EOL 2: Russian panpipe playing (Velitchkina)
Movement patterns 1

Head

Audio 2
170K .au
The lead (five-part) player starts and the accompanying player joins on the second repetition of the period.

The accompanying parts

The 'deep structure' of the tune manifests itself most directly in the melodic patterns of the accompanying parts (the priduval'nye and the gukal'nye parts, see figure 2). The interest in playing the accompanying parts lies in the rhythmic co-ordination of these parts with the para (the five-pipe set) players. Whatever their concrete rhythmic pattern, the accompanists always accentuate the notes which rhythmically interlock with those of the leader. In other words, their 'strong beat' is out of phase with the rest of the ensemble, except for one or two places in a period when they switch and join the leader on her strong beat. This syncopation is invariably done at the last position of each period, but it can appear at some other positions as well. Audio 2 demonstrates the simplest version of the pattern for the accompanying part played with the lead part.⁽¹⁴⁾ In this case the player chose to syncopate at position 9, in addition to the last position. Figure 4 transcribes Audio 2 transposed to C, providing an easy comparison with the patterns of the other instruments in previous example.

Figure 4
Transcription of Audio 2, transposed to C

While the villagers always recommend learning to play panpipe by starting with the accompanying parts, playing them well is in fact no simpler than playing the lead part. The main difficulty lies in maintaining precise rhythmic pulsation and coordination with the leader. When the lead player starts making the vocal/instrumental counterpoint with herself, clearly marked pulsation may disappear from her part as a point of reference for the accompanists. This added rhythmic complexity, together with the fast tempo, makes the task of the accompanists challenging. The insistence of the villagers on always learning the accompanying parts first can be explained not by the simplicity of playing these parts, but by the close relationships of their patterns to the 'deep structure' of a tune as represented in the rule 1.

Rule 1, when applied to the accompanying part, can generate a number of melodies. According to the recommendations of the village performers, the priduval'nye pattern for Timonia has "to start always in the middle and stop also always in the middle" (the verb "to stop" here refers to the syncopation at the end of each period, the "middle" refers to pipe number 3). Indeed, since the priduval'nye set normally includes pipes 2,3, and 4, the first sound complex (pipes 1,3 and 5, designated by symbol o in the rule 1) is represented by only one pipe (pipe 3, or the 'middle pipe'). The first two positions in the Timonia period are occupied by this sound complex, so the priduval'nye pattern invariably starts with repetition of pipe 3. On the third position of the period, however, one may choose between pipes 2 or 4, both of which belong to the second sound complex. From any of these, at the next position the player returns to pipe 3, etc. Using rule 1 it is easy to generate several versions of the 12-pulse period. The versions of the priduval'nye pattern that the players favour the most are the following two (Audio 3, 4):

||: 3 3 4 3 2 2 3 3 4 3 2 3 :|| Audio 3
||: 3 3 2 3 4 4 3 3 2 3 4 3 :|| Audio 4
	

Although both versions can appear in the part of one player within the same performance, they do not alternate with one another frequently. Usually, a player has a clear preference for one pattern, which she repeats until she becomes tired and wants to reverse the direction of her movements.⁽¹⁵⁾

It seems that an important property of playing the accompanying panpipe part is establishing the pattern of periodic, "pendulum-like" movements, which are performed in an effective, economical and fluent way. Patterns with only two pipes are also possible. For example, if a player wants to reverse her usual pattern, she might use one of the following sequences as an intermediate version (Audio 5, 6):

||: 3 3 2 3 2 2 3 3 2 3 2 3 :|| Audio 5
or
||: 3 3 4 3 4 4 3 3 4 3 4 3 :|| Audio 6

The players clearly avoid versions which change pipes on positions 5 and 6 (i.e., pipe 4 going to pipe 2 and vice versa), although they do not say so explicitly. Thus, all movements between outer pipes (2 and 4 in case of this set) are made only via the middle pipe. In other words, the player's only choices are staying on the same pipe within the same sound complex, or moving to the neighboring pipe when there is a change of the sound complex.

The same rules can be equally applied to the second accompanying part (gukal'nye), which has even less possibility for variation of the basic pattern, since it is usually performed on only two pipes. It shows the basic pattern, common for all players in the ensemble, in its most elementary form (Audio 7):

||: 1 1 0 1 0 0 1 1 0 1 0 1 :|| Audio 7

If the player of this part is using a three-pipe set (pipes 0, 1 and 2)(in this case the set is called big priduval'nye) she may, for example, perform the following version (Audio 8):

||: 1 1 2 1 0 0 1 1 2 1 0 1 :|| Audio 8
		 

In generating the melodic versions, the gukal'nye (second accompanying) part player follows the same rules as the priduval'nye (first accompanying) part, changing only the pipes used from 2-4 to 0-1 or 0-2.

