TECHNES Encyclopedia Database

The Golden Ratio in a Two-part Form: The Example of the Arch Form

This perception of filmic rhythm in reverse proportion to the tempo of the music can also be seen when the viewer is in a position to foresee the form of what he or she is seeing or hearing. A viewer’s expectations with respect to a given temporal logic are an important factor in the perception of time. In music and cinema alike, if the listener or viewer pays close enough attention they will be able to feel formally the duration of the musical events: reprises, the end of a section, etc. The most striking musical example is certainly that of the arch form, characterised by an ascent and then a descent (or the inverse) in the musical intensity in a broad sense with a degree of symmetry. Viewers and listeners can easily be made aware of the predictability of this approach given its simplicity, so that fewer elements are likely to receive their attention, either because they are familiar with it already, or because they are tired and thus less sharp.

The film director or composer will then very often take steps to create surprise, precisely in places where the viewer thinks there no more are to be found. As Ethis remarks,

Having unexpected events create an effect is always possible, and it is generally such events which make us reformulate some or all of our expectations and advance our experience of the work. The relations between works thus correspond to a strategy of jumps ahead and behind, which is why one attempts to construct a consistent configuration of the overall sense of our experience, guaranteed by these constant revisions.^[4]

With respect to the entire work, one frequently sees a shortening of the second part of the arch form. Consciously or unconsciously, shifting the median point closer to the ending brings the proportion between the two parts closer to that of the golden ratio,^[5] whose first part corresponds to a little less than two thirds. The musical examples are legion: Richard Strauss’ An Alpine Symphony (Eine Alpensinfonie, 1915); Gardens in the Rain (Les jardins sous la pluie) in Claude Debussy’s Estampes (1903); and especially Music for Strings, Percussion and Celesta (Zene húros hangszerekre, ütőkre és cselesztára, 1936) by Béla Bartók, who was obsessed with the golden ratio.^[6] We also find this state of affairs in numerous films, which are divided into two parts by the insertion of an intermission: 2001: A Space Odyssey^[7] and Barry Lyndon,^[8] David Lean’s Lawrence of Arabia (1962),^[9] Coppola’s The Godfather: Part II (1994)^[10] and Béla Tarr’s Sátántangó (1994).^[11] In each of these examples, music plays a crucial role around this dramaturgical nodal point between the half-way point of the film and the intermission. We find there the experience of time is contracted through the energy it brings to the viewer, either in order to plunge them back into the storyline or to bring tempo to the end of a section. In the latter case, the viewer’s anticipation is thus a source of pleasure, as it is involved in an immediate process of conclusion which the viewer feels without entirely understanding.

This leads us to conclude in addition that when viewers are already familiar with the original work, time always seems to pass differently insofar as their position, and thus their experience, will be singular, given new form by means of their own temporality: while some elements may be familiar, others which had passed unnoticed will appear new and capture their attention, leading them internally to divide up the time on the screen differently.

To sum up, we are in agreement with the concept “horizon of expectation” defined by Hans Robert Jauss,^[12] who distinguished between the expectations generated by the artwork itself and the social expectations of its audience.