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The blue squares have the same relative area as the openings in the Weltzheimer perf design. The ratio of areas between openings is not very uniform. The orange squares have the same total area as the blue squares, but they have a common ratio as they go from largest to smallest (in this case, 0.332).
The graph shows the logarithm of each opening's area plotted largest to smallest (the Weltzheimer perf in blue, ideal geometric scaling in orange). For each set of points, a line tries to fit through the points. The lines have the same slope (by design), but note the R^2 value for the orange points is 1. This indicates that geometric scaling perfectly explains the ratio of area between openings (as expected in this ideal case). The lower R^2 for the blue points indicates that geometric scaling is a poorer description of the ratio between areas.
Of course, areas don't have to scale geometrically in a design! However, a large number of analyzed perf designs exhibit strong geometric scaling.
Shapes have a visual weight related to their area, position, and color. In this case, color is uniform so the center of mass is equivalent to the visual center. The calculated center of mass for the white shapes is denoted by the red dot.
Inverting the image and calculating the center of mass of the resulting white shapes will give the visual center of mass of the negative space.
The ratio of the distance from the design window center (green dot) to center of mass (red dot) to half the design window height gives a normalized indicate of how balanced the design is visually.
mostly black and the other is mostly white. The assumption, then, is that white and black -- positive and negative -- have equality in the design. Is that
the same thing as equal amounts of each in any configuration on the field ? Does one sort of balance take precedence over another ? Who decides which
was more "important" ?
Did you say that in notan, the ideal is a perfect balance of positive and negative, object and ground ?
Are there other kinds of balance to be evaluated, or have you covered the field ?
To illustrate visual balance (which in this case is equivalent to center of mass), look at the positive (white) space in this design:
As before, the green dot is the overall center and the red dot is the center of mass (visual center) for the white shapes.
Now move the smaller shape to the right. The center of mass moves to the center of the overall design window, like weights on a fulcrum (the green dot is under the red dot now):
In the case of the Yin-Yang design, does the center of mass for the white shapes fall in the center of the overall design? I never considered this, so I centered the symbol from Wikipedia on a black background so the overall center matches that of just the symbol. The visual center of mass for the white space is not centered on the symbol:
What is remarkable to me is that many of Usonian perf designs are so well visually centered despite being much more complex that the simple openings above. For example:
The visual centering is still good when the image is reversed (this is the equivalent of focusing on the mask rather than openings from a computational point of view):
One last point: since perf boards are usually placed in a series of boards, vertical and horizontal flipping of alternate boards will automatically improve the overall balance of the set of boards.
Hopefully, this helped clarify my definitions of visual balance.
p.s. Here's a reference on Notan: https://www.amazon.com/Notan-Dark-Light ... 048626856X
equally when it comes to visual dominance: white (negative ? positive ? figure or ground ?) is the clear winner. What is the implication of this
unequal valuing ?
It's nice to learn that the various designers of these perfs were able, intentionally or instinctively, to balance their graphic images. As you say,
once a pair of perfs is "bookmatched" (mirrored), the result is automatically balanced. The question for me is, what is the value of balance; is an
asymmetrical ("unbalanced") design inferior to a balanced one ? Isn't Wright's predominant mode in this period asymmetry ? Or is that irrelevant,
considering that an asymmetric design (almost all of the perfs are not centered designs, nor are they usually installed mirrored) can be balanced,
in the way you have measured it, while being asymmetrical ?
And that raises the overall question: what do you see as the value of understanding these designs through the lens of your research results ?
Most perforated boards exhibit asymmetrical visual balance. In general, this is much harder to achieve and adds interest/flow into a design that enhances its beauty. Since it is very prevalent across many perf designs (and takes significant attention to create), my interpretation is that the perf design is important as a unit in itself. The next levels up in the design hierarchy (eg, clerestory windows, etc.) that incorporate perf boards result in higher level design units with their own importance to the overall design. I view Usonian design as a system that guides how to combine unit elements. I'm curious on how others think about the Usonian design system...
So what is the value of a quantitative research approach? I think historical research gives us what happened (the artifacts) and some of why (due to gaps in the record). Quantitative research can help understand how it happened (in terms of discovering underlying systems) and maybe shed light on some of the why (for example, is a design quantifiably different from another indicating a different designer, etc.). It is another tool to chip away at understanding things deeper.
The investigations so far have helped better understand the design grammar and suggest how a design might be approached in terms of goals, for example:
- Aim for 50% of the design window to be open area
- Follow a geometric scaling of the opening areas
- Achieve asymmetric visual balance
- Make both the positive and negative spaces interesting
- Use horizontal and commonly angled lines
Qualitatively, we might appreciate one design more than another. Asking why this is gives a better understanding of both ourselves and the design. It also, inevitably, leads to trying to quantify something.
Finally, I personally enjoy trying to use data to uncover new meanings and understanding!
(There's a lot of Bach for us to enjoy; in that way, among others, he reminds us of Wright).
The work is a Prelude and Fugue in E minor, BWV 548. I listened first to a performance by the estimable Gustav Leonhardt; it was a little slow, even
plodding, in its tempo, I thought. Then I found the performance which is presented on video with a scrolling score, so that the listener can follow the
music on the page as it is being heard.
Probably because this is a piece that has moved me in the past, hearing it anew in a fairly convincing performance moved me again. In fact I was in
tears of rapt joy throughout the prelude. One of Bach's favorite ingredients is a scale run -- up, down, fast, slow, a few notes or many. This piece has
plenty of that, among other gratifications. Why that device is so reliably affecting I cannot say. No doubt a musician could explain it easily -- something
about anticipation and reward, perhaps ?
