Notes & Lines discusses the
intersection of math, science, and technology with performing and visual arts.
Topics include bizarre instruments, technically-minded musicians, and cross-pollination of science and art.
A colleague of mine recently heard from a friend that certain black holes make musical pitches—specifically, scientists have observed a black hole “emitting” a B-flat. As it turns out, he was correct: in 2003 Cambridge researcher Andy Fabian discovered that the satellite-borne Chandra X-ray Observatory spotted music-like ripples emanating from a black hole at the center of NGC 1275, a distant galaxy.
The researchers treated these gas ripples as musical sound waves and came up with some pretty wild observations. They calculated that the waves work out to “sound” a B-flat 57 octaves below middle C; for comparison, a standard piano range reaches to a little over 3 octaves below middle C. A keyboard purpose-built to play the black hole’s note would be over 45 feet wide. The wave had a frequency of about 10 million years, which is infinitely far below that perceived by human hearing. In September 2003 Nature magazine proclaimed it the “deepest-ever note.”
Here on Earth, the real deepest-sounding notes belong to the trusty pipe organ. Interestingly, organ builders have used two different methods for accomplishing low notes.
The simplest method is to build a really tall pipe, but this usually isn’t practical. The lowest organ pipe of any musical value would be around 64 feet tall, a dimension not possible in even the largest halls. There are only two true pipes of this size: one resides in the world’s largest pipe organ (and musical instrument) at Boardwalk Hall in Atlantic City, and the other in the Sydney Town Hall Grand Organ in Australia. The sound from these pipes is described as more felt than heard: their pitch resides around 8 Hz, and human hearing sensitivity cuts off around 20 Hz. As the videos below prove, the Atlantic City organ sounds like a rumble, and the Sydney one sounds like, well, flatulence.
The second method relies on the psychoacoustic phenomenon of resultant tones. When pure sine waves are sounded together, they produce two additional sounds whose frequencies are the sum and difference of the two originals. For example, combining two tones at 32 Hz and 48 Hz result in two additional tones of 80 Hz and 16 Hz. Organ builders in the late 18th century were aware of this phenomenon and realized they could use it to produce very low sounds without building massive, costly pipes. So, to get the same 8 Hz as the Boardwalk organ, a builder could simply sound two pipes—one 32’ in length and one 21 1/3’—to generate the desired pitch. One might imagine this effect to be jarring, but the pitches are usually so low that a listener only perceives the low note and doesn’t hear the two combined pitches that produced it (a good audio example is here).
Organs also take the prize for the highest instruments, but that’s a topic for the next blog.
Growing up in the early ‘90s, my family still had a big cream-colored rotary phone stuck to our kitchen wall. At the time I didn’t realize that these phones were pretty outdated and that most other homes already had pushbutton phones. I still remember its sounds: the ratcheting of the dial returning after selecting a number, and the decidedly analog ringing bells.
A German initiative is concerned enough with these outmoded sounds that they’re archiving them. Conserve the Sound describes itself as “an online museum for vanishing and endangered sounds.” The project is run by CHUNDERKSEN, a film production and communication design firm.
Conserve the Sound’s website organizes captured sounds by decade and object type, and they’re all freely available. The group captured sounds from typewriters, desk fans, stopwatches, a host of film cameras, kitchen gadgets, phones, the stamping of a library book, and even the filling of a milk can. (I’ll admit I’ve never been privy to this sound, but it’s pretty close to what I imagined.)
Preserving objects, as museums have been for thousands of years, makes a lot of sense to me, but I’ve never thought of preserving sound. On one hand it’s interesting to generations younger than mine, who’ve never heard a cassette tape jam or a Polaroid camera spit out a picture. Some of them seem to fall a little flat, though—I don’t find the clicking of buttons on a boombox or a running kitchen blender particularly worthy of preservation, for example. But who knows: maybe that’s because I grew up with them.
