Later, she fills me in. 'I virtually camped in the bank, begging the manager to give me the money. One player in the orchestra was about to be evicted from his flat - he's only 18 and living away from his parents, so I was frantic.' The players' salaries for January finally came through from the bank earlier this month. In February the rouble devalued by another 40 per cent or so against the dollar: another test for the commitment of Ensemble XXI's cosmopolitan membership.
Players from Western Europe are hard to attract. Countries currently represented include Cuba, Vietnam, Finland, Ireland and Ecuador in addition to Russia itself and various republics once part of the Soviet Union. To O'Riordan, country of origin is an irrelevancy. 'I've only to listen to the playing of, say, our Vietnamese violist Thu Nguyen, to get very indignant about how much musicians are paid in the West.' Almost all the orchestra's members were trained at the Moscow Conservatoire by teachers in the line that produced the likes of Rostropovich, the Oistrakhs and Bashmet.
The long-term prospects for Ensemble XXI's relationship with its sponsor took a further dive as the Progress Bank withdrew its underwriting of the orchestra's Western European tour this month. To lose faith with halls such as the Concertgebouw, St David's in Cardiff and St John's Smith Square was unthinkable. Friends of the orchestra in the UK, Ireland and Holland have been offering assistance.
In her clipped, precise delivery O'Riordan reflects on how different things might be if Western concert agents were willing to look beyond obvious star names. 'These days, with every Ivanov, Ivanov and Ivanov eager to earn quick money in the West, agents are bored with Russia. And our orchestra seems bizarre. Before our last London concert I invited along an impresario with a longstanding interest in Russia. He just said 'An Irish conductor of a Russian chamber orchestra in Moscow? Impossible.' '
The daughter of an Irish diplomat, O'Riordan grew up in Holland, the USA, Australia, Denmark and Austria. Early musical training from Hungarian teachers both in New York and Sydney led to studies in choral conducting at the Liszt Academy in Budapest. Standards of Hungarian orchestral playing made no great impression until Mariss Jansons arrived to conduct - galvanise - a local orchestra. 'It was electrifying. I decided immediately to go on to study in Russia.'
In the year she auditioned at the Moscow Conservatoire, O'Riordan was the only pupil, from home or abroad, accepted by Gennadi Rozhdestvensky. Ensemble XXI, founded by O'Riordan and a Finnish violinist, Pia Siirala in 1989, is the embodiment of her desire to keep the Russian string tradition alive. 'It's what produces that incredible open sound with such reserves of power - it has to do, for example, with the way the bow is held and the flexibility of the wrist.
'In the past, every string player in a Russian orchestra played that way, whereas in the West you see a range of techniques being used. The tragedy is that so many teachers of this tradition - from primary to Conservatoire level - have left Moscow, often to go abroad, where they can't have the same impact.' To tap into the tradition, Ensemble XXI's new young cellist, Pavel Gomsyakov, traversed O'Riordan's rigorous audition and probation procedures. 'I have to rely on the older cellists in the orchestra to pass on the secrets of this string sound - yet these players are only in their mid-twenties] That's how rapidly things have worsened.'
The facts of life in Moscow show scant respect for Ensemble XXI's idealism. The orchestra abandoned rehearsals at the Moscow Conservatoire because of a rent hike. Now the base is a more modest Dom Kulturi, or House of Culture: a local club. 'It's OK,' says O'Riordan philosophically, 'apart from a large rat which often darts through the orchestra.' The players are convinced the new Russian mafia has moved in on the music business. 'They run the only Moscow shop where we can buy strings,' says the violinist Dmitri Mistrikov. 'Prices are three times those in the West - a set costs a month's salary. Repairs can only be paid for in dollars. A decent instrument costs an incredible price. I'm ashamed to be playing on a paper bag in some of the world's great halls.'
The privations might seem more tolerable if Moscow's remaining musical establishment offered support. 'What we get is suspicion,' says O'Riordan. 'They find me threatening as a foreigner and consider the orchestra's 'experimental' programming as somehow subversive. Instead of concentrating on Russian repertoire we play anything that a string orchestra can play.' Last year the Moscow Conservatoire hierarchy cancelled a concert booking for its main hall by Ensemble XXI. O'Riordan was informed that neither the orchestra nor its repertoire was sufficiently Russian in hue. Her answer was a hunger strike. It brought a climbdown - if no contrition.
Ensemble XXI appears in all the main Moscow halls. O'Riordan's repertoire policy has stirred public interest, but still the best way to guarantee audiences is to offer champagne in the ticket price. With an eight-concert subscription ticket for the orchestra's Dom Kulturi series costing the equivalent of pounds 60, box-office returns constitute no meaningful income. Tours away from Moscow may make a rouble or two. Equally, they can be a matter of . . . well, Russian roulette. A recent trip to Tambov was sponsored by a local political party. On discovering that sleeping arrangements for the train journey amounted to bunks in a cattle truck, O'Riordan paid for proper accommodation and then presented the concert organisers with an ultimatum - no reimbursement, no concert.
'I constantly refused to accept promises that cash would appear the next morning, until finally I gave in to a plea from the head of the political party. The next day: no money. It seemed the official had just lost his seat and was only concerned to pocket the cash from the concert, which was planned as a victory celebration.'
Such adversity has, it seems, bred camaraderie in the Ensemble XXI ranks. Membership has remained stable, largely because bringing good players together has nurtured a collective pride in the standard of performance achieved. And, adds the Ecuadorian violist Fredi Yaramilio, 'I think it makes sense that you should begin your work as a musician in the environment where you studied - even in Moscow.' 'If someone left now,' says the violinist Zsenia Lobas, 'it would feel like bereavement or divorce.'
Cardiff, St David's Hall, 16 March, 7.30pm; London, St John's Smith Square, 19 March, 7.30pm. Repertoire ranges from Vivaldi to Martinu