In conclusion, for accompanying parts the deep structure of the Timonia tune (rule 1) may be completed by the transformational rule, that states two possibilities in terms of movements. The accompanying pattern uses two "operators", M and S, where the symbol S stands for "stay on the same pipe" and the symbol M for "move to the next pipe in a row", while the difference between left and right movement is not significant:

(S) S  M  M  M  S  M  S  M  M  M  M  		(2) 

The same rule is illustrated as a diagram of the movements of the performer's head in Figure 5. The numbers in the horizontal line are those of the pipes, while positions of the period are given in the column.

Figure 5
Diagram of head movements of the accompanying part player

In more formal expression,

Np+1=  M (Np)= {(N+1); (N-1)} or
Np+1=  S (Np)= Np       (3)

where N is the number of the pipe played at position p, where p=1,2, ...12.

Rule 3 differs from rules 1 and 2, since it only lists the possibilities for the accompanying part in terms of the choice of pipes, and does not describe the structure of the tune. It accounts for the behavior of the accompanying parts of all other tunes as well. To generate a pattern of the Timonia accompanying part, rule 3 has to be applied in connection with the rules 2 and 1, which specify proportions of this particular tune's period. The value of this formulation of the rule is that, since all tunes are based on alternation of only two sound complexes, it can be applied to the accompanying parts of all tunes and to any number of pipes, while rules 1 and 2 specifically describe only the structure of Timonia.

The five-pipe part

The grammar for the para (five-pipe) part is different from that of the accompanying parts in several aspects. This part has more pipes, and thus more possibilities for variation. In addition to step-wise movement, a para part player uses skip movements to the other pipes in a row, including movements between pipes which belong to the same sound complex (e.g., from 1 to 3, or from 1 to 5). This increases the possibilities of melodic variation to a practically infinite number, and at the same time prevents the application of rule (2) to this part ( because the "stop/move" distinction is not directly related to the deep structure of a tune in this part). The movements of players' heads are important for this part as well, but must be considered with another level of detail. If the movement patterns of the accompanying parts are standard and governed by the same rules for all players, the para (five-pipe) players seem to use rather individual strategies for their performances.

In playing the para part, in addition to establishing the periodicity of the movements, two other cognitive strategies come into play and influence the choice of the pipes. The first one can be called the "melodic considerations", with rules that are more or less applicable to any melody, although they are quite difficult to formulate precisely. For example, a melody (which in this tradition is confined to one period) tends to have an arch form; therefore, it is more likely to start and finish the period with pipe 1 rather than with 3 or 5, although this would still be in accordance with the tune's deep structure.

Another important influence on the strategy of the para part player is the fact that she is carrying out communication with other players in the process of performance. It is especially noticeable when there are two para players in the ensemble, as in the case study example discussed below.

As material for the following analysis, I chose a performance of Timonia, recorded on January 20, 1991, of four women in the village of Plekhovo, among whom two played five-pipe sets (para), one the priduval'nye set and one the gukal'nye set. The session took place in the house of one of the players, and this particular fragment was recorded after hours of choosing and tuning pipes, discussions, teaching and music-making together. Beyond myself, four of my pupils, members of the children's folk group "Veretentse" from Moscow, aged 13-14, participated in this meeting. The village women felt very flattered by the urban children's attention and interest in their music and tried to play exceptionally well. The other village "music experts" and panpipe players to whom I played this recording later, unanimously approved of this performance as a whole, although some had critical comments about one of the players. Overall, it can be taken as a representative example of the traditional manner of playing, done in a near- traditional context and not influenced by the constraints of concert performance.

The recording technique used was similar to the "play-back" method applied by Simha Arom (1976), that enables one to listen to one player "singled out" on the background of the others. However, unlike Arom's design, all players were actually performing together in an ensemble, while each one was recorded on a separate tape-recorder.⁽¹⁶⁾ This made it possible to observe the process of communication between the players which was going on during the performance. These recordings are given in Audio 9 and Audio10 (Two players' parts, recorded at one simultaneous performance by two tape-recorders). Due to technical problems, the first two notes are missing from the recording in Audio 9, but they are heard on the channels of other players.

