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 {short description of image} (similarly, {short description of image} {short description of image}). 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

{short description of image}

f

{short description of image}

f

{short description of image}

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 {short description of image} is 38, but at larger values of{short description of image} not all the alphabet elements are realized.

4.2. The most used elements are gamma-like ({short description of image}=1) and recitative ({short description of image}=0), the latter corresponding to the sound repetition at the same pitch. As a rule, frequencies of elements with {short description of image} > 1 decrease with the increase in{short description of image}. 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 ({short description of image}=1), the most frequent elements in all orderings are (1 – +) and (1 – –) corresponding to the descending motion of the pitch line (sign "–" at the {short description of image} 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 {short description of image} > 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 ({short description of image}="+"). The pitch jumps with {short description of image} > 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 ({short description of image}="–"). 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 {short description of image}, {short description of image}, {short description of image} 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 {short description of image} positions of IS – code).

Let {short description of image} be an arbitrary bigram and {short description of image} 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 {short description of image} or {short description of image} leads to the frequency increase with all remaining components of IS – codes being unchanged. Conversely, the increase in either {short description of image} or {short description of image} is usually connected with the decrease in the frequency. This regularity does not refer to the transition from {short description of image}=0 to {short description of image}=1 due to high frequency of elements with {short description of image}=1. Table 2 shows the influence of the {short description of image} factor on frequencies of corresponding bigrams.

 

Table 2: The influence of change of {short description of image} 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 {short description of image} factor is reduced to, all other conditions being equal, that usually the bigrams with the alternation of signs of {short description of image} 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 {short description of image} 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 {short description of image}, as a rule {short description of image}> {short description of image}>{short description of image}. 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 {short description of image} 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: {short description of image} , {short description of image} , {short description of image} , {short description of image} .

The second factor is more rigid than the first especially at small values of{short description of image}. 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 {short description of image}) there is none with {short description of image}( – –) in all three orderings. Additionally, there are only four bigrams with {short description of image}( + +) in the Russian sample, as many as that in the French sample, and two in the American sample. The most frequent bigram with {short description of image}( – –) 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 {short description of image} and F(2 – + 3 + –)=18 < F (2 – + 2 + –)=67 for {short description of image}. This unbalance suggests the need to include the bigram 2 – + 3 + – into contrast bigrams.

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