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$45 million for a viola? It's a Strad, but...

How much is that viola in the display case?

Not $45 million—that was the asking price by Sotheby's, but it didn't sell, the auction house said Thursday.

"Sadly not," said Dan Abernethy, a Sotheby's spokesman. "There was interest, but there were no bids at or near 45."

David Aaron Carpenter, the virtuoso violist, holds "The Macdonald" at Sotheby's New York on March 27, 2014.
Stan Honda | AFP | Getty Images
David Aaron Carpenter, the virtuoso violist, holds "The Macdonald" at Sotheby's New York on March 27, 2014.

Violas, which are larger and have a lower pitch than violins, have been the butt of musician jokes for generations. Among them:

What do a viola and a lawsuit have in common?
Everyone is happy when the case is closed.

Did you hear about the violist who played in tune?
Neither did I.

But this one is no joke. Not only is it a Stradivarius, it's extremely rare.

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The $45 million price for "The Macdonald" Strad would have been a record for any musical instrument sold privately or at auction, according to Sotheby's. The top price was $15.9 million for a musical instrument—the 2011 sale of the 1721 "Lady Blunt" Stradivarius violin. The "Lady Blunt" was sold by the Nippon Music Foundation, which used the proceeds to aid victims of Japan's 2011 earthquake and tsunami.

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"The Macdonald" was crafted by Antonio Stradivari in 1719, during the master's "golden period," and is one of only two Strad violas still in private hands. It was named for the 3rd Baron Macdonald, Godfrey Bosville, who acquired it in the 1820s.

It was being sold by the estate of Peter Schidlof, co-founder of the Amadeus Quartet who acquired it in 1964 and died in 1987.

"The finest of all the violas is generally agreed to be 'The Macdonald' of 1719," Tim Ingles, director of the London-based fine instruments auction house Ingles & Hayday, said in a video on Sotheby's website.

About 600 instruments made by the Cremonese master survive, but only 10 are violas, said Ingles, whose company conducted the sale with Sotheby's.

Check out the video here.

"To any passionate musician there is something mystical about it, as if it were the holy grail of string instruments," said violist David Aaron Carpenter, whose video demonstration of the instrument is on Sotheby's website. "Modern violas have tried to imitate it but never equaled it. If I had to compare it to another field of creation, I'd say it's like asking an art lover to choose between the 'Mona Lisa' and a perfect reproduction of the 'Mona Lisa.' Unimaginable!" he wrote on the website.

It's the second time in less than a month that a high-priced Strad failed to sell. Christie's had offered a Strad violin owned by the late reclusive heiress Huguette Clark. The presale estimate was up to $10 million, but the auction house failed to find a buyer.

Read MoreHuguette Clark's Stradivari violin expected to fetch millions

Abernethy wouldn't say whether the viola would be offered at a reduced price.

Now that "The Macdonald" didn't sell, maybe the failure will give birth to a new viola joke. Did someone just say: "Not So Big Mac?"

—By CNBC's Marty Steinberg

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