i am trying to figure out the changes for someday my prince will come. i can't figure out the c#dim chord in bars 10 & 14 (assume the song is in the key of bb). wouldn't it make more sense if this was a fdim so that the chord would be a substitute for a g7b9 so that the progression there would be a normal 3 6 2 5? can anyone enlighten me as to why this chord is used and why it sounds quite good?

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it's hard to say.  where are you learning the tune from?  the miles recording, walt disney sheet music, etc etc?

first thing to do is learn the sheet music from walt disney, then learn the chords that miles used when he recorded it.  

in response, the c#dim chord is how people play it.  it's just a substitution for the g7alt chord you can also play there (you put fdim, but i think you meant gdim).

the progression: dm / c#dim / cm / f7

can also be played:

dm / g7 / cm / f7
dm / c#dim / gb7 / b7
ab7 / g7 / gb7 / f7

see?  lots of subs in there and when the changes for the chart you're looking at came out, the c#dim was probably put in because that's how miles recorded it.  walt disney probably had a g7 in there.

hope this gives you something to go on!
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thanks scot...so are you saying dim chords can be a substitute for alt chords a tritone away? i didn't realise that

i thought that dim chords were generally just substitutes for 7b9 chords - thats why the c# dim chord had me puzzled, because it would be appear to be a substitute for a7b9 / c7b9 / eb7b9 / gb7b9, none of which would seem to fit in the progression in the song
it's pretty common to see diminished chords as "connecting" chords between ii and iii, it's more common to see it  when the bass line is ascending, but here the bass line is descending instead. it's the contrary motion between the bass note and the melody that makes this harmony effective. i wouldn't think  of it as a substitute chord. it is what it is, a  diminished chord connecting two diatonic chords. i think it's more than likely that it is the original progression, i don't think miles put it there.
i too have puzzled over these changes, and agree with jwv76 that the c#dim is linking chord rather than a substitution, as it not a usual sub for g7.  

if it is a sub, then (as superjames points out) it comes from a7b9, the dominant of the previous chord, dm. so it's not so out-of-place - although we jazzers have become used to the dominant chord preceding the tonic, here it follows it!

that's my analysis anyway. chord symbols don't always behave as the theory says they should!
the progression  

| dm | c#dim | cm | f7 |

is a sub for

| dm | g | cm | f7 |

tritone substitution works like crazy by root motion alone. the quality of substitute chord doesn't change the underlying circular motion tendencies.

other alternatives could as easily be:

| dm | c#m | cm | f7 |

| dm | c#7 | cm | f7 |

| dm | c#m7b5 | cm | f7 |

| dm | c#7#5 | cm | f7 |

etc, etc, etc ...
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