Self-portrait, 1910, Zinaida Serebriakova

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Self-portrait, 1910, Zinaida Serebriakova
“Puget Sound Memory - Dunham Cormorant #2″ 2020
Colored pencil on paper.
30″x22″
A Fool and His Money (1912) the first known extant motion picture to feature an all-black cast
Directed in 1912 by Alice Guy Blaché (France). First movie ever with all black cast.(produced in the United States). Short movie of ten minutes with James Russell. Most of the movie of the talented French woman director Alice Guy disappeared, this one was fortunately found back by chance.
I’ve made a little demonstration of Fourier series that shows you how a string vibrates when plucked.
Red is the actual string: L is its length and b and h control where it’s plucked. The solid green curve gives a Fourier series approximation to it, whose precision you can adjust with M. The solid blue curve shows how that Fourier series evolves over time. The dotted green and blue curves do the same for a single term in the series – that is, a single harmonic, which you can choose with q. k controls the wave speed.
For the uninitiated, here’s how this works. A string that’s fixed at both ends can vibrate in certain special ways called harmonics or normal modes (which are displayed on the graph as the dotted curves). In the simplest of these, q=1, the string takes the shape of a half-sine wave, which then oscillates up and down with all points on the string moving in phase. In the next simplest, q=2, the string is shaped like a whole sine wave; the midpoint of the string is perfectly stationary, and the two halves of the string oscillate in opposite directions. In the q=3 mode, three half-sine waves fit on the string, and so on.
Each of these modes oscillates with a certain characteristic frequency, and these frequencies have an elegant relationship: the frequency of mode q is q times the frequency of mode 1 (called the fundamental frequency). So if the fundamental frequency is 440 Hz, the A above middle C, then the second harmonic is 880 Hz, the third is 1320 Hz, and so on.
Now, when I pluck a string, I’m not making any of these smooth sine wave shapes, but a crude, pedestrian angle. But Fourier analysis says that we can see how the wave evolves over time – in fact, how any initial waveform will evolve over time, no matter how complicated – by following a simple recipe:
Write the initial waveform as a sum of normal modes.
Each normal mode in this sum then evolves independently, by oscillating at its own characteristic frequency.
At time t, you can figure out the shape of the string by calculating where each normal mode is at time t, and adding them back together.
This is exactly what you see on the graph.
So that’s the math. How about the consequences for music? First, though you can’t see it in real time, this graph shows that a plucked string actually always has a sharp corner, which moves up the string to the mirror image of the plucking point, and then shuttles back. Hermann van Helmholtz described first described this phenomenon in the more complicated case of a bowed string, where the corner traces out a lens shape as it moves.
Second, the string as a whole vibrates with the same frequency as its lowest normal mode, i.e. the fundamental frequency. But this graph makes it clear that the real vibration has some mixture of the higher harmonics. Exactly how they’re mixed determines the unique timbre of the instrument. So in a violin (with vibrating, continuously bowed strings), a trumpet (with a vibrating air column), or a clarinet (with a vibrating reed), the same principles are at play, but the actual mixture of harmonics is different, producing different sounds. (To complicate things further, the bodies of these instruments vibrate in special ways too, thus amplifying or suppressing certain modes!)
Third, by stopping the midpoint of the string from vibrating, one can silence all the odd normal modes while allowing the even ones to continue. This produces a pitch whose lowest mode is the second harmonic of the previous pitch, making it an octave higher. Stopping the string at one of its one-third points makes it sound at the frequency of the third harmonic, and so on. Guitarists call this “playing harmonics” – you touch the string at one of these points without fretting it all the way, and produce an unusually high and clear tone. The higher of a harmonic you want to isolate, the harder this gets to do: the higher harmonics occur in the plucked-string vibration with weaker amplitudes, and the margin of error for where to touch is smaller.
Fourth, one can also do the opposite, which you can see on the graph by setting b to be an integer fraction of L. For example, if you pluck the string at its midpoint, then the second, fourth, and so on harmonics don’t sound at all. I’ve heard this is important in piano design. The hammers are supposed to hit the strings exactly 1/7 of the way along their length in order to silence the seventh harmonic, which is two octaves and a very flat minor seventh above the fundamental, so sounds dissonant to us.
