond to the transition from the
metrically weaker to the stronger tone (
="–"). These are elements like 0 + –, 1
– –, 1 + –, 2 – –, 3 + –, 4 – –, which
form a special kind of ending – metric ending. The descending motion (sign
I="–") dominates especially in French songs. The most frequent
final element in all the samples is 1 – –, which expresses the
"intonation of the sigh" (27% in the Russian sample, 39% in the
American sample, and 47% in the French sample). Ascending motion of the pitch
line with simultaneous decrease in the metric accent is absolutely non-typical
for endings ( practically no elements such as 1 + +, 2 + +, 3 + +, 4 + +,
etc.).
4.6. Frequency characteristics of the 2nd order
,
,
enable one to judge the
matching between elements of the alphabet. The frequency of bigrams is
determined by two main factors: the frequency of one-grams included into the
bigram and the metric relation (the combination of signs at
positions of IS
– code).
Let
be an arbitrary bigram and
be the frequency of its
occurrence in the sample of melodies. The action of the first factor is
evidenced in that as a rule. The decrease in either
or
leads to the frequency
increase with all remaining components of IS – codes being
unchanged. Conversely, the increase in either
or
is usually connected with
the decrease in the frequency. This regularity does not refer to the transition
from
=0 to
=1 due to high frequency of
elements with
=1. Table 2 shows the
influence of the
factor on frequencies of
corresponding bigrams.
Table 2: The influence of change of
on the frequency of bigrams.
| Russian songs |
French songs |
American songs |
|||
| ± |
F(±) |
± |
F(±) |
± |
F(±) |
| 1 – + 1 + – |
151 |
1 – + 1 + – |
414 |
1 – + 1 + – |
154 |
| 1 – + 2 + – |
65 |
1 – + 2 + – |
53 |
1 – + 2 + – |
20 |
| 1 – + 3 + – |
31 |
1 – + 3 + – |
42 |
1 – + 3 + – |
30 |
| 1 – + 4 + – |
64 |
1 – + 4 + – |
14 |
1 – + 4 + – |
5 |
| 1 – + 1 + – |
151 |
1 – + 1 + – |
414 |
1 – + 1 + – |
154 |
| 2 – + 1 + – |
111 |
2 – + 1 + – |
195 |
2 – + 1 + – |
77 |
| 3 – + 1 + – |
15 |
3 – + 1 + – |
23 |
3 – + 1 + – |
10 |
| 4 – + 1 + – |
9 |
4 – + 1 + – |
13 |
4 – + 1 + – |
5 |
In this sample, only two deviations from the above formulated regularity are observed (1 – – 4 + – in the Russian sample, 1 – + 3 + – in the American sample). In the first case, the deviation is quite explicit. The comparison of bigram frequencies 1 – + 4 + – for all three samples provides enough evidence to consider this bigram as a sufficiently informative feature for solving the problem of classification by the national belonging.
The
factor is reduced to, all
other conditions being equal, that usually the bigrams with the alternation of
signs of
have higher
frequencies, which corresponds to the even meter, i.e. 2/4 and 4/4. In the
sample under consideration, the number of songs with such a meter is 60.8%
among Russian songs, 49.2% among French, and 72.9% among American songs. Then
follow the bigrams with coinciding positive signs of
corresponding to a
three-beats meter. The proportion of such melodies amounts to 19.6% for
Russian, 39.4% for French, and 27.1% for American songs. The least frequent
bigrams are the bigrams with negative signs of
.
In other words, when
, as a rule
>
>
.
That is, the most characteristic ("common") combinations are those
with the alteration of the sound strength and the least characteristic are
those with a double decrease in the sound strength; relatively rare are those
combinations with two strong
in succession. In the case
of the speech, this would correspond to two exclamations in succession. Using
conventional musical notation, this would look like the following:
,
,
,
.
The second factor is more rigid than the first especially at small values
of
. In particular, as is seen
from Table 3, among 30 most frequent bigrams (according to the first factor
these are bigrams with small values of
) there is none with
( – –) in all three
orderings. Additionally, there are only four bigrams with
( + +) in the Russian sample,
as many as that in the French sample, and two in the American sample. The most
frequent bigram with
( – –) is in the
Russian sample the bigram 1 – –1 – – (F=44, rank r=44), in
the French sample the same bigram is the most frequent (F=50, r=72) and in the
American sample the most frequent bigram is 0 + – 0 + – (F=38, r=50).
All the above-listed factors define only general trends of the bigram occurrence. In each sample there are a lot of deviations from the standard. We are interested in the deviations not correlated in different samples. It is these deviations that can show the national specificity. For example, the bigram 2 – + 3 + – occurs abnormally often in Russian melodies, which is evidenced as the violation of the first factor (F (2 – + 3 + –)=73 > F (2 – + 2 + –)=25).
