"Or Neukish," he ponders. "Or perhaps Neukesque." What he means by the bespoke adjective is bespoke programming: the kind of concert that "doesn't come in off the peg", but that fits with the festival's reputation for small-scale, high-class, one-off musical experiences.
East Neuk Festival marks its 10th anniversary this year, and an extended edition brings together many of the artists who have built its boutique image and audience loyalty over the past decade.
A handful of new artists have been brought into the fold - more on them later - but mainly the 10-day line-up features names that East Neuk regulars will already know well. And with a return rate of 90%, regulars make up pretty much all of the audience.
At the heart of the programme is German pianist Christian Zacharias, who hosts a Schubertiad on the closing weekend. Brown explains that "the idea originated from having Christian play Schubert's last sonata" - the great sonata in B-flat, D960 - "to end the Saturday night, and it grew from there to include songs, piano trios, the Rosamunde Quartet, the Arpeggione Sonata".
Chamber partners include Malin Christensson, a terrific young Swedish soprano who makes her festival debut, as well as members of the Belcea and Elias quartets.
String quartets have always been the backbone of East Neuk Festival, and this year the Belceas and the Elias mix and match members across several concerts.
The Elias play Beethoven's Quintet in C with Belcea violist Krzysztof Chorzelski; both quartets team up for Brahms's Second Sextet and Strauss's fervid Metamorphosen. Also returning are the superb Quatuor Ebene: a foursome of French lads whose polished sound and daring delivery are always a thrill to hear. They play Beethoven late quartets (Opus 131 and Opus 132) as well as Mozart and Ravel's quixotic Quartet in F.
Scottish guitarist Sean Shibe returns for concerts celebrating Segovia and Julian Bream - after his recital debut sold out in a flash two years ago, Brown thought it wise to book him for two concerts this time - and festival regular Llyr Williams is back with Schubert's late Impromptus.
The Scottish Chamber Orchestra make its annual festival appearance with two concerts. Its Friday-night programme at Cambo Barn is a typically motley East Neuk (Neukish?) affair with a common thematic thread of landscapes: James MacMillan's stormy I (A Meditation On Iona) opens, followed by John Luther Adams's ... And Bells Remembered..., Britten's Les Illuminations and Sibelius's Seventh Symphony. The tenor is Allan Clayton; the conductor is rising young German talent Clemens Schuldt.
Christian Zacharias takes to the podium for the closing concert, which includes Britten's Serenade for Tenor, Horn & Strings (with SCO principal horn Alec Frank-Gemmill) and Schubert's Unfinished Symphony.
So who is new to the festival? South African early keyboard specialist Kristian Bezuidenhout plays two concerts of Mozart and Beethoven with Edinburgh-based period ensemble Ensemble Marsyas led by SCO bassoonist Peter Whelan.
There is new work from James MacMillan, whose Piano Trio has been co-commissioned by East Neuk and receives its Scottish premiere from the Gould Piano Trio. Brown describes it as a "full-on blaze of a piece".
And the opening weekend is something altogether different: a throwback to the classic jazz era. Clarinettist Julian Bliss kicks off the programme with his swing project, an homage to Benny Goodman; Scottish pianist Euan Stevenson channels Ellington and Bill Evans, and there are solo slots from British guitar heavyweight Martin Taylor and Parisian bassist extraordinaire Renau Garcia-Fons.
Running parallel to the music programme is the usual series of literary events, Littoral, which is bolstered this year by the presence of nature writer Robert Macfarlane. Other featured authors include Richard Holloway, Kirsty Wark and Sally Magnusson.
The festival's visual arts strand also shifts up a gear from cosy craft art to a St Andrews Museum exhibition of Scottish colourists from the Fleming-Wyfold Art Collection, showing East Neuk landscapes by the likes of Gillies, Hunter and Walton.
Brown has been toting up statistics in preparation for the 10th anniversary season. To date, he says, at least 666 artists in 150 different ensembles have performed 307 musical works. The list of most-often performed composers is topped (unsurprisingly) by Mozart, Beethoven, Schubert, Brahms and Mendelssohn.
The more pressing numbers are financial. Since 2005, public funding has dropped 25%, while private funding is up 700% and box office sales have tripled.
Like so many arts bodies, East Neuk's funding structure has had to adjust to a changed economic climate. That the festival has been so adept at gathering private donations is crucial to its success.
Brown also points out that Scotland's classical music landscape has changed a lot over the past decade. Ten years ago there was no Lammermuir Festival, no Cottiers Chamber Project, no Cumnock Tryst. Music At Paxton was up and running but nowhere near as vibrantly as it is today. The other festivals are not competition, he says; rather, the diversity of their programming offers audiences a degree of choice for which, judging by the fact that festival events often sell out, there is clearly an appetite.
As for the next 10 years? Brown sees a case of 'if it ain't broke, don't fix it'. He says: "I don't do novelty for the sake of it. I am a great believer in glacial growth rather than trying to reinvent the wheel. I like where the festival is at the moment. Littoral might expand. We might commission more new music. We might expand the talks side of things, maybe with more ideas-based seminars."
For now, though, the anniversary programme offers classic Neukerie. Book early, because Neukerie tends to sell fast.
The 10th East Neuk Festival is June 27-July 6. Booking opens on Sunday.