This was a concert made in heaven. To hear Per Nørgård's Iris, one of a triptych of symphonic poems composed in the late 1960s, eerie and mysterious, and underlain by the influences of Sibelius and Nørgård's teacher and fellow-symphonist, Vagn Holmboe, would make a rich and rewarding enough occasion in itself. But to follow that with Nielsen's explosive, ear-shattering postwar Fifth Symphony, let alone to insert in between the more theatrical drama of Schoenberg's panicky horror-monologue Erwartung, meant the Royal Danish Orchestra offered Symphony Hall’s sophisticated audience a superlative, dazzling display.

This time-hallowed ensemble has roots dating back five and a half centuries, and plays as pit orchestra to Copenhagen’s leading opera house. Carl Nielsen played violin in, and conducted, this impressive orchestra. Michael Schønwandt, music chief at the Royal Danish Opera, was its principal conductor from 2000 to 2011, a post now occupied by Michael Boder.

What an appointment that was. Nothing seemed unprepared or ineptly treated. Dynamics, balances and pacing seemed just to fall into place. Nørgård, with six operas and eight symphonies to his credit, has no problem turning to the more compact genre of the symphonic poem. Yet Iris is a work of weight; in its elaborate working out you get an idea of the intensity of the workmanship. Initially we almost sense ourselves looking at a myriad of constellations, from some remote Lappland vastness. The work is carefully sectioned, with brass especially marking out the transitions to certain new stages. It ebbs and wanes, comes and goes, with a return to the shimmering start proclaimed by a stunning passages for three flutes (Nørgård's orchestra is large, but the refined colours he evolves from it are quite resplendent). The way Boder kept the brass restrained, and the players responded to those instructions, was impressive. Percussion plays a key role, right to the parting twang of a soft gong.    

How can one sum up Erwartung, a psychodrama so wildly expressionistic as to make Wozzeck seem rather tame? Though composed before the Great War, in 1909, it was not premiered till 1924 – just at the time Schoenberg was polishing and publishing his strict twelve-note principles. The spectacular score of Erwartung (Expectation) often sounds as if he had arrived there already: it feels more proto-dodecaphonic than advanced atonal, though this is partly due to its Pierrot Lunaire-like Expressionist conception.

The text was by Marie Pappenheim, and appears as graphic as the poetry of Richard Gerstl, who briefly stole Schoenberg's wife from him. Indeed the whole exercise seems to hover on the edge of suicide: “Yellow, open eyes...How they stare! No beast, dear God, no beast! I feel such fear”;... “Tis the bloodless moon seems to paint in blood”...“Trapped, am I? ... No, but something is crawling”; ... “Oh so broad a streak of blood...The heart must itself be bleeding”. The Polish-born soprano Magdalena Anna Hofmann is familiar with this kind of nervy repertoire (her credits include the edgy, dream-haunted Mother in Dallapiccola's Il Prigioniero and the seduced, consumptive Carlotta in Schreker's Die Gezeichneten). She sang the role heroically, from memory: a forceful, apt and driven performance. I didn't feel she caught, with her body language, gestures or (admittedly restricted) scope for movement, the visual and dramatic intensity of the role. She had two or three gestures – hands across chest or covering her eyes – but that was all. No director is credited: she patently needed direction. Thus in a very appreciable reading when listened to, an opportunity was missed. The orchestra navigated Schoenberg's far from easy score effortlessly. Boder achieved utter clarity: you heard everything, which is exactly what Schoenberg was striving after. Utterly driven, fascinating when trilling piccolos take the stage or the bassoon trudges, then ripples gradually away: all this was marvellously executed.

And so to Carl Nielsen, and that ongoing 150th anniversary. The first of the Fifth Symphony's two prolonged movements started as it went on: arrestingly, grippingly, with that distinctive Nielsen modalism, like a kind of medieval false relation; there is a surge of chattering massed woodwind; bassoons then flutes accompany an exposed passage for violas alone; canonic, counterpointed horns and an oboe melody over celesta tweeting away on the same note like a kind of bizarre drone; the use of timpani as a kind of transitional pedal point; or the moments when the composer cuts back the orchestra like a shorn hedge so that the refined build-up sounds almost like a Renaissance motet: all these were a signal success with these well-informed players.

Nick Breckenfield's programme notes analysed the work assiduously, but in easily followable language. The impertinent side drum gives a quick whimper some time before it arrives properly. But then its intrusion begins sooner than one expects. Delicious detail included what must, I think, have been an alto flute; but duly on cue arrives the clarinet, the only instrument bold or foolhardy enough to take on the insistent drummer. It's the purified, more pared-down touches where Nielsen so excels here; the use of a second, off-stage and the clarinet's final pirouetting.

Almost for the first time, I listened properly to Nielsen's second movement. Often one is either so exhausted by the drummer's antics in Part One that one has to have a rest – or else can't wait to put the first movement on again. The trumpets came out splendidly here, yelping with a kind of added apoggiatura; the interval of a minor third, which seems to figure prominently in this symphony, appears in the string's long melody. The Copenhagen timpani beat so loud I jumped. But this orchestra knows its fellow countryman's music backwards. Hence so many moments of pacing – even telling silences – really told. What could one compare it to? 20th century Berlioz? There is a mighty first fugue, and then a free-as-air second one, neither of them sounding contrived. The brass has a final flourish and then it's all over.

I should have anticipated the quality of this orchestra, especially with Boder, a real force to be reckoned with, at the helm: equally, the quality of Stefan Parkman's Danish Radio Choir should have reminded me of the greatness that emanates from the Danish capital. I was cheered and uplifted by every note of this concert, as one might be by a Hans Christian Andersen tale: what a treat.