While his name is not a household one, the career of Adelbert Ames, Jr. sprawled across physics, ophthalmology, physiology, psychology and philosophy. He also developed and lent his name to two common optical illusions: the Ames room and Ames window.
The younger Ames was born in 1880. His father was a noted general in the American Civil War and was heavily involved at the Battle of Gettysburg, later becoming provisional governor of Mississippi and an inventor. Ames, Jr. earned a Harvard law degree, studying with William James and George Santayana in the process, but abandoned law to become a painter. Ames figured that he could become a better painter by scientifically studying vision, so he began reading about the optical components of the eye. The study of vision made such an impression on Ames that he abandoned painting and attended Clark University in 1914 to study physiological optics.
Ames began working at Dartmouth College following World War I, and eventually became research director of the short-lived Dartmouth Eye Institute. At the DEI he led research efforts concentrating on binocular vision, specifically cyclophoria—torsion that occurs when the eyes rotate in opposite directions—and aniseikonia, when each eye perceives an identical image to be a different size. Ames published 38 books and papers and held 21 patents. His work covered not only physiological optics but also the psychology of vision and perception. His son, Adelbert Ames III, is a professor emeritus of neuroscience at Harvard.
Ames’ interest in optical illusions may stem from his background in visual art and his interest in the psychology of perception. The Ames room, perhaps his best-known illusion, asks an observer to view a room through a pinhole in one of the walls. The viewer perceives the room to be square, but in reality it’s trapezoidal, so that a person walking from corner to corner appears to grow and shrink. Ames’ original design also included a groove that transported a ball across the room, giving an “anti-gravity” illusion in that the ball appears to roll uphill. TV and movie productions frequently use the Ames room technique to create the illusion that one character is much taller than the rest. The Lord of the Rings trilogy, for example, used several Ames room sets when filming hobbits next to the much-taller Gandalf.
The Ames window is a flat piece of cardboard illustrated with panes to appear as a window. To the observer it appears as a rectangular window oriented toward a focal point, but in reality the cardboard is trapezoidal. The illusion becomes more complex when the window is attached to a rotating shaft; if the viewer assumes that the window is rectangular, it appears to oscillate and rotate at less than 180 degrees. After Ames’ death, psychologists used the window experiment to test whether a viewer’s mental expectation of the rotation could affect their actual perception.
An unusual illusion is the Ames chair experiment. A viewer sees three images through different peepholes, and all three appear to be a line drawing of a chair with a solid white seat. But when shown the actual objects, viewers find that only one object is an actual chair, and it was only the viewing angle that caused the other two to appear that way. In fact, one of the objects, the bottom-middle one in this image, is a mess of wires in front of a backdrop with a white shape painted on it and appearing as the “chair’s” seat. Ames used the illusion to show the inherent ambiguity behind perception.
This blog has occasionally focused on optical illusions and impossible constructs—here’s Part 1 and Part 2 of the impossible object series. This post will take a look at one of the earliest documented cognitive optical illusions, Troxler’s fading.
Ignaz Paul Vital Troxler (1780-1866) was a Swiss physician, philosopher and politician who worked in those capacities in Lucerne, Aarau, Basel and Berne. In 1804 Troxler noticed that when he focused his vision on a central object for a long period, visuals in his peripheral field faded and disappeared. He published his findings that same year in Ophthalmologische Bibliothek, the first ever ophthalmological journal.
Troxler’s fading exploits the adaptability of the brain’s sensory systems. In short, neurons strongly respond to a novel stimulus but become less responsive when the stimulus is deemed constant or static. To demonstrate the specific Troxler effect, a subject is instructed to focus on a central point in an image. Light reflected from a stimulus enters the eye and an inverted image is projected onto the retina. The retinal cells gradually decrease their sensitivity to the static stimulus peripheral to the point of focus and transmit information to the lateral geniculate nucleus (LGN), the area of the brain responsible for perceiving peripheral stimuli away from a fixation point. The LGN aids in the process of neural adaptation that causes a decrease in response to the constant stimulus. Finally, the LGN relays the visual image to the primary visual cortex, which fills in the area behind the disappeared stimulus. You can test it yourself by focusing hard on the dot in the image or the cross in the video.