To analyse the process, I notated the performance in question in its full length (which included 30 repetitions of a period). Figure 6 transcribes the two para parts in traditional European notation.⁽¹⁷⁾

Figure 6

Figure 7
An excerpt from the cipher notation of the two para parts in a Timonia performance on 01.20.1991

The first issue relevant to the discussion of movements is the overall stability of each player's performance. In spite of the impression of the repetitiveness of playing, the notation reveals that both players rarely perform an exact note-by-note repetition of the whole period. The amount of material repeated from one period to the next is on the average 75% for the first player and 57% for the second player.⁽¹⁸⁾ The positions of a period differ significantly in their relative stability. Figure 8 shows the comparison of the positions of the period in their respective repetitions (i.e., the percentage of the cases in the performance when the same pipe is repeated from the same position in the previous period)

Figure 8
Graph of pipe repetitions per position

For the first player, positions 1, 2, 5 and 10-12, i.e., the beginning and the end of a period plus its middle point, tend to be the most stable. In contrast, the middle part of each 6-pulse phrase is less fixed, and it is there that the variations occur. For the second player, however, the overall shape of the cycle is not the same. In her version, the second half of the period is much more stable than the first half, with the stability culminating at position 10. On the contrary, positions 1-3, 5 and 12 are among the most variable. I hypothesize that near the end of each period the second player comes together with the first to a more fixed "cadential" point, while right after it and through the first half, her main effort is directed toward listening and "answering" the vocal sounds of the leader. If we compare the parts of both players, we will see that the most stable (or predictable) points of their periods overlap in such a way that they "deviate" to improvisation in turns. The same principle can be seen in their execution of vocal sounds. This seems to indicate that the communication between the two players is established in the process of performance. During follow-up field trips, I recorded performances of each of the five-pipe part players in this recording in different contexts, solo and in ensemble with other instruments and found that they could change their way of performing depending on the situation.

In order to analyse the movements employed in the performance of the para parts in relation to the structure of a period, we shall first measure the average number of 'steps' (i.e., movements to the adjacent pipe in a row) employed on each position. Positions on which there is no sound are considered as "no movement," because the analysis of video tapes shows that all movements from one pipe to another occur rapidly, right before playing the next note. Figure 9 shows the average difference between the pipe numbers on two adjacent positions, that is, the size of the movement between the pipes that players make to play the next note. The maximum movement equals 4, which is the movement from one outer pipe to another (from pipe 1 to pipe 5 or vice versa), the minimal is 0 (the player repeats the same pipe at the next position). Since the numbers are averaged for all repetitions of the period, the resulting figures are not necessarily integers.

Figure 9
Average size of movements per position

We can see from this graph that the beginning and ending of a period -- respectively, its most "stable" sections in terms of repetitions of the same material -- are also radically different from the rest of the period in the use of head movements. The end is marked by rapid alternation between the positions where the most active movements (i.e., skipping 2 or 3 pipes) occur, and those with complete "stops". For example, position 10 in the part of the first player is usually achieved by a skipping movement, then there is rarely a change from 10 to 11, then, again, a skip movement from 11 to 12, and no change from 12 to 1 of the next period. For the second player the pattern is similar, with the most active shift between positions 11 to 12, preceded and followed by smaller movements. We may conclude that the left/right turn of players' heads within the zone of 10-12 positions coupled with the one position "stay" after each move is the gesture that marks the end of a period. In contrast with this, the first and second positions are the least active ones in terms of head movements. Pipe changes almost never occur on the border between two periods (between the 12th and 1st positions). In this way a panpipe performer "links" periods one after another and ensures a smooth transition and continuation of the flow of music.

The probability model presents another possible approach to the analysis of movements of the para (five-pipe) part players. Considering the pairs of pipes in Figure 7, we soon notice that the pipes have unequal chances to appear one after another. This can be shown mathematically as the matrix of probability of the transitions, called the Markov chain.⁽¹⁹⁾

There are two main criteria for estimating the effectiveness of such models: their level of entropy and their generality.⁽²⁰⁾ We can imagine a process of matrix construction with a gradual increase in generalization, that is, first a matrix of one tune in one particular performance, then a matrix generalizing several performances by the same players, next a matrix for different versions of a tune (played by different performers), and finally for different tunes of the repertoire. There is a danger, however, that with the increase in generality the level of entropy also increases, that is, more generalized matrices predict less than do more specific ones. For this reason, the matrix that describes one particular performance of one tune has been chosen for the discussion. The advantage of this choice also lies in the fact that such a matrix accounts for the process of playing (rather than for just musical text as a stable unchangeable entity), as it specifies possibilities for variations as well as their relative weight in the total performance.

