Week 142 (Music Room Cloud)

At long last the acoustic cloud in the Music Room has been completed!  With 60 panels totaling very nearly 900 sq ft (nearly 1800 sq ft of active acoustic performance since both sides are used), it is a thing of beauty to behold:

But if you look more deeply, many more layers of beauty await…

We begin our appreciation with an acknowledgment of the great American architect Frank Lloyd Wright.  Wright not only promoted the concepts of Organic Architecture, but he advanced them as well.  For example, after Louis Sullivan proposed that that “form follows function,” Wright went one step further and declared that form and function are one.  One of the first ways to test whether form and function have any chance at all of being on the same page is to define the units with which form and function can both be expressed, and then to choose a coordinate system that will allow form and function to be related and ultimately integrated.  There are many candidate systems:

There are many candidate systems:

square grid	triangular grid	hexagonal grid
rectangular grid	rhomboid grid	oblique grid (square)

Wright did use squares and rectangles as the basis of some of his designs (notably Fallingwater), but many of his designs eschewed 90° angles in favor of the more open 120° angles defined by hexagonal and diamond grid plans.  Wright said about the Snowflake House: “It is one of the more elaborate Usonian homes. It is based upon a hexagonal unit throughout. The ‘hex’, being more human than the rectangle, affords easier circulation and nestles more readily into its environment.”  About another floorplan he designed based on the hexagon, Wright said “As an experience the [Honeycomb House] has an inevitability and ease and entering the forecourt is like encountering a warm embrace.”  Wright was clearly not at all afraid to think “out of the box” while remaining strictly “on grid,” for reasons we will get to a little bit later.

Hexagons can be used to tile the plane, but the range of hexagonal tiling patterns is limited to three basic forms:

In other floorplans, Wright designed not around a pure hexagon, but rather a diamond grid based on 60°/120° rhombi.  Tri-axial symmetry naturally creates the possibility of three different interpretations of “straight ahead”:

Rhombille tiling is also possible, and has many more coloring options, just a few of which are shown here:

Coloring need not be explicit in the design, but it does help to illustrate the latent design energy present when a defined program meets the defined grid.  And it makes clear that the 60°/120° rhombus provides considerable choice in supporting the function of a space in more dynamic ways than a pure hexagonal grid while preserving the all-embracing 120° form.  For this reason many Wright houses and buildings employed the Diamond grid, among them the Berger House, the Kinney House, the Strom House, the Teater House, and others we will likely discuss soon, but not right now.

With that background, there is another very important feature that results from using a properly scaled grid of whatever shape: when the grid is honored, everything becomes comparable as simple integer ratios because everything can be expressed in a simple number of grid units, or grids.  Thus when one encounters two grids to the left of a door and three grids to the right of a door…that’s a 3:2 ratio, and it looks as harmonically balanced as sounds.  A room that’s 8 grid units wide and 13 grid units long…those make so much more sense than dimensioning a room based on the lengths of lumber delivered or the number of nails in a ten pound sack!  Ratio and proportion have been studied since antiquity, and much ink has been spilled both about the Golden Ratio and whether certain ancient buildings that had proportions close to it were accidentally close by chance, or accidentally not quite perfect due to the imperfections of building techniques at the time.  Whatever the truth may be, we know that Frank Lloyd Wright knew very well what the Golden Ratio was, and he was happy to use it to enhance his designs whenever he could.  And why not: it is called the Golden Ratio for the simple reason that it looks not only pleasing, but natural.   And familiar.  Indeed, it expresses a form of mathematical self-similarity:

Or visually:

Such self-similarity is the hallmark of fractals, which are not only self-similar at multiple scales but also ubiquitous in nature across space, time, and frequency domains.  Self-similarity in design means that however it may be that the function of the small supports the function of the large, whether drawn by the hand of the designer or a design of nature herself, both share the same form, and thus all are one in the context of organic architecture.  The resonance of self-similarity is also why programs designed using golden ratios are such a delight to behold.  The Fibonacci Sequence (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, etc) are generators of approximations of the Golden ratio φ, with 2/1, 3/2, 5/3, 8/5, 13/8, 21/13, 34/21, 55/34, etc. converging toward the number .  Self-similarity exists in Fibonacci numbers because each one by itself is the sum of two other Fibonacci numbers whose ratio also gives an approximation of φ.  Thus 8 is the sum of 5 and 3, and 5/3 is an approximation of φ.  Every time we express a golden ratio, each side of an explicit golden ratio thus carries within it, more and more golden ratios all the way down to the unit grid.  Which brings us back to not only Frank Lloyd Wright’s fundamental insight about the grid.

