The Genius of J.S. Bach’s “Crab Canon” Visualized on a Möbius Strip

The most impres­sive of Johann Sebas­t­ian Bach’s pieces, musi­cophiles may have told you, will knock you over with their inge­nious­ness, or at least their sheer com­plex­i­ty. Indeed, the music of Bach has, over the past two and a half cen­turies, pro­vid­ed meat and drink to both pro­fes­sion­al and ama­teur stu­dents of the rela­tion­ship between inge­nious­ness and com­plex­i­ty. It’s no mis­take, for instance, that the com­pos­er has offered such a rich source of intel­lec­tu­al inspi­ra­tion to Gödel, Esch­er, Bach author Dou­glas R. Hof­s­tadter, well beyond hav­ing giv­en him a word to fill out the book’s title. Lis­ten to the first canon from Bach’s Musi­cal Offer­ing, and you’ll hear what sounds like a sim­ple begin­ning devel­op into what sounds like quite a com­plex mid­dle. You may hear it and instinc­tive­ly under­stand what’s going on; you may hear it and have no idea what’s going on beyond your sus­pi­cion that some­thing is hap­pen­ing.

If you process things more visu­al­ly than you do aural­ly, pay atten­tion to the video above, a visu­al­iza­tion of the piece by math­e­mat­i­cal image-mak­er Jos Leys. You can fol­low the score, note for note, and then watch as the piece revers­es itself, run­ning back across the staff in the oth­er direc­tion. So far, so easy, but anoth­er lay­er appears: Bach wrote the piece to then be played simul­ta­ne­ous­ly back­wards as well as for­wards. But pre­pare your­self for the mind-blow­ing coup de grâce when Leys shows us at a stroke just what the impos­si­ble shape of the Möbius strip has to do with the form of this “crab canon,” mean­ing a canon made of two com­ple­men­tary, reversed musi­cal lines. Hof­s­tadter had a great deal of fun with that term in Gödel, Esch­er, Bach, but then, he has one of those brains — you’ll notice many Bach enthu­si­asts do — that explodes with con­nec­tions, trans­po­si­tions, and per­mu­ta­tions, even in its unal­tered state. Alter­na­tive­ly, if you con­sid­er your­self a con­scious­ness-bend­ing psy­cho­naut, feel free get into your pre­ferred frame of mind, watch Bach’s crab canon visu­al­ized, and call me in the morn­ing.

Relat­ed con­tent:

A Big Bach Down­load: All of Bach’s Organ Works for Free

The Open Gold­berg Vari­a­tions: J.S. Bach’s Mas­ter­piece Free to Down­load

Glenn Gould Explains the Genius of Johann Sebas­t­ian Bach (1962)

Col­in Mar­shall hosts and pro­duces Note­book on Cities and Cul­ture and writes essays on lit­er­a­ture, film, cities, Asia, and aes­thet­ics. He’s at work on a book about Los Ange­les, A Los Ange­les Primer. Fol­low him on Twit­ter at @colinmarshall.

Mathemusician Vi Hart Explains the Space-Time Continuum With a Music Box, Bach, and a Möbius Strip

Vi Hart, the Khan Acad­e­my’s res­i­dent “Recre­ation­al Math­e­mu­si­cian” turns the space-time con­tin­u­um into some­thing that can be played for­wards, back­wards, upside down, in a cir­cle, and on a Möbius strip.

How you ask?

Music. You know, that stuff that Shake­speare rhap­sodized as the food of love?

The fast-talk­ing Hart has way too much to prove in her less than eight minute video to waste time wax­ing poet­ic. To her, even the most elu­sive con­cepts are explain­able, rep­re­sentable. She does man­age to cre­ate some unin­ten­tion­al­ly love­ly lit­tle melodies on a music box that reads holes punched through the nota­tions on a tape print­ed with a musi­cal stave.

It took sev­er­al view­ings for me to wrap my mind around what exact­ly was being demon­strat­ed, but I think I’m begin­ning to grope my way toward what­ev­er dimen­sion she’s cur­rent­ly inhab­it­ing. See if you can fol­low along and then weigh in as to what you think the math­e­mat­i­cal­ly-inclined Bach might be doing in his grave as Hart blithe­ly feeds one of his com­po­si­tions through her music box, upside down, and back­wards.

Relat­ed Con­tent:

How a Bach Canon Works. Bril­liant.