I barely read music; I can follow what's happening in the score, but it appears impossible to me that anyone could keep their eyes on both staves
while using both hands and feet to translate those ridiculous little spots on paper into music, in "real time."
I have often wondered if I would enjoy this music more if I understood it in the way that a musicologist or a performer does. What is it made of ? What
are the elements of its composition ? What are the devices used by the composer to elicit the kind of emotional satisfaction that it delivers ? I can
only say that it brings me a full measure of joy as a lay listener.
Not being a trained musician but having, say, an ability and an interest in delving into it with means of quantification -- in an effort to understand it
better -- would I be well-advised to apply my tools to it ? Without a foundation in music, it seems to me I would be stabbing in the dark, measuring and
comparing elements in a more or less haphazard way, without really knowing what I should be looking for. I would use my tools to measure things
that those tools are able to measure -- whether those things were really essential to understanding the music, or not. They say that to a man with a
hammer, everything begins to look like a nail.
"Most perforated boards exhibit asymmetrical visual balance. In general, this is much harder to achieve and adds interest/flow into a design that enhances
its beauty." I can see how this may appear to be so, as in a symmetrical design the content is mechanically reproduced in reverse to complete the
composition. But as a designer I can say that there is nothing intrinsically more difficult about making an effective design that is asymmetrical.
The rest of that paragraph frankly fails to make sense to me, though as before I may be missing the intent.
I guess a set of rules for the creation of new perf designs that mimic those made by Wright and his apprentices would be useful -- assuming that the
goal was an honorable rather than a fraudulent one -- so your list of five desiderata is potentially useful. No, the content of any given perf design
isn't able to tell us what the designer's goal was, except perhaps by supposition.
I suppose that man will always try to understand what he sees around him -- especially those things that intrigue or delight. It is clear that you "enjoy
trying to use data to uncover new meanings and understanding." Don't stop now; just remember that the designers of these perfs were using personal
creative tools bearing little resemblance to the ones employed in their latter-day dissection . . . as I see it.
Much like Wright, there is that sublime balance between predictability and surprise. (This is what I donÃ¢â‚¬â„¢t like about Mozart... too weighted in the direction of predictability). Structure is important, but extremely difficult to fathom upon first listening. ItÃ¢â‚¬â„¢s like watching water flowing down a stream. At first glance, it seems to repeat itself, but upon closer inspection, there is the feeling of randomness but with a structure that exists only in another dimension. ItÃ¢â‚¬â„¢s no surprise that Bach was a gifted improviser. Many of his pieces seem to churn along determined only by the preceding musical phrase. The structure is so well concealed that itÃ¢â‚¬â„¢s nearly impossible to identify it.
Much of the regularity comes from the rhythmic pulsation which is almost machine like.
Listen and weep:
Brandenburg #3 1st movement
Aria from Orchestral Suite No. 3 in D, BWV 1068.
What is the mandolin-like instrument in that performing group ? This is one of the less common additions to the modern Baroque ensemble; its warm deep tones are a
pleasant contribution. I recently heard a harpsichord concerto recording in which, rather than miking the keyboard to hold its own against a perhaps too-large orchestra,
this instrument was added, doubling the harpsichord, randomly, and generally getting in the way -- but pleasantly, and audibly !
Years ago, I sang with the Bach Society in Mpls. We worked on two pieces for concert, Bach's B Minor Mass and Mozart's Requiem Mass. My friend (a Bach expert) said going from Bach to Mozart was like leaving a cathedral and entering a thatched cottage. Perhaps a bit hyperbolic, especially when it comes to the Lacrimosa, but not entirely false.
Brandenburg #3 is sublime, so too the less often performed #5, which is a happier piece.
I believe it is one thing to listen to such magnificent music as the Bach B Minor, and quite another to sing it, especially the Sanctus and Dona Nobis Pacem (my vote for the most glorious piece of music ever written). I just wish I had the ability to play either piano or cello, but my laborers hands lack dexterity.
admittedly not the same as hearing a live performance. The theorbo must pack a sonic wallop . . .
Thanks for those notes, RG. Performing is certainly a way into the music unavailable to the passive listener. I did some choral work in an earlier day;
my reading was just adequate to that task. My brother sang the B Minor mass in college; I envied him. The St John Passion has taken my interest in recent
years -- the opening chorus paints an awe-inspiring musical picture that must be much amplified (literally ?) in the cathedral . . .
https://www.youtube.com/watch?v=SiKgrevzT-g (Boo to double opening ads on YouTube !)
Better ? https://www.youtube.com/watch?v=sidU7AUqQUk
Herr, unser Herrscher, dessen Ruhm
Lord, our ruler, whose glory
In allen Landen herrlich ist!
is magnificent everywhere!
Zeig uns durch deine Passion,
Show us through your passion,
Dass du, der wahre Gottessohn,
that you , the true son of God,
Zu aller Zeit,
at all times
Auch in der grÃƒÂ¶ÃƒÅ¸ten Niedrigkeit,
even in the most lowly state,
Verherrlicht worden bist!
The ones beginning with a bright "ta-da" chord, must have been the inspiration for the supposed first thing Wright did whenever he sat at a piano...
For me, a Landowska or a Scott Ross are worth a hundred Glenn Goulds. But to each his own !
(I hope the thread is not irreparably besmirched by this excursion into music. Perhaps it will be excused -- on the grounds that Wright and Co's perf designs are his "architectural music" personified ?)