Theoretically, this sort of thing is applicable to guitar or violin technique, too, though. I haven’t seen this actually used, but I have seen classical techniques where one plays close to the bridge or end of the string (sul ponticello). As you see if you make b close to L, this accentuates the higher harmonics relative to the fundamental, producing what I’d call a sharp, metallic sound. (You might also notice that the approximation gets worse as b approaches L, which is another instance of the same phenomenon: the higher terms in the series which are cut off by the approximation become more relevant.
I got into this from the happy coincidence of playing guitar and teaching Fourier analysis. Do you know things about the acoustics of other instruments, or other aspects of music production that can be mathematically modelled? I’d love to hear from you!
Werner Herzog Eats His Shoe (Les Blank, 1980)
(you can watch it here, 19 minutes)
Werner Herzog ate his shoe because Errol Morris finished his first film: Gates of Heaven (1978).
Happy 75th birthday, Werner Herzog!
Onibaba | Kaneto Shindô | 1964
Jitsuko Yoshimura, Nobuko Otowa
The golden perfection of the aortic valve
Marco Moscarelli, Ruggero De Paulis, 2015
“As cardiac surgeons, by observing the perfect geometry of a tricuspid aortic valve, we speculated that an approximation to the golden ratio might be present between its components, and the Fibonacci spiral would fit into the valve, representing a very interesting way to describe its fascinating symmetry.
In order to do that,we proceeded as follow: 1) A trans-esophageal short axis view of the aortic valve was obtained and three golden rectangles with a+b/a=a/b=1.618were created, approximating the two dimensional silhouette of the sinuses of Valsalva, from the internal edge to the external edge and a golden hexagon was then generated from the union of the rectangles (Fig. 1b/c). 2) The free margins of the aortic leaflets were marked in red, and the center of the valve was approximated to the center of the hexagon made of the three golden rectangles (Fig. 1d/e). 3) In order to create the Fibonacci spirals for each leaflet, every rectangle was split in four golden rectangles and squares with the same aspect ratio (Fig. 1f/g). 4) Six Fibonacci spirals were drawn following the Fibonacci sequence (Fig. 1h/i). 5) The six spirals were highlighted (Fig. 1). 6) The hexagon that includes golden pentagons, rectangles, squares and triangles with the same aspect ratio of 1.618 resembling the ‘golden perfection of the aortic valve’ was then finalized (Fig. 1).”
more on researchgate
Dessin de la friche de la Corniche des forts à Romainville
Paul Froelich, Man in Blue (c. 1944)
Otto Dix, Self-Portrait (1912)
Carnet tout noir
[ quasi symmetric relation ] • mw
Alien creature lands on earth
“I realised that I was deaf, but everything around me was deaf too, as though the world could no longer hear itself.”
— J. G. Ballard, The Kindness of Women
In Singapore, in the airport, a darkness was ripped from my eyes. In the women’s restroom, one compartment stood open. A woman knelt there, washing something in the white bowl.
Disgust argued in my stomach and I felt, in my pocket, for my ticket.
A poem should always have birds in it. Kingfishers, say, with their bold eyes and gaudy wings. Rivers are pleasant, and of course trees. A waterfall, or if that’s not possible, a fountain rising and falling. A person wants to stand in a happy place, in a poem.
When the woman turned I could not answer her face. Her beauty and her embarrassment struggled together, and neither could win. She smiled and I smiled. What kind of nonsense is this? Everybody needs a job.
Yes, a person wants to stand in a happy place, in a poem. But first we must watch her as she stares down at her labor, which is dull enough. She is washing the tops of the airport ashtrays, as big as hubcaps, with a blue rag. Her small hands turn the metal, scrubbing and rinsing. She does not work slowly, nor quickly, like a river. Her dark hair is like the wing of a bird.
I don’t doubt for a moment that she loves her life. And I want her to rise up from the crust and the slop and fly down to the river. This probably won’t happen. But maybe it will. If the world were only pain and logic, who would want it?
Of course, it isn’t. Neither do I mean anything miraculous, but only the light that can shine out of a life. I mean the way she unfolded and refolded the blue cloth, the way her smile was only for my sake; I mean the way this poem is filled with trees, and birds.
Mary Oliver, Singapore