Arnold Schoenberg Creates a Hand-Drawn, Paper-Cut “Wheel Chart” to Visualize His 12-Tone Technique

“These go up to eleven,” Spinal Tap famous­ly said of the ampli­fiers that, so they claimed, took them to a high­er lev­el in rock music. But the work of Aus­tri­an com­pos­er Arnold Schoen­berg, one of the best-known fig­ures in the his­to­ry of avant-garde music, went up to twelve — twelve tones, that is. His “twelve-tone tech­nique,” invent­ed in the ear­ly 1920s and for the next few decades used most­ly by he and his col­leagues in the Sec­ond Vien­nese School such as Alban Berg, Anton Webern, and Hanns Eisler, allowed com­posers to break free of the tra­di­tion­al West­ern sys­tem of keys that lim­it­ed the notes avail­able for use in a piece, instead grant­i­ng each note the same weight and mak­ing none of them cen­tral.

This does­n’t mean that com­posers using Schoen­berg’s twelve-tone tech­nique could just use notes at ran­dom in com­plete atonal­i­ty, but that a new set of con­sid­er­a­tions would orga­nize them. “He believed that a sin­gle tonal­i­ty could include all twelve notes of the chro­mat­ic scale,” writes Brad­ford Bai­ley at The Hum, “as long as they were prop­er­ly orga­nized to be sub­or­di­nate to ton­ic (the ton­ic is the pitch upon which all oth­ers are ref­er­enced, in oth­er words the root or axis around which a piece is built).” The math­e­mat­i­cal rig­or under­ly­ing it all required some expla­na­tion, and often math­e­mat­i­cal and musi­cal con­cepts — math­e­mat­ics and music being in any case inti­mate­ly con­nect­ed — become much clear­er when ren­dered visu­al­ly.

Hence Schoen­berg’s twelve-tone wheel chart pic­tured at the top of the post, one of what Arnold Schoen­berg’s Jour­ney author Allen Shawn describes as “no few­er than twen­ty-two dif­fer­ent kinds of con­trap­tions” — includ­ing “charts, cylin­ders, book­lets, slide rules” — “for trans­pos­ing and deriv­ing twelve-tone rows” need­ed to com­pose twelve-tone music. (See the slide ruler above too.) “The dis­tinc­tion between ‘play’ and ‘work’ is already hard to draw in the case of artists,” writes Shawn, “but in Schoen­berg’s case it is espe­cial­ly hard to make since he brought dis­ci­pline, orig­i­nal­i­ty, and play­ful­ness to many of his activ­i­ties.” These also includ­ed mak­ing spe­cial play­ing cards (two of whose sets you can see here and here) and even his own ver­sion of chess.

As Shawn describes it, Koali­tion­ss­cach, or “Coali­tion Chess,” involves “the armies of four coun­tries arrayed on the four sides of the board, for which he designed and con­struct­ed the pieces him­self.” Instead of an eight-by-eight board, Coali­tion Chess uses a ten-by-ten, and the pieces on it “rep­re­sent machine guns, artillery, air­planes, sub­marines, tanks, and oth­er instru­ments of war.” The rules, which “require that the four play­ers form alliances at the out­set,” add at least a dimen­sion to the age-old stan­dard game of chess — a form that, like tra­di­tion­al West­ern music, human­i­ty will still be strug­gling to mas­ter decades and even cen­turies hence. But appar­ent­ly, for a mind like Schoen­berg’s, chess and music as he knew them weren’t near­ly chal­leng­ing enough.

Relat­ed Con­tent:

Vi Hart Uses Her Video Mag­ic to Demys­ti­fy Stravin­sky and Schoenberg’s 12-Tone Com­po­si­tions

The Avant-Garde Project: An Archive of Music by 200 Cut­ting-Edge Com­posers, Includ­ing Stravin­sky, Schoen­berg, Cage & More

Inter­views with Schoen­berg and Bartók

John Coltrane Draws a Pic­ture Illus­trat­ing the Math­e­mat­ics of Music

Based in Seoul, Col­in Mar­shall writes and broad­casts on cities and cul­ture. He’s at work on the book The State­less City: a Walk through 21st-Cen­tu­ry Los Ange­les, the video series The City in Cin­e­ma, the crowd­fund­ed jour­nal­ism project Where Is the City of the Future?, and the Los Ange­les Review of Books’ Korea Blog. Fol­low him on Twit­ter at @colinmarshall or on Face­book.

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