Syntax

[ed. note- the blogger interface is a bit clunky and wouldn't let me change the order of the posts after the fact, so just navigate up to the open listening post before reading this.]

The syntax for Mr. Tambourine Man is very simple, squarely in the American folk tradition of simple chord structures, mostly focusing on I, IV, and V, at least for songs in major keys, and incorporating simple, memorable meolodies on top of them. Dylan plays it in drop D tuning, which means that the low e string on the guitar is tuned down to a d, with a capo on the third fret. In folk music, drop D is usually used to give the D chord more presence as a tonic, and to serve as a pedal note for the other chords: in standard tuning, the lowest note played in a conventional open D chord is the low A, making the chord 6/4, and the low D makes it sound a little more complete in a tonic setting. The strings of his guitar from lowest to highest are therefore F C F Bflat D G. The structure of the song is as follows:

Chorus (strange in 60s pop to have a chorus start the song, but not so strange in folk songs), Verse, Chorus, Verse, Chorus, Verse, Chorus, Instrumental, Extended Verse, Chorus, and it fades out on the chorus.  or-

ABABABABB'A

 While although the basic framework of the song is in no way revolutionary, Dylan's signature style is present in that there are more verses and more lyrics than a typical folk song, and that the last verse is extended; he always likes to make the biggest lyrical statements in the last verse, to twist and juxtapose ideas in order to give the first verses a different context and deepen their meaning.
The chords he uses in the first half of the chorus are B flat in first inversion, C 2nd inversion, F, B flat in first inversion, F, B flat in first inversion, and ending on the C, in a half cadence.

IV V I IV I IV I IV Vsus4-3 V

He then plays these again in the same sequence, but instead of ending in a half cadence, cuts out the third B flat chord, and does a Perfect Authentic Cadence to end.

IV V I IV I IV V I

The verse is almost the same exact melody and chord structure as the chorus, having two sections, although in the verse it is just the same music sequence played twice.  The chord structure is also slightly different, although the melody remains almost the exactly the same, altering slightly each time to fit the words:

IV V I IV I IV I ii7 Vsus4-3

The melody, or at least the first part of it is shown this picture:

Its a mostly stepwise, diatonic melody typical of all pop music, but folk music especially.  The simple nature of the song structure, chords, and melody of most folk music stems from the focus, compositional, on the lyrical themes that are laid bare by the lack of complex musical movement.  Mr. Tambourine man is a perfect example of this. 

The strumming style is mostly uniformly consistent throughout, with a hard hit on the 1 and the 2, and then a down-up-down strum with a quarter-note triplet feel during the last two beats.  The second guitar arpeggiates the chords throughout the song in a cyclical motif, going up the B flat chord F Bb A and then down the F chord C A F in the upper registers of the guitar as Dylan cycles from Bb to F on his guitar.  

The recording was done in 1964, and produced by Tom Wilson.