Wim van Zanten (1983: 93) indicates two possible approaches to the treatment of data for construction of a probability matrix. In the first one the data are treated as a 'chain' of elements, that is, with regard to the relative time that a given element occupies within the structure of a tune. The second approach presents the data as a 'sequence' of elements, focusing only on transition possibilities and excluding pauses or repetitions of the same chord from consideration. Cipher notation of the two para parts shown in figure 7 provides an example of chain presentation, because it lines up the sounds with their respective positions in a period. The same material as a sequence of elements looks like the following (for the first player's part): 1 5 1 2 5 1 2 5 1 5 1 2 5 4 5 1... etc. For the purposes of the present discussion, it is sufficient to analyse the possibilities of transition in terms of the sequence only, since the relative position of each note within the period has been already assessed by other methods of analysis. We therefore consider the matrix which defines only the probability of the movement from one pipe to another without the reference to the positions of the period and exclude repetitions of the same pipe, where there is no movement.

The process of matrix construction is simple. First, one has to count the number of transitions from one pipe to each of the others in the total performance for both players (for example, pipe 1 is followed by pipe 2 in 19 cases, by pipe 3 in 2 cases, etc.), and sum them up to obtain the total number of transitions from a given pipe. After that the probability of each particular transition from the pipe in question (e.g., 1>2, 1>3, 1>4 and 1>5) is calculated by dividing the number of transitions to each pipe by the total number of transitions from a given pipe. For example, if pipe 1 is followed by pipe 2 in 19 cases, and the total number of transitions from pipe 1 equals 190, the probability of transition 1 to 2 is 19 : 190 = 0.1.

The sum of the probabilities in each line of the matrix should equal 1, i.e., each "state of pipes" necessarily makes a transition to the next state. Table 1 shows the completed matrix.

Table 1
Matrix of probability for two para players
The left column is the number of pipes at the beginning of a transition, the top row is the number of pipes at destination.

Table 2
Modified probability matrix
'P' stands for preferred transitions, 'A' - for avoided ones

First, one can note that the fifth pipe can follow any other pipe with a high degree of probability. This confirms the performers' notion of the predominant role of the fifth pipe in playing. On the other hand, village listeners criticize excessive use of the fifth pipe when it is done without alternation with other pipes, as in the second player's part on the analyzed recording, hence their comment that the second player does not walk enough across the pipes (see note 18). Beyond the movement to pipe 5, all pipes have also another choice of one of the neighboring pipes for a step-wise movement. The fifth pipe itself has two probable transitions, step-wise to pipe 4 and a skip to pipe 1, which are the choices of either the smallest or the largest possible movements.

Unlike pipes 1 and 5, the middle pipes (pipes 2,3, and 4) are much more restricted in their use. For example, it follows from table 2 that pipe 3 forms a sub-system that cannot be entered from any other state of the system. Such a state is called ephemeral in mathematical terms (Cox and Miller 1965: 91). Indeed, in the performance in question this pipe was used very rarely by both players, making the probability of transition to it from other pipes close to zero, although this pipe is featured rather prominently in the opening periods of both players. Unlike all other lines in the table 1, the probabilities of transition from pipe 3 are all in the same range, i.e. the entropy level in the transition from the pipe 3 is very high (see table 1). We may conclude that the use of the third pipe in both players' parts in this performance has been coincidental in character. The avoidance of pipe 3 after the first period in this performance may be due to the fact that this pipe is actively used by an accompanying player, eliminating the need for the para (five-pipe) players to duplicate this sonority.

Another observation from table 2 is that the transitions 2 > 4 and 4 > 2 are avoided. This restriction is similar to the one formulated in the previous section for the priduval'nye (accompanying) part. Overall, the para part, despite its seemingly broader variation possibilities, is as restricted in the choices of movements as the accompanying parts. In conclusion we may formulate these choices as the rules:

1. The para (five-pipe) player has only two major choices for transition from any pipe to the next - one with skip movement and another with stepwise movement.
2. The stepwise movement avoids the third pipe, except the opening period.
3. The skip movement is always done to the fifth pipe, or from the fifth pipe to the first pipe.
4. The probability of skip movements increases toward the end of a period, while on the border between the periods head movement is avoided.

Using these rules in conjunction with the 'deep structure' of a tune (rule 1) we can obtain very good predictions of the melodic variants produced by both players of this recording. The applicability of these rules to other players and other tunes, however, requires further research.