Please can anyone explain this violin solo / modulation!???

The item in question is the violin solo half way through Vivaldi's Four Seasons Spring Mov.1. Can anyone please help me understand each bars movement.

The first bar of the solo is an arpeggio fitting the E Major Key scale nicely.

The second bar has an A# not part of the E Major key?

The third bar now has an B# not part of the E Major key!

Is Vivaldi modulating through different keys here? Or is he using modes? Or am I completely off track?

The next few arpeggio bars dropping in pitch fit "E Major" fine, but then there is (I believe) a Tritone in the last bar resolving to C# Minor?

If anyone can please explain this short piece I would be forever grateful!

Many thanks.

Yes, it modulates. This is a very typical passage for Vivaldi with those sequences, even though a II-V-I sequence would be even more typical.

Measure 1: E-major, then he adds a 7th to make it a dominant of A, which follows (implied) on the first beat of measure 2. Then he uses the C# to create a connection to F#-major, a mediant chord, which he uses again as an intermediate dominant to B (second to last beat of measure 49).

He repeats this exact game once more: From B he moves a minor third lower to G#-major and uses this as an intermediate dominant to C#-minor (first beat of measure 51). Here, he first stays on C#-minor (having reached the VI of the original E-major) which becomes our new key. He then moves in measure 52 to a G#-minor 6th chord which he then simply shifts downward step by step (F#-minor 6th, E-major 6th, D#-diminished 6th) until he arrives at the C#-minor 6th chord, i.e. a I6, still analysing in C#-minor. This passage of 6th chords going downwards I wouldn't analyse too much functionally - just moving 6th chords in "parallel" along the notes of a specific key is a typical sequencing effect that is more held together by its simple build than harmonic function (it also appears a lot in Beethoven). But if you want you can call it, beginning from the G#-minor 6th chord (analysing in C#-minor): v6, iv6, III6, ii6, I6. (I -wouldn't- write it like that personally though, since it implies a functional harmonic progression.)

Now that we're again in C#-minor on that 6th chord (measure 53) he begins the final cadence with a G#-major with 4th suspension (V) and the final C#, i.e. our tonic.

So all in all one -might- write:

E-major: I6 - V56/IV - IV = A-major: I - V56/II - II = B-major: I - V56/ii - ii = C#-minor: i - i - v6 - iv6 - III6 - ii6 - i6 - V4 7-6, i.

But this is probably more confusing than helpful. It will get a lot clearer to you if you try playing this on a piano and finding fitting bass notes for it.

E.g.:

E | A F# | F# B | G# | C# | B A | G# F# | E G# | G# C# |

All in all, only the first measure is clearly in E-major, after which he already begins to slowly modulate towards C#-minor (with the intermediate steps of A-major and B-major). The actual C#-minor first appears in measure 51 and stays the main key until the end, closing with a nice consolidating cadence.