It is not just his “big” band. Everything about the music of Pedro Giraudo is vast, enlarged in space, time and ambition, extended to the far-off horizons that the sounds he makes compel us to visualize. His compositions feel as though they traverse landscapes, squeezing whole journeys into musical adventures that set out as from one distant outpost to another, now an easy walk, then an arduous climb, then those moments when the breath must be caught, then the glimpse of a destination that, it turns out, the trick of an eye made seem closer than it turns out to be, and so the slog and the last push and the little hint of joy in the spry final steps that bring you to it.

That, it seems to me, is the basic structure of Giraudo’s jazz pieces, a few of which I listened to over brunch on Sunday at the Blue Note. There is a touch of genius in Giraudo – who but a person of deep talent could envision such pieces, whether they are literally inspired by the landscapes of his native Argentina, or by lines of poetry, or passages from Martin Fierro, the epic work that I have heard called the Argentine Iliad and Odyssey and to which I must one day turn my attention? At times, when he is not playing one of the string instruments that are his direct contribution to the sound he has envisioned, you can see him closing his eyes and re-living an imagined journey, as his caravan of musicians re-create its every rest and respite, its easy trots and heavy lifts.

I think that one day – unless it has without my knowledge already happened – his big band belongs in a great hall in this city, Carnegie, City Center, Town Hall, Lincoln Center, take your pick: he belongs there, for he presses the limits of the little spaces I have seen him in. The walls of a place like the Blue Note want to curve outwards, like a lung filled to bursting, not due to loudness (for Giraudo never strains the listener’s ear) but because of the limitless range of his musical vision. That his frequent guest vocalist is Sofía Tosello, who on Sunday gave us a rest from the band’s musical odyssey with a rousing, hand-clapping folk song called “Viernes de Salamanca,” makes him all the more indispensable.

The Pedro Giraudo Big Band will perform Dec. 10, 2015, at Zinc Bar. For information, click here.