Wright justified the use of the grid as the only possible way to “hold all to scale,” a problem that Johann Sebastian Bach faced when he composed The Well-Tempered Clavier.  In a recording studio the concepts of architectural and musical scales are not only equally important: they are one and the same (as Wes Lachot explained when he was invited to Taliesin in 2007 to give a lecture on the subject.)  But Wes also points out that even when we focus only on the architectural challenge to “hold all to scale”, this is just another way of saying that the property of self-similarity is only possible if you create a “self’ to be similar to, that “self” being the unit.  Vitruvius said pretty much the same thing about two thousand years earlier.  Greek and Roman architecture are all about the unit system, and what that does for harmonic ratios and self-similarity.  And self-similarity is everywhere in nature…and not only when it comes to the more pleasing ratios of line segment lengths.  There is the Golden Angle, which nature uses to arrange the florets of sunflowers:

There is of course the Golden Rectangle, which is so famous that people will see it even when it is not even remotely expressed:

And there is the Golden Spiral, which is an idealized form of the Fibonacci Spiral.  Fermat’s Spiral (seen in the sunflower photo below) is based on Fibonacci numbers, and hence carries with it the DNA of the golden ratio (which can be verified by noting that the two outer sequences are 55 and 34 elements).

So, what do you think you get when you try to integrate the form of the diamond grid with the function of the Golden Ratio?  Give yourself a Golden Star if you guessed the Golden Rhombus:

There are nearly 500 buildings we know to be designed by Frank Lloyd Wright, and to my knowledge none of them ever attempted this particular version of “form and function being one.”  And it’s not really a surprise.  The 60°/120° rhombus tiles the plane perfectly, and despite many other indignities that Wright demanded his clients to suffer, he never forced them to walk on a floor that’s not remotely flat.  If you try to put three golden rhombi together, you quickly find that they don’t lie flat at all: the 180° plane to which we are all accustomed shrinks to 144°, and if you were to stand on the seam between two of them, instead of standing 90° to the floor, the floor would make a pair of 72° angles to you.  Nature herself had some fun with the Golden Rhombus: if you keep putting them together to make a convex solid, you get a Rhombic triacontahedron:

which is such an amazing shape I don’t dare even begin to get into the details.  (Be advised that the info in that link you just skipped over is scary-cool!)  But Frank Lloyd Wright never found a way to integrate the Golden Rhombus into his diamond grid, and this is where Wes Lachot has truly made an inventive step in the realm of organic architecture.  Manifold Recording needed an acoustic cloud that would be planar at room scale, but which would balance diffusion and absorption across a wide spectrum of sound-frequencies, ideally beyond what could be achieved using conventional planar configurations.

By unfolding the Rhombic triacontahedron (as visualized above), Wes was able to integrate the functions of acoustic balance and control, the delightful form of the Golden Rhombus, and the all-important form/function of our diamond grid.  His design enhances performance by double-digit percentages while enhancing the aesthetics of the room rather than trampling them.  Look again (and note how “right” this 120° degree angle actually looks):

Every one of the 60 diamonds in the cloud are golden rhombi, 30 of which are 2″ rigid fiberglass absorbers and 30 being custom-made RPG BAD™ panel diffusors.  Since there are 30 golden rhombi in a rhombic triacontahedron, you can think of the cloud as the unfolding of two such solids, the yin of absorption (in the panels containing the lamps) and the yang of diffusion (those panels not containing the lamps) integrated together.  Because our panels are rhombic instead of rectangular, RPG founder Peter D’Antonio created an entirely new product just for us.  The template for that work (in its square-world format) looks like this:

Whether in square or rhombic form, the BAD panel matrix contains its own mathematical expressions of self-similarity that scale down (and thus up to high frequencies) as well as supporting the modular logic to combine these grids to scale up (and thus down to lower frequencies).  And as previously mentioned, the macro shape of the cloud further enhances its acoustic performance, trapping bass and diffusing waves across an estimated frequency range of 50Hz to 12kHz.

But the fun does not stop there…On each end of the minor axis of its golden rhombi, the Rhombic triacontahedron has nodes that connect 3 edges, as do we.  On each end of the major axis it has nodes that connect 5 edges whereas ours connect 6 edges.  (The unfolding is achieved by alternating convex and concave foldings instead of going convex all the way, thus we effectively zig half the time where the other one zags.)  But the logic of the 5/3 ratio remains embedded in our cloud design, with 3 6-way nodes across the “width” of the cloud and 5 6-way nodes along its two diagonals.  Notice also we have a pattern that’s 3 large hexagons long and 2 large hexagons wide: that’s a bold 3/2 ratio!  The design of the cloud speaks volumes about the integrity of the grid, the function of acoustic control, and yet carries within it the humor of nature herself as golden ratios form and dissolve across three dimensions in a constantly evolving dance.  If that were not enough, there’s something special about the dihedral angles between every two rhombi in the cloud: the 72° angle from perpendicular is precisely the angle of the two isosceles angles of the Golden Triangle:

Here’s the pattern of golden triangles expressed by the negative space of the cloud:

To me this proves that if one invites Nature into the design, the design will be filled with all the magic that Nature has to offer.  What more could be hoped for?

There is more progress to report, but I think it’s best to keep this posting to its principle topic, the Music Room cloud.