Keywords: Dance structures

“Structures analysis” (see Kaeppler and Dunin, 2007)^[1] is one perspective of dance research which helps understand ideas of dance “families” or types, and ideas of variations, based on the notion that dance movements have to have some form that is recognisable and repeatable for both the dancers and spectators to attribute cultural value and meaning to the movements.

In community dances the ideas of structure tend to be far more organised as it is an activity involving a number of people doing something together in a structured way. This structure involves the arrangement of, and relations between, the movement elements through which dance is created.

As dance researchers, we look for the “stable” features or in scientific speak, the “invariant”. Within all the details of the movements of a given dance genre there will be a simplified stable concept, but this aspect is very dependent on the culture of the dance genre.

Bob Leibman (a mathematician by profession) formulated a system based on his research of southern and western Balkan dances.^[2] Using Bob Leibman’s system to notate step “weight changes” we end up with a simple concept that generally remains invariant between different variants with a family of dances – for example Serbian Kolo 0111, Romanian Hora 1101, the ubiquitous Balkan dance 011 etc.

Variations in Balkan dances in terms of weight changes

The following explanation uses quotes from Bob Leibman’s PhD dissertation.^[2] Dance takes very many forms, however, in the Balkans the old form is generally a chain dance. The “primary focus of most dancing In the Balkans is the footwork, the patterned movement of the feet and legs” (Leibman, 1992:237). The arms and body are of secondary focus as the connection in the chain by means of their hands or arms “minimizes the possibilities of doing much with the body and arms” (Leibman, 1992:238).

Considering weight changes as a Structures analysis, “for the purposes of getting at an invariant structure which underlies the surface level performances that we see, we need to consider each action taken by the dancer as an action which either does or does not involve the shifting of the body’s weight from one leg to the other” (Leibman, 1992:259).

Considering the most common form of Balkan dances, “most dances in the Balkans are made up of a single dance phrase which, with variations, is repeated over and over. The phrase generally begins with movement onto the preferred foot in the preferred direction of motion” (Leibman, 1992:280).

There are variations between dancers in the chain, and variation between interpretations of the same dance in different communities or contexts, considering the foot with weight support, “in general, a variation on any part of the dance phrase must leave the dancer in position, at the end of that variation, to be able to continue from that point on with the regular pattern. In other words, at the end of the variation, he/she should have his weight on the same foot as all of the other dancers. This is true whether the variation lasts for one count, one measure or the entire dance phrase” (Leibman, 1992:258).

Thus forming a rule for variations, “a sequence of actions which is a variant of another should leave the dancer with his/her weight on the same foot as does that other sequence” (Leibman, 1992:258).

Therefore, “it is the parity (evenness or oddness) of the number of weight shifts rather than the actual number of such weight shifts which is critical and must be the same for all dancers” (Leibman, 1992:259).

To capture this, Bob uses “the notation of modulus 2 arithmetic (the remainder when dividing by 2) in which all odd numbers are ultimately represented by 1 and all evens by 0” (Leibman, 1992:260).

This methodology works very well for the chain dances of Macedonia, Serbia, western Bulgaria etc. where the pattern of even and odd weight changes is generally invariant between variations within the chain and other versions of the dance from the same family of dances.

Extensions to the theory of weight change parity

Direction of movement

The direction of movement relative to the chain of dancers can be notated under the notation, and the whole dance sequence can be formed by a number of sub-phrases (with repetitions), for example the dance Seljancica (Leibman, 1992:281):

Multi-measure subsequence

There are cases where the underlying structures defined by the sequences of 0 and 1 is not invariant. This case can be seen in the connection between hora in 1101/1101 and hora în patru (Cetvorka) in 0001/1101.^[3] “The parity of the two-measure subsequence which they form is preserved — i.e., 00 -> 11 ->, 10 -> 01 or 11 -> 00” (Leibman, 1992:268).

Changes of direction

Leibman comments that changes of direction, “will generally be effected on measures of odd parity. This is a natural consequence of the preference, described above, for beginning lateral movement with the same foot as the direction of motion” (Leibman, 1992:282). Although this is generally the case, there are occasions that this is not the case, such as in Banat brâul.^[3]

When considering dances that continue in one direction, which can include a period of dancing in place, compared to bi-direction dances where phrases are repeated in opposite directions, Bob Leibman comments: “If the dance is not entirely unidirectional, then the beginning of each repetition of the dance phrase will almost always be the point at which there is a return to the preferred direction of motion. “Moreover, if the dance involves movement back in the opposite (non-preferred) direction, this movement, likewise, is normally begun with a weight shift onto the corresponding (non-preferred) foot” (Leibman, 1992:280), he gives an example of Srbijanka, “where an extra odd measure of dance is added whenever there is a need to change direction” (Leibman, 1992:283).

Application to Romanian dances

In Romanian dances the change of weight and direction is more often achieved by a conversion of the motif from 0 to 1 rather than insertion of an extra measure. The application of Bob Leibman’s method to Romanian dances is far more complex as the construction of most dance, types apart from the basic hora, does not feature a dance phrase with an invariant weight change structure. More often the dance variation is created by repeats, inserted motifs, and division of rhythmic passages. However, changes of weight have to be conserved during the rhythmic step variations.