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I only have a little knowledge of music theory and was unable to work out how to use roman numerals to denote a chord sequence of one of my old tunes which starts in Fm. I have listed the chord sequence a follows:

Fm Ebm F#m Bbm played twice, then, Fm Ebm Em Dm Bdim A

I know this has a modulation at the end but I don't know how to set Roman Numerals to the chords.

Roman numerals can be really helpful for music the follows traditional harmonic syntax. But if music is really chromatic, sometimes Roman numerals really aren't helpful at all. Unfortunately, I think your progression is one such case: we can stick Roman numerals to the chords, but it won't tell us much (if anything) that's helpful.

Fm   E♭m  F♯m  Bbm  Fm   E♭m  Em   Dm   B°   A

i    vii  ♭ii  iv   i    vii  v    iv   ii°  I

          ***                 ###

Two caveats of the above progression:

• The chord marked *** I have interpreted enharmonically as G♭ minor so as to understand it as ♭II (a modified Neapolitan chord).


• The chords beginning at ### are no longer understood in F minor, but in A.

Since Roman numerals aren't all that helpful, we can perhaps better understand this progression as an example of planing. Planing is when we take a particular chord type and just move it up and down in musical space. In this case, you plane a root-position minor chord and move it up and down through the chromatic universe, and then you use it to reach a pretty clear iv–ii°–I cadence in A major.

Roman Numeral Analysis wouldn't do much good for chord progressions like these because it's not clear what key these progressions belong to, especially the second progression. Something important to note about music theory, compared to other lofty kinds of theory (physics, mathematics, etc) is that music theory does not dictate how one should or shouldn't write. It simply allows us to communicate what's happening in the music in a succinct, formal, and analytic format. What I see in your progression is, instead, a root-movement relationship built on intervals. However just because that's what I see in there does not magically mean that's why you wrote it that way.

The first progression could be said to be "constant structure" minor chords (i.e., entirely minor chords) built upon an increasingly large root movement: Major second/diminished third between Fm/Ebm, minor third between Ebm/F#m, and major third between F#m/Bbm. The second progression looks to me like a chain of seconds of varying sizes: Fm->Ebm = M2, Ebm->Em = m2, Em->Dm = M2, Dm->Bdim = A2(m3), Bdim->A = M2. The diminished and major chords in this progression provide significant color differentiation to break up the monotony of the minor chords.

This is simply how I would explain the construction of these progressions, and I'm sure several other people would have different analyses as well.