85,000 Clas­si­cal Music Scores (and Free MP3s) on the Web

A Big Bach Down­load – All Bach Organ Works for Free

Ayun Hal­l­i­day took piano lessons for years. All that remains are the open­ing bars to Hel­lo Dol­ly. Fol­low her @AyunHalliday

The Acoustic Guitar Project Gives Songwriters Worldwide a Guitar and One Week to Write a Song

The White Stripes’ song “Lit­tle Room” is all about re-con­nect­ing with the space of cre­ativ­i­ty with­in you—the “lit­tle room” where emo­tions become ideas—when you’re feel­ing over­whelmed (by suc­cess? Or maybe just kids, bills and the IRS). Their garage-rock dit­ty is a nice mar­riage of form and con­tent, the lyri­cal sim­plic­i­ty enacts the men­tal par­ing down Jack White rec­om­mends. No telling how often White goes to his “lit­tle room,” but he’s such a well­spring of song­writ­ing ideas, solo and in a con­stel­la­tion of side projects, that I’d guess it’s pret­ty often. As a song­writer myself, I have found White’s advice utter­ly unim­peach­able (which must be why I duti­ful­ly ignore it so often).

But the lit­tle room isn’t just a com­fort­ing place in the head, like Hap­py Gilmore’s hap­py place. It’s also a phys­i­cal space—differently arranged for artists of dif­fer­ent media. For the singer/songwriter, it’s gen­er­al­ly a famil­iar, seclud­ed place where you can put all of your focus on a gui­tar, a notepad, and a record­ing device (the sim­pler the bet­ter). That’s the space con­jured up by The Acoustic Gui­tar Project, “cre­at­ed to help musi­cians recon­nect to the orig­i­nal moment that inspired them to be singer-song­writ­ers.” Con­ceived in April, 2012, the project’s stat­ed mis­sion is three­fold:

  • Inspire artists to take action.
  • Tell sto­ries from a truth­ful, mean­ing­ful point of view.
  • Strive to give peo­ple some­thing to believe in.

If these goals sound a lit­tle too vague and pollyan­naish to com­mu­ni­cate much, lis­ten to the won­der­ful sim­plic­i­ty of The Acoustic Gui­tar Project’s premise: 1) the project selects a musi­cian, and pro­vides him or her with an acoustic gui­tar and a hand­held recorder. 2) the musi­cian must pro­duce an orig­i­nal song with­in one week, using only the equip­ment pro­vid­ed. 3) the musi­cian, once fin­ished, choos­es the next musi­cian for the project, and, I sup­pose, “pays it for­ward.”

It’s a real­ly neat idea, and you can see the results on the site, which fea­tures over forty singer/songwriters so far who have been passed the gui­tar. Each musi­cian has their own page with a pro­file, pho­to, and the audio and lyrics of their song. The first three stages of the project took place in New York City, Helsin­ki, Fin­land, and Bogo­ta, Colum­bia, respec­tive­ly, and the fourth stage moves to Port-au-Prince, Haiti. Joel Wald­man of Bogo­ta is one of these brave trou­ba­dours. You can see him per­form his song, “Como Una Lla­ma” (Like a Flame) live above. (See Joel’s page for the lyrics to his song, in both Span­ish and Eng­lish.)  In the video below, Joel very thought­ful­ly dis­cuss­es the feel­ing of writ­ing a song—a process, he says, of com­bin­ing infor­ma­tion and inspi­ra­tion.

Relat­ed Con­tent:

James Tay­lor Gives Free Acoustic Gui­tar Lessons Online

The Best Music to Write By: Give Us Your Rec­om­men­da­tions

Josh Jones is a writer, edi­tor, and musi­cian based in Wash­ing­ton, DC. Fol­low him @jdmagness

The Troggs Tapes: ‘Put a Little Bit of F***ing Fairy Dust Over the Bastard!’

Reg Pres­ley, lead singer of the Six­ties rock group The Trog­gs, died Mon­day at the age of 71. The Trog­gs (short for Troglodytes) are often men­tioned as a major influ­ence on the punk rock move­ment of the 1970s. They record­ed a string of hits between 1966 and 1968, most notably “Wild Thing.” The Trog­gs are also remembered—much to the band’s chagrin—for one of the most noto­ri­ous bootlegs ever: “The Trog­gs Tapes,” described by Uncut mag­a­zine as a “hilar­i­ous, 12-minute swearathon.”

