Coltrane’s Circle of Fifths

From Open Culture:

Physicist and saxophonist Stephon Alexander has argued in his many public lectures and his book The Jazz of Physics that Albert Einstein and John Coltrane had quite a lot in common. Alexander in particular draws our attention to the so-called “Coltrane circle,” which resembles what any musician will recognize as the “Circle of Fifths,” but incorporates Coltrane’s own innovations. Coltrane gave the drawing to saxophonist and professor Yusef Lateef in 1967, who included it in his seminal text, Repository of Scales and Melodic Patterns. Where Lateef, as he writes in his autobiography, sees Coltrane’s music as a “spiritual journey” that “embraced the concerns of a rich tradition of autophysiopsychic music,” Alexander sees “the same geometric principle that motivated Einstein’s” quantum theory.

Neither description seems out of place. Musician and blogger Roel Hollander notes, “Thelonious Monk once said ‘All musicians are subconsciously mathematicians.’ Musicians like John Coltrane though have been very much aware of the mathematics of music and consciously applied it to his works.”

Etienne-Jules Marey and his Chronophotographic Gun


Marey, Etienne-Jules (1830 - 1904)

A polymorphic scientific, Etienne Jules Marey explored numerous techniques and disciplines, obsessed by one unique concept: movement. First interested in flight, he studied birds and imagined mechanical devices capable of flying. From 1878, he focused on movement within human beings and, inspired by Edward Muybridge he had met in 1881, used photography to document his research. He thus imagined, in 1882, a camera entitled photographic gun that enabled him to capture a moving subject in twelve poses. Etienne Jules Marey thus decomposed the gestures of men practicing sports, animals in motion, everyday tasks precisely observed and even the migration of air. He also invented the chonophotography that would be the precursor of cinema. Photography in its early days was the ultimate accomplice of reality but with Etienne Jules Marey (and Edward Muybridge), photography suddenly also captured the invisible.”


Marey, Etienne-Jules (1830 - 1904)

Marey started by studying blood circulation in the human body. Then he shifted to analyzing heart beats, respiration, muscles (myography), and movement of the body. To aid his studies he developed many instruments for precise measurements. For example, in 1859, in collaboration with the physiologist Auguste Chauveau and the watch manufacturer Breguet, he developed a wearable Sphygmograph to measure the pulse. This sphygmograph was an improvement on an earlier and more cumbersome design by the German physiologist Karl von Vierordt.[3] In 1869 Marey constructed a very delicate artificial insect to show how an insect flies and to demonstrate the figure-8 shape it produced during movement of its wings. Then he became fascinated by movements of air and started to study bigger flying animals, like birds. He adopted and further developed animated photography into a separate field of chronophotography in the 1880s. His revolutionary idea was to record several phases of movement on one photographic surface. In 1890 he published a substantial volume entitled Le Vol des Oiseaux (The Flight of Birds), richly illustrated with photographs, drawings, and diagrams. He also created stunningly precise sculptures of various flying birds.”


Marey, Etienne-Jules (1830 - 1904)

Marey studied other animals too. He published La Machine animale in 1873 (translated as “Animal Mechanism”). The English photographer Eadweard Muybridge carried out his “Photographic Investigation” in Palo Alto, California, to prove[dubious – discuss] that Marey was right when he wrote that a galloping horse for a brief moment had all four hooves off the ground. Muybridge published his photos in 1879 and received some public attention.”


Marey, Etienne-Jules (1830 - 1904)

Marey’s chronophotographic gun was made in 1882, this instrument was capable of taking 12 consecutive frames a second, with all the frames recorded on the same picture. Using these pictures he studied horses, birds, dogs, sheep, donkeys, elephants, fish, microscopic creatures, molluscs, insects, reptiles, etc. Some call it Marey’s “animated zoo”. Marey also conducted the famous study about cats always landing on their feet. He conducted very similar studies with a chicken and a dog and found that they could do almost the same. Marey also studied human locomotion. He published another book Le Mouvement in 1894.”

Newton’s colour circle

“In a mixture of primary colours, the quantity and quality of each being given, to know the colour of the compound.”


Newton's colour circle

from wiki – Throughout Opticks, Newton compared colours in the spectrum to a run of musical notes. To this purpose, he used a Dorian mode, similar to a white-note scale on the piano, starting at D. He divided his colour wheel in musical proportions round the circumference, in the arcs from DE to CD. Each segment was given a spectral colour, starting from red at DE, through orange, yellow, green, blew [sic], indigo, to violet in CD. (The colours are commonly known as ROY G BIV.)

The middle of the colours—their ‘centres of gravity’—are shown by p, q, r, s, t, u, and x. The centre of the circle, at O, was presumed to be white. Newton went on to describe how a non-spectral colour, such as z, could be described by its distance from O and the corresponding spectral colour, Y.