A lot of tunes are heavily syncopated. Hornpipes are the classic example, since they're written to be played with dotted rhythms. Play them as runs of even eighth notes and they just sound dumb.
Me, I tend to syncopate freely, even for reels written as straight runs of eighth notes.
Some traditions don't do that sort of thing. Listen to a great klezmer band, like Di Naye Kapelye or the Klezmatics, and you'll hear straight-ahead eighth notes. Breaking my tendency to syncopate is one of the things I had to learn to play klez.
There are, however, excellent reasons to unlearn this even to play dance tunes. Let's look at Texas Quick Step, or Rachel. (Pete Chielmowiec tells me these are different tunes, because one starts on the coarse, the other on the fine. I start with the coarse and can never remember which one that is, so I use either name.)
The coarse is an arpeggio in D, followed by an arpeggio in G, capped with a mix of scales and arpeggios in A and, finally, D. Try running through those arpeggios as a bunch of crisp, poppy, even, eighth notes If you're a music reader, think of it as moving your dots from next to the notes to under them. If you're not, think of trying to sound like a typewriter or a machine gun. Now go back and play it syncopated -- "Good & Plenty, Good & Plenty, ...," and you'll hear what I'm getting at.
Even if your fiddler's cross-tuned to D, switching from this tune to Fisher's Hornpipe gives you a clean contrast. Dancers will hear that tune change.
After this difference jumps out at you, it's another arrow in your musical quiver. You can switch back and forth from part to part, and even within parts, to spice up individual fiddle tunes.
Rachel's also a good vehicle for working on arpeggios.
As Walt Disney teaches us all, in The Aristocats, tunes are just scales and arpeggios, with a few "passing phrases" thrown in. This is, I'm guessing, why students still buy zillions of copies of Hanon: practicing scales improves your playing. And it's as dull as a car covered with primer.
Finding a few tunes that emphasize scales and arpeggios, instead, gives you a chance to work through the mechanics without making yourself or the people you live with listen to half an hour of "Do-Mi-So-Do-Do-So-Mi-Do."
You only need a few because there are, after all, only a handful of keys: D, G, and A mostly.
What's to work on? First off, just noticing that they're there. If I'm showing someone the tune, I can say, "Watch closely: D, F#, A, D, F#," or just say, "Start with a D arpeggio, low D right up to the F#."
Tunes like Hairlip Suzie and Woodchopper's Reel? Easier to learn. Funner to play.
And don't take your fingers off (or, if you do, don't take them off much). That's the second thing. You already know how to make that chord, so just slap your left-hand fingers down as a group.
Think of the melodies vertically, instead of horizontally. In Rachael, the same thing goes for the G chord, which follows that D. Two chords get you half the A part -- every note.
Jumping to the B part for a second, the melody starts with two quarter notes: an F# and a G. Think of these vertically, too. It's the same D and G chords.
If you play the chords, instead of just thinking of them, you make that part more interesting. You can punch the pair, strum them, or play them as arpeggios. You can play them as double-stops -- as two-note chords. Whichever way you pick, when you learn the melody you're not learning a pair of notes, you're learning a pair of chords.
Thinking vertically lets you vary tunes without thinking, "I suppose I could throw in a trill or a pull-off here to spice things up." Your right-hand creates melodic variation by changing how it plays the chord.
As an added benefit, since you no longer have to think hard about where to put your left hand, you can listen for whether you want to syncopate or un-syncopate your right.