The Trog­gs Tapes were record­ed in Lon­don in 1970. The band was work­ing on a song called “Tran­quil­i­ty,” but things weren’t going well, and the ses­sion degen­er­at­ed into a foul-mouthed orgy of acri­mo­ny and recrim­i­na­tion. A copy of the record­ing some­how made it onto the boot­leg mar­ket and became leg­endary. Sat­ur­day Night Live par­o­died the Trog­gs Tapes in a sketch with Bill Mur­ray, John Belushi and oth­ers play­ing a group of frus­trat­ed medieval musi­cians who say the word “flog­ging” over and over. The tapes are also par­o­died in This is Spinal Tap, dur­ing the record­ing scene at the “Rain­bow Trout Stu­dios.” In a piece this week pay­ing trib­ute to Reg Pres­ley, the Tele­graph music crit­ic Neil McCormick writes:

Before the inter­net, The Trog­gs Tapes were hard to find, yet every­one seemed to know about them, an elu­sive­ness that only added to their allure. I remem­ber get­ting my hands on a copy in a Dublin flea mar­ket, then sit­ting aroud late at night with friends laugh­ing our­selves sil­ly at the inani­ty and pal­pa­ble sense of frus­tra­tion as the musi­cians fail to find a way to artic­u­late and cap­ture some sound idea, beyond the reach of either their lan­guage or their tech­ni­cal abil­i­ties.… In truth, it is the kind of con­ver­sa­tion you can hear every day in record­ing stu­dios all around the world, but there was some­thing lib­er­at­ing and myth-bust­ing about the expe­ri­ence of eaves­drop­ping on these unguard­ed musi­cians at work.

You can lis­ten to an abridged ver­sion of The Trog­gs Tapes above. To learn more about Reg Pres­ley, you can read his fit­ting­ly uncon­ven­tion­al obit­u­ary in The Tele­graph. And to end things off on a pos­i­tive note, we offer a glimpse of The Trog­gs when things were going con­sid­er­ably more smooth­ly, with the band per­form­ing “Wild Thing” in 1966:

Relat­ed Con­tent:

Hear the 1962 Bea­t­les Demo that Dec­ca Reject­ed: “Gui­tar Groups are on Their Way Out, Mr. Epstein”

8,976 Free Grate­ful Dead Con­cert Record­ings in the Inter­net Archive, Explored by the New York­er

French Philosopher Jean Baudrillard Reads His Poetry, Backed By All-Star Arts Band (1996)

jean-baudrillard

Image by Euro­pean Grad­u­ate School, via Wiki­me­dia Com­mons

French post-struc­tural­ist philosopher/sociologist Jean Bau­drillard—usu­al­ly iden­ti­fied with his post­mod­ern the­o­ries of sim­u­lacra—is a lit­tle bit of a fringe fig­ure in pop cul­ture. Known to hip aca­d­e­m­ic types and avant-garde-ists, he’s maybe the kind of thinker who gets name-dropped more than read (and he’s no easy read).

But in the audio clip above, Bau­drillard reads to us, from his poet­ry no less, while backed by the swirling abstract sounds of The Chance Band, an all art-star ensem­ble fea­tur­ing Tom Wat­son (of The Miss­ing­men), George Hur­ley (of The Min­ute­men and fIRE­HOSE), Lynn John­ston, Dave Muller, Amy Stoll, and guest vocal­ist, the­o­rist Alluc­quère Rosanne (“Sandy”) Stone. It’s an odd, one-time, assem­blage of artists and thinkers UbuWeb describes as “unbe­liev­able but true!”:

Record­ed live as part of the Chance Fes­ti­val at Whiskey Pete’s Casi­no in State­line Neva­da, 1996. You’ve nev­er heard Bau­drillard like this before! Music to read Niet­zsche to.

Indeed. The track above is num­ber two on a twelve-track album called Sui­cide Moi, released in 2002 by Com­pound Annex Records. You can buy the CD here or stream and down­load indi­vid­ual tracks for free on UbuWeb.

Relat­ed Con­tent:

Avant-Garde Media: The UbuWeb Col­lec­tion

Der­ri­da: A 2002 Doc­u­men­tary on the Abstract Philoso­pher and the Every­day Man

Josh Jones is a writer, edi­tor, and musi­cian based in Wash­ing­ton, DC. Fol­low him @jdmagness

James Taylor Teaches You to Play “Carolina in My Mind,” “Fire and Rain” & Other Classics on the Guitar

Some days you’d think that Salman Khan was the only per­son who had the bright idea of putting tuto­ri­als on YouTube. But, if you’re an ama­teur gui­tarist, you know bet­ter. You know that gui­tarists have been post­ing free lessons on YouTube since Day 1, teach­ing new­bies how to buy an acoustic gui­tartune it by earstrum it, and play chord pro­gres­sions. And, what’s more, you can find clips that will read­i­ly teach you how to play your favorite tunes, whether it’s Bob Dylan’s Love Minus Zero/No Lim­it or Led Zep­pelin’s Kash­mir.

Think you just hit pay dirt? Well, it gets even bet­ter.

