UFPr Arts Department
Electronic Musicological Review
Vol. 6 / March 2001

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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 {short description of image} 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 ({short description of image}) is equal to 0.144, for the sample of "Day of Victory" songs (songs about the Second World War, 58 melodies, N=5126) {short description of image} =0.169, for samples of the Russian and French folk songs twice decreased randomly the recitativity factors are {short description of image}=0.147 and {short description of image}=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: {short description of image} 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: {short description of image}

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 {short description of image} in the Russian samples is 2–3 times larger than that in the French and American samples. For example, {short description of image} (the upwards octave) is equal to 28 (for {short description of image}), 22 {short description of image} and 10 ({short description of image}); similarly, {short description of image} is equal to 29 (for{short description of image}), 19 ({short description of image}) , and 12 ({short description of image}). 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 {short description of image} (in terms of IS –representation). A large value of {short description of image} 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 {short description of image}).

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{short description of image}, {short description of image}, and {short description of image}, i.e. the unique l–grams represented only in one of the samples ({short description of image},{short description of image}, or {short description of image}). Secondly, we consider the chains from the intersection {short description of image} 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 {short description of image},{short description of image}, or {short description of image}, these chains are divided into subsets{short description of image},{short description of image} and{short description of image}.

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{short description of image}. Chains with {short description of image} and {short description of image} but presented in one melody are eliminated from {short description of image} and {short description of image} . When electing the contrast chains two constraints were applied:

1) {short description of image};

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 {short description of image}(l=3) include 44 chains for{short description of image}, 84 for{short description of image}, and 106 for{short description of image}. The 3–grams selected identify unambiguously 56% of all the melodies in {short description of image}, 70% in{short description of image}, and 76% in{short description of image}. Sets {short description of image} are larger: {short description of image} {short description of image} and {short description of image} (chains). The learning samples are overlapped by the unique 4-grams as follows: 84% (for{short description of image}), 86% ({short description of image}), and 97% ({short description of image}). Some examples of chains from {short description of image} and {short description of image} for different samples with the indication of their occurrence frequencies in ({short description of image}) and the number of melodies in which they were found ({short description of image}) 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 ({short description of image}–type is determined by maximum {short description of image}).

 

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 {short description of image} and {short description of image} supports the regularities mentioned in the preceding section: the presence of large jumps (by 4-7 degrees) in chains from {short description of image}, recitative motives in chains from {short description of image} with rarely occurring metric combinations "– –" , saw-like steps one fourth upwards and downwards in chains from {short description of image}, rare metric combinations "+++", etc.

Note that the 4 types of sets of informative l–grams obtained ({short description of image}, {short description of image},{short description of image}, {short description of image}) are quite independent. The independence of {short description of image} and {short description of image} of {short description of image} and {short description of image} 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, {short description of image} and{short description of image} (similarly, {short description of image} and{short description of image}) 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 {short description of image} with the maximum number of chains from {short description of image} can be naturally called "typically Russian". At the same time, the melody from {short description of image} with the maximum number of elements from {short description of image} can be called "the most French among Russian melodies". Since sets {short description of image}, {short description of image}, {short description of image}, {short description of image} 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 2

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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