In Irish Fiddle Music I believe the following is fairly accurate.
A Jig is in 6/8 time
A Reel is in 2/4 time
A Hornpipe is in 2/4 with a different accent.
In Minstrel Banjo
A Walk In The Parlor Jig could be considered 6/8 time but most other Jigs would not be.
Do the terms Jig, Reel, Hornpipe, Walk Around, etc. have any meaning regarding the structure of the musical piece?
I'm not at home, so I don't have access to my resources, but as I recall, early on, jigs were dance pieces for an individual dancer, and were generally something you would expect to hear on a banjo, or by an african american player, or among the common/lower classes. In that classification, time signature did not matter.
Reels were popular from the 1830s through the 1850s (and still today in some circles). I've seen reels both in 2/4 and 6/8. Reels were dances where you would have 3-8 ladies lined up on one side, and their partners on the other, facing one another. Being both a dance master, and having played for balls, the tempo for a reel is more important than just about anything else. You want this to be between 88 and 120 beats per minute (usually). Too slow and the dance is dull, too fast and the dancers can't keep up.
Hornpipes are usually in 2/4, and the rhythm associated with them are a dotted eighth note followed by a sixteenth note.
Lucy Long is an example of a walkaround. I've often think of walkarounds as being show stoppers or the final act of a show. I don't think that many rules applied with walk arounds. I'm hoping someone else can contribute more to some of this.
From The Musiclover's Handbook 1893:
Jig comes either from Geige, an obsolete variety of fiddle, or from Chica, a rapid Spanish national dance. Now a rapid rustic dance of no fixed rhythm or figures. In the classic suite the jig is the last movement, written in 6/8 time and often very elaborately treated in fugal form.
Reel. A lively dance, nationalized in Ireland and Scotland; supposed to be of Danish origin, as the same kind of dance is found under the Danish name of Hreol.
Hornpipe. An old English dance of lively, rapid character.
Other than the 6/8 classical movement reference- no indication of time structure. The rules could be modern.
It is funny that they forgot to mention the Ireland connection to all of them- or is that a post Cheftain/bodhran/folk thing?
I'd be very interested in an in-depth study (and one that was not influenced by the authors personal agenda of "Irish music") on just how our concept of popular Irish characteristic music came to be.
The Irish stereotype was a part of the cork opera, and most of the "Irish jigs" in our tudors were likely put there for Paddy (in cork, fake red beard and green suit) to dance a jig, get into brawls and give drunken speeches. Some of them were even written by a boy born in Massachusetts and who grew up the son of a music teacher in New York.
Then there are our beloved "Irish" songs from Tin Pan Alley written in New York by a Jewish man.
Most of the 'Jigs' of Minstrelsy are not a true Irish Jig, but 'Ditties.' Irish jigs come in a few forms - the Single Jig - 4 notes to the bar with the downbeats dotted, The Double Jig - 6 notes to the bar, the first of each group of 3 notes slightly accented. The Slip Jig - 9/8 time - the ones that sound like fast waltzes, and kind of a hidden away "jig" style from the Rushy Mountains in Ireland, They would never call it a jig, it's the Slide - the basic form goes like this - DUN da -da da da and can be played very fast. Irish Polkas also come from that region.
Single Jig DUN da DUN da
Double Jig Da da da Da da da
Slip Jig (Are there even any Minstrel 9/8 jigs?) DUN da da da DA DUN da DA da da-da-da
Different Jigs, different dances.