“Orange Blossom Special”? Yes, that was the famous bluegrass fiddle tune the Miro String Quartet was furiously fiddling its way through in Calgary in September at the first Honens International Piano Festival.

And yes, again, the same Miro Quartet can be heard playing Mozart, Glière, Franck and Schubert Thursday for Music Toronto at the St. Lawrence Centre’s Jane Mallett Theatre.

An ensemble with a split personality? Not exactly. It just so happens that William Fedkenheuer, the quartet’s second violinist, hails from the Alberta metropolis and used to specialize in country music as a member of the Calgary Fiddlers.

“I grew up with this music,” Fedkenheuer acknowledged by phone the other day from Austin, where the Miro is quartet in residence at the University of Texas’ Butler School of Music. “My violin teacher was the wife of the founder of the Calgary Fiddlers. I toured with them all across Canada and as far as Japan.”

It was as a student at Rice University in Houston that the native Calgarian fell in love with string quartets and it was in 2011 that he joined the Miro, 13 years after his colleagues had won first prize at the Banff International String Quartet Competition.

Now one of the continent’s leading chamber ensembles, the Miro is celebrating its 25th anniversary this year, and because 2020 happens also to be the 250th anniversary of the birth of Beethoven — “luvely, luvely Ludwig van,” as Alex called him in Anthony Burgess’ novel “A Clockwork Orange” — the German composer features prominently in its schedule, in the form of a complete recording of his 16 string quartets, released six weeks ago in a boxed set on the Pentatone label.

A 2005 set of the Op. 18 quartets had announced the Miro’s arrival on compact discs, now this new album the culmination of 14 subsequent years of recording.

And yet Thursday’s program contains not one note of Beethoven, because in Toronto the Miro will be replicating a 25th-anniversary program played by North America’s first quartet to tour regularly — the Kneisel, back in 1910.

As one of its own silver-anniversary undertakings, the quartet is touring this season with what it calls its Archive Project — a rotating set of three programs performed by distinguished predecessors, the Flonzalay and Kolisch Quartets as well as the Kneisel.

Times have obviously changed musically since 1910. In one of his volumes of memoirs, the pianist-wit Oscar Levant recounts an occasion in the 1930s when the Flonzalay performed at a party hosted by a rich Los Angeles socialite. At the end of the performance, Levant recalls, the socialite thanked the quartet, offering some extra money so the players could expand their band.

In his early years John Largess, the Miro’s violist, actually studied with Eugene Lehner of the Kolisch Quartet and all four Miros seem conscious of their debt to the players of the past.

The Kneisel Quartet knew Dvorak and even premiered his “American Quartet.” Typical of ensembles of the era, it also presented more varied programs than are typical today.

As an example, the 1910 program the Miro is reviving for Toronto includes the solo “Fantasie sur deux Airs Russes” by the Belgian composer Servais, because Alvin Schraeder, the Kneisel’s cellist, happened to be a virtuoso.

Whether the Kneisel would have played something similar to the “Orange Blossom Special” is, of course, another question.

Today’s concert programs tend to be more narrowly focused than their early 20th-century counterparts. On the wall of my study hangs a Berlin Philharmonic program from 1900 conducted by Arthur Nikisch, featuring Glazunov’s Sixth Symphony, excerpts from Berlioz’ “Damnation of Faust” and character pieces by Heinrich Hoffman, with Saint-Saens’ Third Violin Concerto and solos by Bach and Beethoven played by the Belgian violinist Eugène Ysäye.

But has the standard of playing risen since then? Look at the Miro’s facsimile programs this season from 1929 and 1935 and you will find music by Berg, Bloch and Bartok that continues to challenge players today.

Nevertheless, would any of these earlier players have been able to play the cycle of Elliott Carter quartets as I heard them played several years ago at a contemporary music festival in Buffalo by the Juilliard Quartet? I frankly doubt it. Technically, the standard surely has risen.

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But the musical standard? Again we face another question. Listen to Artur Schnabel’s pioneering recording of the Beethoven piano sonatas, from more than 80 years ago, and you will find plenty of evidence of struggle. You will also find insights many of today’s pianists might envy.

The Miro Quartet is very much an ensemble of today. It is also an ensemble with an appreciation of the tradition that has nourished it.