Last week the Royal Scottish National Orchestra moved into its new home last week; last night it gave its first public performance there. The so-called RSNO Centre is a substantial extension around the back — or the front, depending on how you look at it — of the Glasgow Royal Concert Hall. If it’s tricky to visualise exactly what used to fill that north-facing stretch of Killermont Street, that’s probably because it wasn’t much to look at in its previous guise as a service yard. Now the facade is clean, glassy, functional. Across the road at Buchanan Bus Station, the glory that is George Wyllie’s Clyde Clock kicks us cheerfully toward the Concert Hall’s revamped entrance.

The inaugural brochure for the space is emblazoned with a bold slogan: “NEW HOME: NEW DIMENSIONS”. First and foremost, the RSNO Centre is a state-of-the-art rehearsal room for the orchestra, which until last week had been preparing its programmes a couple of miles west across town in the Henry Wood Hall. That former church had a certain faded charm, not to mention proximity to the zillions of hip lunch spots of Finnieston, but acoustically it was a washy non-starter. There was a joke going around last week at the orchestra’s first rehearsal in the new space. One musician says to another, “wow, we’ve been colleagues for years and today is the first time I’ve really heard you.” The other musician replies, “exactly; can we go back to Henry Wood Hall, please?”

All joking aside, the new space has the potential to work wonders for the RSNO. Think of the knock-on effect of daily rehearsals in high-definition sound. Individual playing and ensemble cohesion will benefit. Conductors will be able to delve into more forensic detail. Who knows; maybe the change in listening culture will enable the orchestra to venture into more intricate corners of the repertoire. New dimensions might well be in store.

But the RSNO Centre is more than simply (simply!) a swank new rehearsal space. This is a public concert venue, too, with fine-tuneable acoustics, capacity to accommodate an audience of up to 600 and balcony seating that can be added or removed to suit the occasion. The orchestra’s full-scale concerts will still take place on the main stage of the Concert Hall, but the new space will host chamber recitals and ensembles like Alchemy, the RSNO’s fledgling contemporary music project.

This is also where the orchestra will record, where its administrative offices are now located and where various multi-media education projects will be filmed and streamed across the country. “Four in one!” is the excited phrase I keep hearing from RSNO quarters. Incidentally, the building’s name is yet to be finalised. If anyone out there is feeling particularly generous, there is still the option to secure your name in lights above the entrance.

Downsides? The visuals are nothing to write home about. The RSNO Centre is owned by Glasgow City Council and was designed by the Council’s in-house architect department under the same chief architect, Kerr Robertson, who revamped Glasgow’s City Halls a decade ago. There is a standard-issue municipal feel to the surface aesthetic of the place: those thick, brushed-steel banisters, that veneer flooring, those chunky, plasticky air vents. The auditorium has the vibe of a school gym, maybe a basketball court.

But here’s the thing. The building cost around £19million, with funds contributed from Glasgow City Council, the Scottish Government, Creative Scotland, private and trust sponsors as well as £12million the RSNO itself. That cost isn’t a great deal more than the £14.5million that Scottish Opera spent on its new Theatre Royal foyer extension a couple of blocks away on Hope Street. The RSNO Centre might not look hugely stylish, but to acquire a new rehearsal space, recording studio, education hub, concert venue and office block for the same price as a posh lobby seems rather good value.

The new space was proposed in 2010 and was originally supposed to open in time for the Commonwealth Games. Instead — these things always taking longer than planned — the building arrives at the start of the RSNO’s 125th anniversary season and one month into the tenure of the orchestra’s new Chief Executive, Krishna Thiagarajan. A pianist-turned-arts-administrator who moved to Glasgow with his family at the end of July, the German-born Thiagarajan has spent the past couple of decades in the United States where he held senior management posts at the Orpheus Chamber Orchestra, Symphony in C and the Rochester Philharmonic Orchestra. He’s a compact, bright-talking operator with the shiny confidence of someone who has thrived in the American culture of arts philanthropy.

“I grew up in Dortmund,” he tells me cheerfully, “which is a heavily industrialised city in Germany, so I wasn’t about to be put off by Glasgow’s industrial heritage. To be honest, this move is a chance for all of my family to reconnect with Europe and we are all happy about that.” The only reason why the move to Glasgow doesn’t yet feel complete, he says, is that his beloved 1922 Steinway Model A is currently stuck States-side, awaiting certificates for its ivory keys.

Thiagarajan describes his transition from musician to arts administrator as something that crept up on him. “I was always entrepreneurial,” he says, “and I always enjoyed helping friends organise concerts.” During a couple of years off between completing his Master’s and starting his doctorate — whose thesis explored changes in sonata form at the turn of the last century, with particular focus on Alban Berg’s Opus One Piano Sonata — he found himself planning concert series in his home state of North Rhine-Westphalia.

When he returned to the States he joined the education department at Rochester Philharmonic and within six months was promoted to artistic planner. “I wanted to make an effect on a larger scale,” he says. “I like to focus on getting things done rather than politics, but I also have the diplomatic skills when required. I think people took to that mix.”

Are American models of private arts funding applicable in the UK? “Yes and no,” Thiagarajan ponders. “It’s true that I’m still learning how to navigate the codes of government funding here. At the same time, we are finding ourselves in a period when government funding is being evaluated. I suspect my skills from my previous life will very much come in handy.”

Thiagarajan has faith in touring and recording — neither conventional orchestral money-makers — to raise the international profile of the RSNO. He won’t specify what at this point, but he does allow that the facilities now imbedded at the RSNO Centre mean more frequent recordings are most definitely on the cards. “I made my decision to come to here because I was hearing recordings of the orchestra on American public radio while I was driving in my car to and from Manhattan. Great recordings from the Gibson, Järvi and Deneve years. There are a huge number of Scots abroad who have reason to stay in touch with their home orchestra. There are a huge number of music fans everywhere who deserve to hear this orchestra.”

The RSNO Centre is now open on Killermont Street, Glasgow