Using Harmonic Dissonance Fluctuation as a structural aspect of music mapped as architecture

The task of technically relating music to architecture is a very tricky task. Being that there are multiple ways in which the two disciplines can be equated with each other, it is necessary to find common ground between them and explore them as cohesively as possible.

The most basic and straight-forward definition of harmonic dissonance is, “An unstable tone combination…that’s tension demands an onward motion to a stable chord.” —Roger Kamien (2008), p.41[7]

Dissonant chords are are referred to as ‘active’ chords because they’re utilization intrinsically suggests and demands proportionately increased musical dynamism. They are chords which have traditionally been used to express pain, grief, and conflict. And are indeed a staple of many forms of modern and contemporary music. While it is arguable how this precedent came to be made a prescient aspect of NON pedagogical classical music, none-the less, it has remained as crucial a staple to widely consumed music of the past 50 years across the board, from Jazz to heavy metal, to experimental and conventional electronic dance music, establishing itself as crucial an element universally as the importance of consonance has been to maintaining developments of classical and folk musics in the previous century and before. (It must be noted that dissonance has always played a vital role in music of all kinds, but it’s overwhelming emphasis and development in the modern age has been unparalleled.)

In Western musical theory, a harmonic cadence (Latin cadentia, “a falling”) is a progression of (at least) two chords that concludes a phrase, section, or piece of music.[1] Cadences give phrases a distinctive ending that can, for example, indicate to the listener whether the piece is to be continued or concluded. Therefore, instances of harmonic dissonance which occur within a closural cadence, as in Schoenberg’s Opus 23 no.2 the case study for this investigation, can be said to posses their own distinctive qualities (as oppose to a cadential instance that indicates that a piece is to be continued, or an instance of harmonic dissonance occurring in another part of a given composition.)

Spatial Application:

But what does harmonic dissonance and dissonance fluctuation in musical composition have to bear against architecture? I was stricken by an image in the book “Structural Functions in Music” by Wallace Berry, in which the concluding dissonance fluctuations of Schonberg's Opus 23 are graphed. The graph's shape reminded me of the contours of the Phillips Pavilion constructed by Iannis Xenakis.














In an attempt to reconcile what I have begun musing on, I decided to take another look at the philips pavilion designed . Again, what struck me about the pavilion was the manner in which the structural intersection points could easily be represented graphically in much the same way as the Dissonance Fluctuations of the Schoenberg piece had been, and given Xenakis's pechant for dissonance and musical texture, it seemed to be a more than appropriate point of departure.

http://www.drawingcenter.org/exh_past.cfm?exh=662&do=vexh&type=V

Xenakis’s usage of hyperbolic paraboloids in his musical as well as architectural compositions are well known and acceptable expressions. For my own purposes, I decided to plot out the vertices using maya 's NURBS generator and see what came out.

http://en.wikipedia.org/wiki/Non-uniform_rational_B-spline

Thanks largely to the introduction of NURBS surfaces in most 3D graphics programs, a vast majority of the hardcore computation needed to accurately represent paraboloidal surfaces of the hyperbolic as well as other varieties has been taken over by the computer.

Conclusion

Here then is an illustrative and expressive method of mapping musical information directly as architectural form that has been informed and inspired by a number of musical and architectural sources. The mapping of dissonance relations in music can be applied to creating a sense of surface dissonance and fluctuation in architectural spaces, which as one moves through one or the other, ultimately comes to a resolution; thus, the use of harmonic dissonance, when graphed, can be directly translated into spatial dissonance in an architectural setting yielding arguably similar effects.