Table 3. The most frequent bigrams in melodies of Russian, French, and American folk songs.
|
N |
Russian songs |
French songs |
American songs |
|||
| bigrams |
freq. |
bigrams |
freq. |
bigrams |
freq. |
|
| 1 |
2 |
3 |
4 |
5 |
6 |
7 |
| 1 |
1 – + 1 – – |
798 |
1 – + 1 – – |
1094 |
0 + + 0 + – |
406 |
| 2 |
1 – – 1 – + |
509 |
1 + + 1 + – |
928 |
1 – + 1 – – |
347 |
| 3 |
1 + + 1 + – |
298 |
1 – – 1 – + |
794 |
1 + + 1 + – |
340 |
| 4 |
1 – – 0 + + |
244 |
0 + + 0 + – |
786 |
0 + – 0 + + |
260 |
| 5 |
1 – + 1 – + |
243 |
1 + – 0 + + |
530 |
1 + – 0 + + |
256 |
| 6 |
0 + + 1 – – |
238 |
0 + – 0 + + |
481 |
1 – – 1 – + |
232 |
| 7 |
0 + + 0 + – |
232 |
0 + + 1 – – |
468 |
0 + + 1 – – |
213 |
| 8 |
1 + – 1 – + |
182 |
1 + – 1 + + |
442 |
0 + + 1 + – |
206 |
| 9 |
1 – – 1 + + |
166 |
1 – – 0 + + |
431 |
1 + – 1 – + |
201 |
| 10 |
1 + – 0 + + |
160 |
1 – + 1 + – |
414 |
0 + + 0 + + |
187 |
| 11 |
1 – + 1 + – |
151 |
1 + + 1 – – |
391 |
1 – – 0 + + |
162 |
| 12 |
1 – – 2 – + |
150 |
1 + – 1 – + |
381 |
1 – – 2 – + |
158 |
| 13 |
2 + + 1 – – |
147 |
0 + – 1 – + |
346 |
1 – + 1 + – |
154 |
| 14 |
0 + – 1 – + |
144 |
0 + + 0 + + |
343 |
0 + – 1 – + |
140 |
| 15 |
2 + – 1 – + |
139 |
0 + + 1 + – |
338 |
1 + – 1 + + |
133 |
| 16 |
0 + + 1 + – |
120 |
1 – – 1 + + |
286 |
2 + – 0 + + |
115 |
| 17 |
1 + – 2 – + |
114 |
2 + + 1 – – |
263 |
3 + – 0 + + |
109 |
| 18 |
1 + – 1 + + |
111 |
1 + – 2 – + |
261 |
1 + + 1 – – |
108 |
| 19 |
1 – – 2 + + |
111 |
1 – + 1 – + |
261 |
2 – + 1 – – |
104 |
| 20 |
2 – + 1 + – |
111 |
1 + + 2 – – |
231 |
0 + + 2 + – |
101 |
| 21 |
1 + + 2 – – |
104 |
1 – + 1 + + |
230 |
1 + – 2 – + |
99 |
| 22 |
0 + – 0 + + |
103 |
0 + – 1 + + |
213 |
0 + + 2 – – |
89 |
| 23 |
1 + + 1 – – |
102 |
2 – + 1 + – |
195 |
1 – – 1 + + |
83 |
| 24 |
2 – + 1 – – |
98 |
1 – – 2 – + |
187 |
2 – + 1 + – |
77 |
| 25 |
1 – + 1 + + |
80 |
1 – – 2 + + |
185 |
2 – – 0 + + |
76 |
| 26 |
1 + + 1 – + |
78 |
3 + – 0 + + |
171 |
1 – + 1 – + |
73 |
| 27 |
2 – + 3 + – |
73 |
1 + + 1 + + |
156 |
2 – + 2 + – |
67 |
| 28 |
3 + – 1 – + |
72 |
2 + – 0 + + |
152 |
0 + + 3 + – |
65 |
| 29 |
0 + + 0 + + |
66 |
0 + – 2 + + |
148 |
0 + –1 + + |
61 |
| 30 |
1 – + 2 + – |
65 |
2 – – 0 + + |
140 |
0 + – 2 – + |
60 |
At the same time, in the American and French melodies this bigra m occurs within the normal range and the first factor is not violated (F (2 – + 3 + –)=46 <
F(2 – + 2 + –)=83) for
and F(2 – + 3 +
–)=18 < F (2 – + 2 + –)=67 for
. This unbalance suggests the
need to include the bigram 2 – + 3 + – into contrast bigrams.
