In theory, Jonathan Mills’s first Edinburgh “festival of ideas” has had a lot going for it: lashings of early music – all but ignored by his predecessor, Brian McMaster – surrounding the 400th anniversary of the first performance of Monteverdi’s L’Orfeo, from which thematic strands have sprouted across all the art forms. A subtext of the focus on Monteverdi has been the composer’s concern for the dynamic between words and music, most notably in opera, in which, he believed, harmony should be the obedient daughter of the verse.

Prima la musica, dopo le parole (first the music, then the words), or vice versa, is the motto behind Richard Strauss’s valedictory opera, Capriccio, written during the latter years of the Third Reich, when his relationship with the Nazi rulers was at its low point and he feared the worst for the Jewish members of his family (his daughter-in-law and grandsons).

In this unpropitious period, towards the end of his long life, he found new musical inspiration in an arcane theatrical discussion about the importance of art in society, the relationship between words and music in opera, the role of patrons vis-à-vis theatre and music professionals and the eternal riddle of love. Capriccio is an allegorical opera in which a beautiful 18th-century French countess, torn between love for a composer and for a poet, represents the spirit of the opera she wants them to create for her. After arguments, amorous encounters, entertainments and auditions, she is left alone to ponder her dilemma – words or music; the composer or the poet – in Strauss’s most glorious operatic outpouring for the soprano voice, after a “moonlit” orchestral interlude with solo horn (his father’s instrument) of breath-taking loveliness. Strauss’s critics have found it hard to square the beauty of the music with what was going on around him. (The opera was premiered in Munich in 1943, just down the road from the slaughterhouses of Dachau.) The composer who made an opportunistic Faustian pact with the Nazis is damned for looking back, musically, to a more comforting and (to Strauss) better world.

Mills’s decision to invite the Cologne Opera to create a new Capriccio may have seemed an inviting idea on paper, but in practice it has foundered on a production that seems more interested in the historical hinterland than in the content, and on vocal standards that fall way below the level one has a right to expect here. Christian von Götz’s staging looks smart, in Gabriele Jae-necke’s stark, abstract set, but the setting – Nazi-occupied Paris, with the Countess throwing a Louis XV-themed party – looks contrived when Gestapo officers lurk in the wings, and a spurious subplot that turns the prompter, Monsieur Taupe, into a concealed Jewish fugitive is manufactured to fit a questionable subtextual concept.

If the opera were better sung, one might tolerate such extraneous, unilluminating fantasies, but Cologne’s resident ensemble proves no more than provincial, and the two big starring roles, the Countess and the theatre director La Roche, are woefully undercast. Michael Eder struggles with the range of his credo monologue, and Gabriele Fontana’s soprano is worn in the middle and lower registers and devoid of radiance at the top. She looks and acts well in the part, but she sounds old and unlovely. In the pit, the conductor, Markus Stenz, and his Gürzenich Orchestra of Cologne offered compensating Straussian pleasures (especially in the Moonlight interlude and the serene concluding pages), but a few more rehearsals would not have gone amiss. Mills might have been better advised to import a production already up and running.

It must have seemed a bright idea to programme a concert performance of the work that inspired Capriccio, Salieri’s theatrical divertissement Prima la musica e poi le parole, of 1786. Alas, the festival shot itself in the foot by omitting to print the recitative dialogue (and English translation), leaving the Italian-singing but entirely English-speaking cast to convey the meaning as best they could through wild gesticulation. Despite the best efforts of the singers, Roderick Williams, Neil Davies, Giselle Allen and Gillian Keith, and Nicholas McGegan’s sprightly conducting of the Scottish Chamber Orchestra, the performance fell hopelessly flat.

The Dido and Aeneas with which it was paired fared only slightly better, with a statuesque but unmoving – and occasionally below pitch – tragic heroine in Jane Irwin outsung by Jennifer Johnston’s vocally glamorous, uncackling Sorceress and Williams’s nobly declaimed Aeneas.

The finest singing I heard last week came from the lustrous throat of the American soprano Christine Brewer, who pinned us all to our seats and threatened to demolish the walls of the Queen’s Hall with her ecstatic new Brünnhilde voice in her selection of Strauss lieder, Wolf’s four Mignon Songs, Britten’s Cabaret Songs and a suite of spirituals by the enigmatic 20th-century American composer John Carter. It was a pity – and surprising – that Brewer used the music as a safety net in the Strauss and Wolf, but she relaxed visibly as she intoned Britten’s ritzy Auden settings, Calypso, Tell Me the Truth About Love and Funeral Blues, delighting the audience with her witty and informal way with the words. And she was simply devastating in the spiritual arrangements, singing with all her heart and soul and the sultriest vocal allure of any US soprano since the great African-American diva Leontyne Price.