So when you say improvise, do you mean catching the melody by ear, and playing it in real time?
Or embellishing a melody on the fly by ear?

Are you talking about a tune one already knows, or one never heard previous?

The former for both.
I can go somewhere when the tune is slow but fast, it’s basically impossible! :|

Something you can try when everybody else is going at a million miles per hour is to just do simple, long one note pulls.

I most often just try to get sense of the simple basic melodic line, and then maybe embellish on that.

Ok this I do quite often. its not easy and to do it well is hard. Some suggestions:
Know the melody well
Know the chord structure of the tune
Have a 'bag o' tricks' at your immediate command for all sorts of keys and phrases
Have really good bow control; be able to change bow patterns etc on the fly
Be able to think ahead on the melody, like auditorily visualizing what you want to do
Relax!!!
Confidence!

I find most fiddle tunes are made up of smaller segments that appear in others too. Study these snippets and create variations on them. They dont need to be 2 bar improv wonders, most times tweaking them can make a solo memorable and different.

Good Luck

If you know the chord flow and the double stops that fit those chords, you have a good start on it.

Johnny Gimble said, 'get so if you can hum it, or whistle it, you can play it.'

Thing is, one can bounce a bow faster than whistle or hum. So one just thinks it.
It does depend on your musical depth and vocabulary. If you're plane spoken, or if you're more sophisticated.

As far as tempo: One can double, match or cut the beat in half and still be in time. 

Know which cords go together in the key. Memorize blues pentatonic scales that go with the chords. Pick up a few of the melody notes, preferable the first few and the last few. Then play double stops and blues scales with the chord changes. Add syncopation to your break. No, it is not easy. But it does get easier with time. Enjoy the process.

I pretty much only play fiddle tunes on my fiddle so I don't think about chord progressions or breaks... Sometimes I'll "quote" other players. For ex: I play this tune called Phoebe Ice/Up Jumped Jenny. I'll vary the phrases and "quote" the players I got it from, drawing from sources I've "studied". Sometimes it's in the moment... digging in a long downbow with a drone... playing around with phrasing/syncopation... changing up melody/bowing sometimes predictably and sometimes finding a "solution" in the moment...

improvise
/?m?pr?-v?z?/
intransitive verb
To make, compose, or perform with little or no preparation.
improvise a solution to the problem; improvise variations on a melody.
To make or provide from available materials.
improvised a dinner from what I found in the refrigerator.
To make, compose, or perform something extemporaneously.

Yes, definition.
I asked for that. Didn't get it.
Many in the piano community define improvising as simply playing by ear.

Yeah, Theory, licks, motifs and all that. Grapelli said improvising is composing on the fly, who am i to disagree?

Chord-Tone Scale... A scale that emphasises the notes of the chord, common in bluegrass: Omit the 6th ascending, and omit the 7th descending. Each chord has a different scale.

Snippets/Motifs... Short phrases of four note/finger patterns, played in sequences or mixed. Create, memorize and transpose them. Eg, 1 2 3 4 can be played in any key.

Basic Melodic Line...Follow the contour of the melody: 'Billy in the Low Ground' is a good example; it moves through an octave in the first few bars, vary the notes in between. Cultivate an internal sense of the phrase.

Change/Improvise just one phrase of the tune at a time.

Avoid learning (some) tunes note by note to force yourself to improvise, but know the chord progression.

As everyone has stated..

I see these chord tones in MY head.

These days I'd say, "faster the tune, less time to hear my mistakes"

I think in jazz, blues, and Country/Americana music where chord progressions drive the music people approach improvising differently than fiddle tunes... licks, tricks, theory...

but the questions was about "fiddle tunes"... traditional fiddle tunes aren't based on chord progressions

You need to practice thinking at that pace. If it were me, I'd listen to a lot of music that is above your comfort zone and get the brain used to it. Start trying to make stuff up, in your head while you listen. Improv, the kind that's not just a bunch of licks strung together but on the spot creativity, also requires practice. Unfortunately, I can't tell you how to be creative. Maybe record your slow improv and try repeating it note for note , then try speeding up your newly created mprov lines (metronome helps, no need for the backing music, it's an exercise). As stated at the top, the brain needs to practice creating  the music at the speed of thought essentially. 

