In the middle of Erich Wolfgang Korngold’s suite of incidental music for “Much Ado About Nothing,” there’s a march meant to accompany Dogberry, Shakespeare’s comic constable, and his fellow watchmen.

Written in the late 1910s, and played by Ensemble Modern at Zankel Hall on Friday as part of the Carnegie Hall festival “Fall of the Weimar Republic: Dancing on the Precipice,” the march stepped along crisply, with dryly officious humor. But it also had an edge of sincere sternness. Cast over the bumptious charm was a hint of the ominous, of a real (rather than satirical) military buildup.

The same uneasy combination of optimistic energy and dark clouds characterized Germany during the Weimar Republic, an experiment in democracy that began in the wake of the country’s defeat in World War I, in 1918, and lasted until the Nazi takeover in 1933.

Weimar has lately been seized on by many Americans who see in it parallels to our own era. (To wit: tenuously free republican institutions, mainstream conservative complicity with the far right, divisions on the left, fear of a fascist overthrow, etc.)

For Election Day 2020, two former U.S. attorneys general published an opinion piece in The Washington Post, saying that images from the Weimar era were “fresh enough in memory to offer a cautionary tale.” A few months later, Foreign Policy offered “Weimar’s Lessons for Biden’s America.” This January, Bernie Sanders said that if President Biden couldn’t prove government’s efficacy to voters, “then we are the Weimar Republic of the early 1930s.”

That month, Carnegie opened “Fall of the Weimar Republic,” now in its final weeks. Past Carnegie festivals have focused on South Africa, Vienna, Berlin, Venice and migrations to America, among other topics.

But none have been so pointedly connected to current events. Carnegie promised that “Fall of the Weimar Republic” would yield “many lessons about the fragility of democracy.”

A tall order, even if the festival were single-mindedly focused on the culture of the Weimar period — its devil-may-care decadence and world-weary cynicism. But the programming has been a bit unpersuasive.

Earlier standard repertory works have been thrown onto many programs, often dominating them, with the weak explanation from Carnegie that during Weimar people listened to Beethoven, too. The impact of Stravinsky’s “Rite of Spring” (1913) is so familiar that surely we didn’t need to hear it twice in two months.

Some groups understood the assignment. The Cleveland Orchestra opened the festival with Bartok works from the right period and Ernst Krenek’s rarely heard Little Symphony (1928), as well as Krenek’s completion of the Adagio from Mahler’s 10th Symphony. (The festival has featured swaths of Mahler, whose frenetic juxtapositions can seem to anticipate what was to come though he died seven years before the Weimar Republic was founded.)

The Knights played Kurt Weill’s Symphony No. 1; the Philadelphia Orchestra, his Symphony No. 2. The Vienna Philharmonic performed Paul Hindemith’s Konzertmusik for wind orchestra; the American Composers Orchestra, George Antheil’s “A Jazz Symphony.” Chamber concerts have offered all kinds of little-played treats from the period. On May 2, the Bavarian Radio Symphony Orchestra comes with Hindemith’s “Rag Time (Well-Tempered)” and Alexander Zemlinsky’s aching “Symphonic Songs” — before, yes, Mahler’s Sixth.

In Ute Lemper and Max Raabe’s Palast Orchester, Carnegie had experienced purveyors of Weimar-style cabaret. Partnerships with other institutions around the city encompassed film screenings, art exhibitions, plays and talks.

But why were there only glimpses of important composers like Erwin Schulhoff and Hanns Eisler? I wanted more Zemlinsky, even a note of Hans Pfitzner and a bigger helping of the era’s innovative music theater and opera.

And I understand Carnegie’s notion of presenting the music that formed the context for Weimar in addition to Weimar-era works, but really: The Bamberg Symphony, from Germany, is coming on April 24 under the festival’s auspices with standards by Wagner, Schumann and Brahms, the latest of which was written in 1883.

Ensemble Modern’s concert on Friday was one of the festival’s few fully Weimar programs — and all the more compelling for that. The group, from Frankfurt, played with a precision and lucidity that showed two facets of the period as more similar than antithetical: the jazzy, angular urbanity of Hindemith’s Kammermusik No. 1 (Op. 24) and, written just a few years before, the stylish nostalgia of Korngold’s “Much Ado About Nothing.”

Schoenberg’s brooding “Accompaniment to a Cinematographic Scene” was the perfect lead-in to Weill and Bertolt Brecht’s “The Seven Deadly Sins.” Performed in a recent arrangement for reduced forces by HK Gruber, who conducted the concert, and Christian Muthspiel, this “ballet with singing” — a sung monologue about a fanciful journey through America, with ensemble interjections — was delightfully intimate and witty.

The mezzo-soprano Wallis Giunta, joined by members of the vocal group Amarcord, guided the audience through a parade of misadventure with a light, meticulous touch, neither too offhand nor too exaggerated — as bracing yet sweet as a shot of schnapps.

If only the entire festival had been this fixed on its subject. For classical institutions seeking contemporary political relevance, there are few more appealing topics these days. (Just before the first pandemic lockdowns, the Los Angeles Philharmonic and the conductor Esa-Pekka Salonen put on their own multidisciplinary Weimar festival.)

But the connection between 1920s Germany and 2020s America already has its limitations, and has served to overshadow other, possibly even more helpful historical analogies. The Carnegie festival shies away from a clear, thorough reckoning even with the period’s music, making it harder to help us learn from Weimar where we are and where we might be going.