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My first ("blind") guess was that it is in rondo form with two themes, but when I performed analysis, it somehow doesn't fit any form that I can think of.

This is what I figured out:

intro a b a' a b a' b1 b2 b3 a1 b4 a2 b5 a3 c a+b coda

3

The Danse is a Symphonic Poem like others by Saint-Saens, if a rather short one. These compositions don't have to follow traditional forms like "Sonata movement" or "Fugue", although they can. Their point is rather to let the music follow the extramusical narrative regardless of the constraints of strict form.

That said, a rondo can have quite a few different variants - the defining characteristic is the reappearance of the main theme multiple times in a relatively unchanged manner. I'd say that certainly applies to this composition.

  • Ok, so it doesn't matter if structure is not strictly ababab... Just in case of symphonic poem or also with rondo in general? – sam Jul 5 '18 at 7:34
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Stealing shamelessly from the front page of a Google query,

Danse Macabre is considered a symphonic poem (or tone poem), which is a piece of orches- tral music that represents a particular story line, or plot, rather than just conveying emotions or a general idea.

and

The broad waltz theme in the Danse macabre may be recognized as a variation on the Dies Irae, the ancient liturgical chant for the dead.

and

Danse macabre, Op. 40 by French composer Camille Saint-Saëns is an art song for voice and piano (first performed in 1872) with a French text by the poet Henri Cazalis which is based in an old French superstition.

and

The romantic tone poems Danse Macabre and ... are examples of single-movement concert waltzes for orchestra.

So, you pays your money and you takes your choice.

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