Improv on a fiddle tune is tricky if you want the listener to know you're playing the tune (and I assume there will be a listener, even if it is just you)

You can't throw a curveball to yourself. What I did was listen to the radio, with my fiddle in hand. Find the key to the song, and if there was enough time, try to play along. Even if it was just a note or two. The song would end, and another would start, and the process would start over.
Another thing I did is learn standard fiddle tunes. Five tunes learned turns into ten tunes, turns into 20 tunes, etc. Tunes have sisters, brothers, and cousins. Tunes have common keys. If I heard a tune somewhere, by the time I had my fiddle in hand, it would usually come out in D. Then, eventually, i may find the common key and may have to transpose. That's a good drill, too. If you really want to get familiar with a tune, transpose it to a key that's more than just moving over a string. Transpose, not transcribe.

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Originally posted by Shawn Craver Fiddler

I think in jazz, blues, and Country/Americana music where chord progressions drive the music people approach improvising differently than fiddle tunes... licks, tricks, theory...

but the questions was about "fiddle tunes"... traditional fiddle tunes aren't based on chord progressions

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RE: fiddle tunes  i find mostly revolve around the pentatonic scales and their neighbours/companions. IE: only 1 note difference between the Pentatonic minor or major scale that forms the basis for the tune.

The pentatonic scales and their inversions (for me), are derived from the modes of the major scale minus the 4th and 7th of the Ionian mode or Major scale.

if you play a pentatonic version of the tune substituting any missing notes from the 7 note (ionian mode, or major scale) with standard harmony notes within the pentatonic scale. (eg: 3rds, 6ths and 5ths/4ths, or chromatic lead in notes etc). That will yield a basic pentatonic improvisation for the tune with added notes. And incidentally a bunch of double stops to play around with also.

Then there are rhythms, subdivisions, dynamics,tone, ornamentations and effects  etc to play around with...."Fill your boots"... But you will still need the theory, techniques, creativity and knowledge etc to do so....Or you can just wing it, as i did when i first started

Improvising on a tune is the same as playing a variation on the fly. In Classical music this is called 'Theme and Variation', where the chords in the latter follow exactly those in the theme. There might be some closely related substitutes, but the order of the chords (chord progression) will be the same on each repetition for the purpose of harmonisation.

The theme can be based on a chord progression, if not, it is allotted a set of chords anyway, so the variations will harmonise with the accompaniment. The theme must also harmonise within it self by making emphasis on chord tones which determines the type of chord for the accompaniment. The same harmony needs to run through each variation so the listener still actually hears the main theme.

Depending on which rhythm is chosen for the improvisation, the fast rhythms have less time to think about every note, thus we think in note groups, motifs or snippets which have been assimilated into the subconscious mind. This allows us to focus on the notes that outline the harmony and fill in between these notes with motifs and snippets.

Uh oh, I have to learn theory..? Eek I didn’t think I needed it !!

Thanks everyone. I’m gonna try and get in some extra practice time this week, hopefully I’ll get better at this!

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Originally posted by HappyTune

Uh oh, I have to learn theory..? Eek I didn’t think I needed it !!

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it is a lot easier to do, than it sounds when someone is trying to explain it.

quote:

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Originally posted by HappyTune

Uh oh, I have to learn theory..? Eek I didn’t think I needed it !!

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Music Theory for Dummies... a fun read and you'll LOVE it.

Theory? Well you kinda need a bit, or at least know what notes you can select from for a given key and what effect different ones yield. Me, I know a bit but more like I know when to throw something outside the expected. Useful is a good set of ears and good taste! Fast or slow, I think good improvisation needs those.

Knowing the difference between a note and a chord. Knowing what a key is. Possibly knowing Nashville numbering. Knowing a large percentage of tunes have three chords or less. This little bit of 'theory' helps answer how it's done.