Experiment cØrdes
Cordes experiment attempts to find a harmonious relationship from sound frequencies and transfer it into a three-dimensional space model [1]. The time factor is included as an implicit layer in this process (see Figure1).
Figure1. Diagram of conceptual process
Usually, architecture is designed with three spatial dimensions, but without considering the appearance of n-dimensions from the latest physical theories, nor the temporal dimension. Yet, the time factor itself is included in sound and music, because it is an essential element of its own existence.
To perform this experiment, we proceed to interconnect the time domain of the sound field, and the three-dimensional architectural domain, articulating space and form. In turn most decisions are made by automatisms and other generative processes. An analogy with frequencies F1 and F2 is constructed, by using the golden ratio as a paradigm of balanced proportion and establishing a relationship of Phi (i.e. F1 = F2 1.618). These frequencies are inherently sound units measured in cycles (Hertz). A Hertz is one cycle in unit time (1second). Thus this unit determines a spatial path (which will develop a 1 second cycle). Taking this unit of time as measure, it can be concluded that the relationship between F1 and F2 develops as a certain wavelength at a rate determined by a propagation medium.
Ultimately, if the units of time and propagation velocity are constant, we establish that the relations between F1 and F2 correspond to relations in terms of wavelength, and therefore to a unit of dimensional measurement (meters or cm). In conclusion: wavelengths remain in the golden relationships (see Figure2.1 and Figure2.2).
Figure2.1  Relationships of frequencies and Phi
Figure2.2  Sequence of the process
An application has been developed with the visual programming language Pure-data, to visualize the resulting waveform of the frequency ratio (see Figure3). Using a capture at a regular interval (it has been based on the time unit one second), taking the frozen waveform for each regular interval.
Figure3  Detail of the programmed audio tool for the experiment
These cuts in time are captured regardless a series of 34 cycles.
The number of cycles in this sequence could have been varied. The number 34 is chosen because it belongs to the Fibonacci series, which is directly related to the golden ratio. Likewise, number 34 shows a sequence sufficient to model a route with certain size.
In this series we proceed to perform a sequence of progression, as a metaphor for a pulsation or vibrational motion. Ultimately, the course of the 34 catches corresponds to a greater pulse, sway, or systolic / diastolic movement. It starts from rest, can range up to values ​​of -1 and +1 and ends in the same initial state.
The 34 catches are transformed into vectors, establishing them as sections of a formal and dimensional experiment [2]. Once this operation is done, we proceed through 3d applications (Sketch-up and Rhino) to place them in equal distance sequence [3] (see Figure4).
Finally, when they are positioned as sections, a continuous surface between each of them is woven. The result can be seen in the illustration of Cordes (see Figure5).
Figure4  From diagrams to surfaces
Figure5  Renders of the 3D model.
This experiment may not determine whether the sections and resulting spaces become the golden ratio in absolute terms and strictly dimensional level. However, this is a test where the relationship is implicit in the formal generation. The process takes three-dimensionality with the move and sequence of these sections. This sequence is constantly articulated with fixed distances in time. Being a formal experiment, it might be reimagined as an architectural application with multiple solutions.
One possible solution is to settle a half buried space where the topological surface becomes a flat roof outside (see Figure6). In it, the underground vertical planes correspond to starting height and end of the piece. The virtual prism defined by previous planes intersects this surface and generates communication sockets and lighting. This is an experiment which has an expression close to a geological formation, connecting it to a landscape view. The most significant aspect is that all this comes exclusively from sound data in a temporal path equivalent to a pulsation [4]. This is the minimum conceptual expression of a sound vibration.
Figure6  Architectural approaches
Another possible architectural application can be a large marquee, or even a skate park urban surface type. This experiment could have different applications in another scale. For example, it could be an element of street furniture.
We have to interpret sound and this can be done in many ways. Even though there is a mathematical relationship between frequencies (Hz) and the metric system, (due to the wave length), there are other ‘subjective’ considerations. These subjective intentions include: the stretching of the waveform’s screening, the dimensions used to articulate the sequence and the time of capturing the waveforms.
However, as already mentioned in the preceding text, those parameters are taken as unity measures (one second between captures, one single oscillation to develop the whole form and unitary dimension as the length sections intervals). In conclusion, decisions follow the most possible conceptual path, because this is an abstract experiment, without specific size and program requirements. An important point of consideration is that the development of all the sequence as a generative process means that the ranges and limits are static, inside an unlimited state of variability. Generative processes are of a dynamic order, therefore departing from certain reference parameters, will have different and specific solutions. Usually these solutions can be considered as variations or combinations of a main root. Cordes is a formal experiment of data translation and sound. In other words, the sound synthesis becomes an engine of formal generation.


[1] The golden ratio  has been used repeatedly in the history of architecture, providing  spaces and architectural forms  with a proportional system,  based on a ratio found in  nature. It is believed that the golden ratio provides harmonic spaces that have an effect on the quality of living and perceiving space.
[2]  These values ​​ in the sound domain are the frameworks of  maximum reference, because a range  greater than  1 or -1 (in absolute value of acoustic signal), will be cut and therefore cause distortion.
[3]  Distance is taken as a constant for each section in order to accomplish the golden ratio.
[4] Pulse or pulsation becomes the minimum element so that any vibration occurs. Starting from rest, it takes a fluctuating route to return to its point of origin (rest).






Experiment by Bea Goller
Text licensed with a CC license > by-nc-sa 2014
All images by Congoritme CC license > by-nc-sa 2014

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