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Schoenberg, who was not really proficient on any instrument, used to go through his completed compositions in his head, with a stopwatch; then dividing the final time by the number of bars, reached a metronome mark. That is why all his metronome marks are either impossible to play, or ridiculous to try.

Somehow this well-known habit of Schoenberg's, has been attributed to Bartok!

Walter Ramsey

Although I must say, the third movement of the Sonata for 2P + P confirms frighteningly well to the GS hypothesis.

Hmm :o)

As suggested here, I presume Bartok intended the timings to be a guide, and/or perhaps he worked out the timings exactly for his own purposes and included them on the score for the sake of completeness, I would if I were him, why leave them out when you bothered to calculate them? (not exactly evidence, but if we can only speculate, it will do)..........................................................

Re the golden section, all the analysis I have read either says nothing about the Golden Section (Elliot Ankoletz: The Music of Bela Bartok...its a been a few years since i read it but I dont remember any reference to golden ratios etc, nor in George Perle`s analysis, though most of that is harmonic, still, the 'theory' should hold, harmony is proportion too) or evidence is presented to the contrary....................................................

'..Musicologists such as Lazlo Somfai have debunked this notion. Somfai inspected "the complete existing source material of Bartok`s compositions as well as manuscripts of folk-music transcriptions, drafts of articles, and scattered scrap papers in the Hungarian and American estate.".

He observed that "not a single calculation of the proportions of a composition - with Fibonacci or other numbers - has been discovered," despite "the composers notorious lifelong habit of keeping and recycling every bit of paper." But the legend still lingers.

The idea of a Bartok-Fibonacci connection traces to the musicologist Erno Lendvai.

In his writings, he presented many examples from Bartok`s works, purporting to show how Bartok suffused that music.

Interestingly, even Lendvai stopped just short of claiming that Bartok deliberately used Fibonacci numbers and the golden ratio as compostional devices.

Rather Lendvai wrote, "I have no wish to prove that he aspired to an arithmetic or geometric system; he did, however, by going back to the roots of music, discover fundamental laws and "root" correlations which may be expressed by formula-like mathematical symbols".

The legend has since expanded to that of Bartok, the numerological composer.'..........................

The Math Behind The Music: Leon Harkleroad.................................

Harkleroad goes on to say that Lendvai basically shoehorned in connections to the golden section.......................

His six volume piano collection Mikrokosmos alone consists of 150 pieces. With such a body of music it would be miraculous if you could`nt find several instances in which the count for something or other turned out as a Fibonacci number or two counts stood approximately in golden ratio'...........................................

It seems this Fibonacci stuff is mythological, or perhaps more generously, has not been established, yet (a lack of evidence).

KG replies: Thanks for the update, I'd been wondering what current thinking has been. Although I must say, the third movement of the Sonata for 2P + P confirms frighteningly well to the GS hypothesis.

The do-the-math counting with a stopwatch only works if the movement has only one tempo. Since a lot of Bartok's works have different tempos inside movements, that means there are a lot of calculations being made. Not saying he didn't do that, just that it speaks to his potentially dogged determination.

Back when I reviewed concerts, I'd time movements so I could compare how fast Conductor A was versus Conductor B. I always gave a little bit of leeway when Mahler was on the program because of all the adjustments to a movement's basic tempo.

Durations of pieces are very important in 20th century because of recordings and broadcasts and royalties. Each piece that Bartok registers for GEMA must have duration. Bartók is just being a responsible 20th century musician.

I buy the Golden Section claim. Barkton was a proportion freak, everything was proportions inside proportions with him. My guess? He figured this stuff out down to the fraciton of a measure, then did math with the tempo to get the total duration. It's probably a misperception to think Barkok demanded that people get exactly that length when they played his stuff, more like "Okay, I've figured all these proprotional distribution of the measures out down to the last crotchet, so I'll give a total duration as an extra piece of info."

Sort of like those impossible metronome markings on Beethoven mss. Not because he expected folks to actually play that fast, but just to kick 'em in the ass and say, "Hey! Snap it up! This ain't that leisurely Haydn stuff, boys!"

Another possible explanation : Bartok was slightly obsessive-compulsive.

That might explain something I've always been curious about. Bartok did an edition of the WTC. It's fussy beyond belief -- you can hardly see the notes for the editorial articulations, phrase marks, and the rest. I always wondered what would motivate anyone to do that to Bach.

As far as I know,
Bartok never conducted.

there is such a thing as a conductor's stopwatch: if i remember correctly you conduct for six beats and it'll tell you the tempo you're at. my conducting professor at umass (e. wayne abercrombie, an excellent choral conductor, now retired) had one. god knows if they make them anymore. but you could perform a piece, then time six beats of it, then do the math to figure out how long the piece is. or maybe he got together with a friend and the friend timed the piece.

on the surface it seems anal to keep track of such information so meticulously, but having filled out many a grant proposal, i started keeping records of (approximately) how long ASM pieces are, because the powers that be want to know.

Another possible explanation : Bartok was slightly obsessive-compulsive. His son Peter seems to be the same way. As a record engineer, and somebody who also operated the cutting lathe for LP masters, you can ALWAYS tell if Peter Bartok was working on the disc, mostly on his own label BARTOK RECORDS but also some LPs for FOLKWAYS : just before the needle is led to the end grove, the last 20 seconds or so of groove before the spiral-in is silent. Always! And very visible. Again, why? (It MAY have something to do with reducing as much end-groove damage as possible to avoid distorting the music, but again, why only 20 seconds?)

I wondered about the golden section aspect as well, but always assumed that he actually would play his pieces through on his piano (even his orchestral works---Bartok was a formidable pianist and I am pretty sure composed at the piano).

Mr. Gann,
I'd always assumed they were connected in some way to the Golden Section aspect of his work. Mayhap that I assume it because it fits in with my geekiness?
Jason W Clark

KG replies: Well, I've read that too. I've always analyzed the golden sections in terms of beats or measures, but I suppose I should add up the timings and check the golden section hypothesis there. But I hoped someone would save me the trouble. And I would say that geekiness has more to do with the word "mayhap," but it probably has even more to do with analyzing Bartok in the first place. :^)