It may seem a small point, even an obvious one, but playing in tune makes a difference. In these days of high technical standards, most professional string quartets play in tune, pretty much. But it takes an ensemble like the Modigliani Quartet to remind one that, rather like the especially privileged denizens of George Orwell’s “Animal Farm,” some quartets are more in tune than others.

There is a world of difference between “around the note” and “smack in the middle of it.” And when musicians of the caliber of Philippe Bernhard, Loïc Rio, Laurent Marfaing, and François Kieffer achieve the latter level of execution, passages in the music that previously seemed knotty and impenetrable suddenly take on a pristine clarity, all supposed problems magically resolved.

Debussy’s String Quartet can sound, I will not say impenetrable, but somewhat turgid in texture and plodding in gait. When I first heard the Modiglianis play it, six years ago in Montreux, Switzerland, they threw dazzling new light on this sometimes underrated work. What was so remarkable about their performance was the linear independence they brought to music that is too often allowed to sound ploddingly simplistic in texture.

In anticipation of their appearance Tuesday evening in Meany Hall, I was a little nervous: Would they have maintained the standard they manifested back in 2007? I need not have worried. Their magisterial Debussy showed that they are even better now.

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Their program opened, enterprisingly, with the Quartet No. 3 by Juan Crisóstomo Arriaga, perhaps the most amazing of all the musical prodigies that history records. He was born on Jan. 27, 1806 – surely a sign of destiny, for that would have been Mozart’s 50th birthday – and he died at the age of 19, leaving an opera, a symphony, and three fine string quartets as a tantalizing glimpse of what might have been.

Next, on Tuesday, came Beethoven. In his music-critic days, George Bernard Shaw asked, “Why should I be asked to listen to the intentional intellectualities, profundities, theatrical fits and starts, and wayward caprices of self-conscious genius which make up those features of the middle period Beethovenism of which we all have to speak so very seriously, when I much prefer these beautiful, simple, straightforward, unpretentious, perfectly intelligible posthumous quartets?”

The Modigliani Quartet’s Opus 135 had all those qualities. Individual lines were easily audible within the overall texture, so that even the most heavily scored passages, especially in the finale with its blend of the epic and the childlike, emerged lucid and airily transparent. And it was not just players’ personalities that we were apprehending, but Beethoven’s ideas in all their invincible integrity.

Two encores — a Schubert piece, shaped with sovereign grace, and a Shostakovich polka, tossed off with cheeky insouciance — sent us home happy. Prediction is a dangerous business. But on the strength of the Modiglianis’ 10 years of achievement thus far, I do not think it excessively rash to suggest that their future will be a story of mastery further deepened.

Bernard Jacobson: bernardijacobson@comcast.net