A related tactile effect can be tested by placing a hand on a wall or other surface. When a person’s hand first touches the wall, the surface is felt most acutely, but as the hand is left in contact for a longer period the sensation fades.
On a biographical note, Troxler is all but forgotten except in regards to the optical illusion he documented, but he made some waves in early 19th century Europe. His 1828 magnum opus Naturlehre des menschlichen Erkennens oder Metaphysik [The nature of human knowledge or metaphysics] reflected the primitive state of vitalistic science at the time, but it also contains some surprisingly forward-looking psychological concepts of perception, consciousness and the nature of the self. He was also one of the first doctors to advocate for mass vaccination and federal oversight of physician exams.
Ikutaro Kakehashi, an electronic music legend who founded the Roland Corporation in the early 1970s and pioneered digital music standards in the ‘80s, died last week at the age of 87.
Kakehashi started his musical career in Japan repairing electronic organs while running his own electrical appliance shop. In 1958 he decided to devote his career to designing an ideal electronic musical instrument and founded Ace Tone in 1960. Ace Tone primarily manufactured electronic organs and guitar amplifiers, but Kakehashi’s passion was developing an electronic drum. After a few prototypes, he patented an “Automatic Rhythm Performance Device” in 1967. Kakehashi used a diode matrix circuit involving a number of inverted circuits connected to a counting circuit. The circuits’ synthesized output became the desired rhythmic sounds. He commercialized the design as the FR-1 Rhythm Ace, essentially the first drum machine, featuring 16 preset rhythms and four manual percussion sounds.
Kakehashi left Ace Tone to start the Roland Corporation in 1972. He continued to improve his drum machines and introduced several new models before releasing the iconic TR-808 in 1980. By this point drum machines were becoming popular in New Wave and electronic music, and several rival manufacturers were already making digitally sampled models. The 8-bit Linn LM-1, which debuted that same year, was the first device to use digital sampling of acoustic drums and also one of the first programmable drum machines, but it retailed at a whopping $4,995. (Here’s a video demo of the LM-1, showing its superior sounds.) Despite the fact that microprocessors were becoming more common, the TR-808 used analog subtractive synthesis common to synthesizers of the previous two decades to reduce manufacturing and retail costs.
The TR-808 had an odd design history. Kakehashi hired rogue American musician and engineer Don Lewis, who was known to extensively modify electronic instruments for his own use, to design Roland’s drum machines. In the spirit of Lewis's unconventional approach, Kakehashi deliberately ordered faulty transistors to give the drum machine a characteristic sound. The unique cymbal tone was supposedly discovered when a Roland engineer spilled tea on a breadboard prototype, and the design team had to work for months to recreate the pssh sound.
Despite retailing at less than half the price of digital drum machines, the TR-808’s unrealistic sounds made it a commercial flop and production ceased in 1983. It picked up a cult following, however, and is heard on many hit songs starting with Marvin Gaye’s “Sexual Healing” in 1982. Most hip-hop groups of the ‘80s used the TR-808 to create their beats, and it’s still heard regularly in mainstream pop and hip-hop. Rapper Kanye West's 2008 album 808s & Heartbreak is an ode to the device, and West used it on every track.
During the TR-808’s run, Kakehashi began promoting the idea of digital music standardization. Talks with other electronic instrument manufacturers led to the introduction of the Musical Instrument Digital Interface (MIDI) standard in 1983. MIDI allowed interoperability between any type of digital instrument, provided a standard voice library for digital keyboards, and allowed a single controller to play several digital instruments at once. Over 30 years later, MIDI is still the dominant technical standard for digital music.
Kakehashi retired from Roland in 2013, and the company still manufactures keyboards, synthesizers, stage pianos, recording equipment, and digital music software. While his name may never be a household one, his influence and legacy are felt and heard throughout the digital music world to this day.