Digital Harmony (John Whitney, 1980)

Digital Harmony is a book by the American animator John Whitney (1917–1995), published in 1980. In it he described the principle behind the computer films he had made since the late 1960s: picture and music can be built on the same kind of harmony, with movements in whole-number ratios to each other.¹

From cams to computers

Before he worked with digital computers, Whitney made films on an analogue machine he had built from a wartime anti-aircraft gun director; that machine and the film Catalog (1961) are described in the note on John Whitney's Catalog.² In 1966 IBM took him on as artist in residence, the first major corporation to have one, and until 1969 he worked with the company's digital computers. Jack Citron wrote the programs for the IBM 360.^1, 2

His first computer film there was called Homage to Rameau, after the composer whose Treatise on Harmony (1722) had given Whitney his direction. In the films that followed, Permutations (1968), Matrix I–III (1971–72) and Arabesque (1975), he showed what he called "harmonic progression". The film historian William Moritz sees the book as the culmination of that work.¹

The principle

Give every element of the picture its own speed. "If one element were set to move at a given rate, the next element might be moved at two times that rate."³ The third moves three times as fast, and so on: the same ratios as the harmonic series in music. Because every speed is a whole-number multiple of the slowest, all the elements line up again each time the slowest has gone round once.⁴

Between those moments the elements form figures. When the slowest element has gone a fifth of the way round, every fifth element is back in the same direction, and the line through them draws a five-pointed figure; at a third of the way round, a three-pointed one.

New drawing

The same whole-number ratios make the closed curves in Lissajous figures and the Spirograph. The wider history of art made from rules and systems is in JAEV's Generative Art.