Jeffrey Kresky offers a service to music theorists, debunking various urban legends in the aptly titled "'Urban Legends' for Music Theorists," Music Theory Spectrum Vol 25, no. 1 (Spring 2003), 121-125. I have changed the format to something more familiar.
Claim: The opening E minor chords of Symphony of Psalms were spaced to imitate the natural shape of two hands stretched out at the keyboard.
Origins: The unusual spacing of the chord has isolated G's played by the thumbs in the middle register, with a wide gap between the thumbs and the rest of the fingers, just as a normal hand position. This has been confirmed by Stravinsky expert Claudio Spies, that while Stravinsky did not speak of the hand position directly with Claudio, "it definitely played into his thinking."
Claim: The opening chords of Beethoven's Eroica Symphony are voiced so each instrument plays the note with which it will start its next entry.
Origins: Milton Babbitt has made this claim, among other famous theorists. Examination of a score reveals that the theory works for certain instruments: first violin, cello, contrabass, 3rd horn, 2nd trumpet, oboes, and timpani. It does not reflect the behavior of the second violin, viola, 1st and 2nd horn, 1st trumpet, flutes, clarinets, or bassoons.
Claim: In the first movement of Mozart's 40th symphony, the key changes in the development section trace a descending G minor scale.
Origins: Milton Babbitt again, that trickster. The development does start (unusually) in G minor before quickly shifting to F# minor (m. 103). Next is E minor (m. 115). D minor is very stable, but it is part of a circle of fifths, so the next key after E minor is really A minor, followed by D minor, G minor, C major, F major, and Bb major. If we decide to pick every other key from this circle of fifths, we do get Emin, Dmin, Cmaj, Bb maj, so almost all of the scale. All we need is A, which is where things break down. A is melodically present in the D dominant that signals the recapitulation, but it is never given its own key.
Claim: The hornpipe in Gilbert&Sullivan's Ruddigore is the inversion of a standard hornpipe.
Origins: Leslie Bailey's The Gilbert and Sullivan Book, as well as other older sources. The hornpipe is quite charming, and the composer was asked how he was able to compose one that sounded so authentic. The reported reply is that he took the well-known standard hornpipe and turned it upside down. Here is the Sailor's Hornpipe. Here is an arrangement of Sullivan's hornpipe (pdf). I can see a flipping around of the opening direction (down becomes up) and the four eighth-notes are somewhat reversed (down-down-up becomes up-down-down). The leaps within the original hornpipe have the descending octave first and the ascending fourth second; Sullivan has the ascending (fifth) first and the descending octave second. However, Kresky is correct that no section of Sullivan's hornpipe is a true inversion of any section of the standard hornpipe. In fact, inverting Sullivan's music creates a decidedly un-hornpipy sound, even when altering the quality of intervals to stay tonal. Perhaps Sullivan was being flippant, really meaning that he took features of the original hornpipe and added his own flavor to it. But don't believe any claims that it is a true inversion of the standard hornpipe.
Claim: The "Sirens" episode from Ulysses by James Joyce is set in the form of a fugue.
Origins: William Tindall, A Reader's Guide to James Joyce: "The method is fugal, says Joyce, and the structure that of a fugue." Hugh Kenner, Joyce's Voices: "a stylistic caper is in progress... nothing less, if we are to trust the schema, than an effort to construct a prose fuga per canonem." Stuart Gilbert, in his James Joyce's "Ulysses," attempts to analyze the scene as a fugue. The problem comes in identifying what the subject is. Any musical fugue consists of a musical theme, the subject, which is realized in each of the 2-6 voices of the fugue. There can be free episodic material between each statement of the subject, and the subject can be stated any number of times as long as each voice gets it once at the beginning (the exposition). An example of a verbal fugue can be seen in Ernst Toch's Geographical Fugue (cheating, as this is really still a musical piece) or in Douglas Hofstadter's Godel, Escher, Bach: an eternal golden braid. But said imitation does not occur in Joyce's work.