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Could you please help me make sense of the accompaniment for 'Moon River' in terms of why certain chromatic chords seem to be the only solution and if certain modulations are implied when using some chords? In C major, the accompaniment for the words: '...you heartbreaker, whenever you're going, I'm going your way' is: F - Bb7 - Am7 - F#dim - B7 - Em7 - A7 - Dm7 - G7.

I am interested in hearing about all the chords, but I would really appreciate an explanation, at least about the Bb7 chord.

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Despite the chromaticism this song is firmly rooted in the key of C. The F chord you are starting on is actually bar 11 of the song. That is a IV chord. The next chord, Bb7 is a tritone substitution dominant (bII7) chord to Am, the VIm chord. It is a substitute for V7/VIm, which would be E7. That makes IV, bII7/VIm, VIm.

The next series of chords are three sets of 2-5s, where each V7 chord resolves to the next IIm7 chord, creating a cycle of descending 5ths bass movement. The final V7 chord, G7 resolves back to C, the I chord. Incidentally the F#dim is actually an F#m7b5, or half diminished. That chord is often used as a IIm chord in a 2-5 when resolving to a minor chord.

My last comment is that these chords are not “the only solution”, they were chosen by the composer and if someone wanted to use different chords in their own arrangement of this song they could certainly do that.

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    The best way to think of it is a tritone substitution is an alternate way to play a dominant to tonic progression. In this case. It is not a substitute for E7 because Bb7 is the original chord. That is just the way it is identified and analyzed, as a dominant chord a tritone away from the actual V chord. These two chords use the same 3 and b7, D and Ab(G#), they are just reversed. An E7 would probably sound more in place to you if you add a #9 to accommodate the melody. Commented Oct 1, 2023 at 5:30
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    As for the F#m7b5, it is not a substitute, it is the chord more commonly used as a 2 chord in a 2-5 to a minor tonic. In minor keys the IIm7b5 is a diatonic chord so it makes a more natural 2 chord in a 2-5 to a minor key. In this particular case the melody contains a C note, which is the b5 of F#m7b5 making an F#m7 (no b5) a very bad choice. However it is not unheard of for some songs to contain a regular Iim7 chord leading to a minor tonic. Commented Oct 1, 2023 at 5:43
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    Also since you are new to the site I would like to point out that although I appreciate the thanks in comments the thing to do is if you like a question or answer give it an upvote with the arrows. This helps everyone build reputation. I liked your question so I upvoted it. Another thing is after you allow some time for multiple answers to your question you can “accept” the one you feel best answers your question. Welcome, I look forward to you asking other questions. Commented Oct 1, 2023 at 5:47
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    Great answer! Just to add - playing only the D and Ab (G#) from the 'so-called' Bb7 chord works well, as they're the two common notes shared by Bb7 and E7. And the whole sequence could be played using 3s and 7s, a common jazz ploy. +1.
    – Tim
    Commented Oct 1, 2023 at 7:11
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    @Irina I like and am used to the Bb7 as I have been playing this song for decades (!) Ideally it sounds best if you add tensions to the chord, 13 and #11 which are the melody notes, Commented Oct 2, 2023 at 3:36

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