You can take lessons straight from James Tay­lor, the singer-song­writer him­self. On his YouTube chan­nel/web site, Tay­lor demon­strates how to file your nails, tune your gui­tar, and then start play­ing his clas­sic songs. Fire and Rain? JT has that cov­ered. Car­oli­na in My Mind? That too. And also Enough To Be On Your WaySec­ond Wheel, Lit­tle Wheel, and Coun­try Road. Stick around for a while and you might get “Some­thing in the Way She Moves” next.

Relat­ed Con­tent:

James Tay­lor Per­forms Live in 1970, Thanks to a Lit­tle Help from His Friends, The Bea­t­les

Jim­my Page Tells the Sto­ry of “Kash­mir”

A Young Eric Clap­ton Demon­strates the Ele­ments of His Sound

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Bruce Springsteen Performs “Growin’ Up” & “Henry Boy” When He Was an Opening Act (1972)

You’ll be hear­ing the name of Green­wich Vil­lage folk scene god­fa­ther Dave Van Ronk in the com­ing days, what with the Coen broth­ers upcom­ing Inside Llewyn Davis, a fic­tion­al­ized take on Van Ronk’s life based on his 2005 posthu­mous mem­oir (with Eli­jah Wald), The May­or of Mac­Dou­gal Street. And while Van Ronk’s is a name well-known to stu­dents of the 60’s folk revival, he nev­er achieved the fame of pro­tégés like Bob Dylan and Joni Mitchell. But there was anoth­er singer/songwriter and future super­star breez­ing through Van Ronk’s Vil­lage scene. I’m talk­ing about Bruce Spring­steen who, before he became an are­na rock sta­ple, opened solo for Van Ronk on acoustic gui­tar at Max’s Kansas City in 1972.

In the video above, watch Spring­steen play “Growin’ Up,” a song that appeared the next year on his debut album Greet­ings from Asbury Park, NJ. The album ver­sion of the song is the kind of rous­ing, anthemic fist-pumper Springsteen’s known for, but above, he strips it down to its essen­tials, and reveals that, like most every­thing he’s writ­ten, it’s a lyri­cal tour-de-force (which is prob­a­bly why Bowie record­ed a ver­sion). The 23-year-old Spring­steen also shows us that, band or no band, he was always a phe­nom­e­nal per­former. “Growin’ Up” is still a part of Springsteen’s set, no less anthemic, although the song takes on a much more nos­tal­gic air now that Spring­steen is six­ty-four. Below, watch a longer ver­sion of the clip, includ­ing MC Sam Hood’s intro­duc­tion and Bruce’s open­ing tune, “Hen­ry Boy.” If Van Ronk’s per­for­mance from that night made it on film, it hasn’t made it onto YouTube, but there are any num­ber of his inter­pre­ta­tions of old coun­try blues online.

Relat­ed Con­tent

Bruce Spring­steen Stumps/Sings for Oba­ma: A Free Six-Song Set

Heat Map­ping the Rise of Bruce Spring­steen: How the Boss Went Viral in a Pre-Inter­net Era

Bruce Springsteen’s Per­son­al Jour­ney Through Rock ‘n’ Roll (Slight­ly NSFW But Sim­ply Great)

Josh Jones is a writer, edi­tor, and musi­cian based in Wash­ing­ton, DC. Fol­low him @jdmagness

Fake Bob Dylan Sings Real Dr. Seuss

Five years ago, a 30-some­thing music pro­duc­er from Hous­ton, Texas got a big idea. Why not take his two favorite things — Bob Dylan and Dr. Seuss, of course — and mash them up into one orig­i­nal cre­ation. Hence came Dylan Hears a Who, a mock album that took sev­en Dr. Seuss clas­sics and put them to the melodies and imi­tat­ed voice of Mr. Dylan. The cuts went viral, giv­ing Dylan-Seuss fans world­wide the chance to enjoy cre­ative takes on Green Eggs and Ham (above); The Cat in the Hat; Oh, The Thinks You Can Think! (below); Too Many Dav­es; and The Zax. Soon enough, the songs fad­ed into YouTube obliv­ion, await­ing the day when a dig­i­tal archae­ol­o­gist would come along and do an exca­va­tion. Well, today’s the day. Enjoy!

Relat­ed Con­tent:

The Epis­te­mol­o­gy of Dr. Seuss & More Phi­los­o­phy Lessons from Great Children’s Sto­ries

New Archive Show­cas­es Dr. Seuss’s Ear­ly Work as an Adver­tis­ing Illus­tra­tor and Polit­i­cal Car­toon­ist

Bob Dylan Clas­sic, “For­ev­er Young,” Ani­mat­ed for Chil­dren

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