This is probably enough basic info about the tune, from A Fiddler's Companion:

JENNY PUT THE KETTLE ON [1]. AKA and see "Molly Put the Kettle On," "Polly Put the Kettle On." Old-Time, Breakdown. USA, Missouri. D Major. Standard. AABB. A version of "Molly Put the Kettle On." The title appears in a list of traditional Ozark Mountain fiddle tunes compiled by musicologist/folklorist Vance Randolph, published in 1954. That the tune was also in African-American tradition was attested to by Ashe County, North Carolina, musician Hobart Smith (b. 1897), who said: "The first fiddle I ever heard in my life was when I was a kid. There was an old colored man who was raised up in slave times. His name was Jim Spenser. He played 'Jinny, Put the Kettle On' and all those old tunes like that. And he would come up to our house and he'd play..." (quoted in Cecilia Conway's African Banjo Echoes in Appalachia, 1995). See also Bayard's note for "Bonaparte Crossing the Alps." Source for notated version: Frank Reed (Randolph County, Missouri) [Christeson]. Christeson (Old Time Fiddlers Repertory, Vol. 2), 1984; No. 66, pg. 46.

JINNY PUT THE KETTLE ON. AKA - "Polly Put the Kettle On," "Molly Put the Kettle On." Tune (and title, presumably) learned by Hobart Smith from black fiddler Jim Spencer.

LOWER EDGE OF BREATHITT, THE. Old-Time, Breakdown. USA, Kentucky. A "crooked" tune similar to Emmett Lundy's "Molly Put the Kettle On."

MÁIRE CUIR SIOS AN COIRE, A. AKA and see "Molly Put the Kettle On."

MOLLY PUT THE KETTLE ON [1]. AKA- "Jenny Put the Kettle On," "Polly Put the Kettle On." Old-Time, Breakdown. USA; Georgia, Mississippi, Virginia, Missouri. D Major (Brody, Phillips): A Dorian (O'Neill). Standard. ABB. African-American fiddler Joe Thompson plays the piece in FCGD tuning. Sources for notated versions: The Skillet Lickers (north Georgia) [Brody]; Emmet Lundy (Va.) and Joe Politte (Mo.) [Phillips]. Brody (Fiddler's Fakebook), 1983; pg. 194. Phillips (Traditional American Fiddle Tunes), Vol. 1, 1994; pg. 154. Columbia 15380 (78 RPM), Leake County Revelers (Miss.). Columbia 15746 (78 RPM), Gid Tanner and His Skillet Lickers (N. Ga.). County 506, The Skillet Lickers- "Old Time Tunes." County 529, Leake County Revelers- "Traditional Fiddle Music of Mississippi, Vol. 2." Folkways FA 2399, New Lost City Ramblers - "Vol. 4." Global Village C217, (Black fiddler and banjo player) Joe and Odell Thompson - "Old Time Music From the North Carolina Piedmont." Marimac AHS #3, Glen Smith - "Say Old Man" (1990. Learned from Creed Smith). Marimac 9038, Dan Gellert & Brad Leftwich - "A Moment in Time" (may be version #4). Rounder 0058, Haywood Blevins (southwestern Va.) - "Old Originals, Vol. II" (1978). Victor 21518, Ernest Stoneman - "Serenade in the Mountains."

MOLLY PUT THE KETTLE ON [2]. Old-Time, Breakdown. USA, West Virginia (probably) Not similar to the "Polly/Molly Put the Kettle On" versions of the tune, but seems related to the tune "Yew Piney Mountain." Folkways 31062, Ship in the Clouds- "Old Time Instrumental Music" (1978. Learned from Vermont fiddler Pete Sutherland).

MOLLY PUT THE KETTLE ON [3] (A Maire Cuir Sios An Coire). AKA and see "Jenny's Bawbee." Irish, Reel. A Dorian/G Major. Standard. AB (O'Neill/1850 & 1001): AA'BB' (O'Neill/Krassen). The melody was used for a well-known country dance and nursery song in the 18th century; the rhyme is still found in Mother Goose collections. O'Neill (1850), 1903/1979; No. 1363, pg. 254. O'Neill (Krassen), 1976; pg. 126. O'Neill (1001 Gems), 1907/1986; No. 616, pg. 112.
T:Molly Put the Kettle On [3]
L:1/8
M:C|
R:Reel
S:O'Neill - 1001 Gems (616)
K:A Minor
cded cAAc|Bcdc BG G2|ceed cBAG|EDE^G A2A2|cded cAAc|Bcdc BG G2|
cBcA B2 AG|EDE^G A2A2||cde^f g2 fg|aged cA A2|cde^f g2 fg|
age^g a2a2|cde^f g2 fg|aged cA A2|cded cAAG|EDE^G A2A2||

MOLLY PUT THE KETTLE ON [4]. Old-Time, Breakdown. USA, North Carolina. No relation to "Molly Put.." [1]. This version is from North Carolina fiddler Manco Sneed via contemporary old-time master Brad Leftwich. Sneed, Osey Helton and Marcus Martin, all western North Carolina fiddlers who had their heyday in the early 20th century, learned the tune from Jamed Dedrick Harris, of Flag Pond, Tennessee (and who lived for some time in North Carolina), who had been the fiddler who accompanied Governor Bob Tylor in his whistle-stop campaign called the "War of the Roses" (Hartford). Harris was born in 1859, made fiddles and travelled, according to John Hartford. Flying Fish FF-055, Red Clay Ramblers- "Merchant's Lunch" (1977. Learned from Manco Sneed). Rounder 0392, John Hartford - "Wild Hog in the Red Brush (and a Bunch of Others You Might Not Have Heard") {1996. Learned from fiddler Brad Leftwich}. Shanachie Records 6040, Gerry Milnes & Lorraine Lee Hammond - "Hell Up Coal Holler" (1999).
T:Molly Put the Kettle On
S:Tape recording of Manco Snead
A:Cherokee, North Carolina
N:Manco mumbles a bit, so it's unclear whether
N:he says "Molly" or "Polly." Calling it "Molly"
N:keeps it separate from the common song tune.
I:/ above a note indicates a slide up to that note,
I:+ above a note indicates sharpening, V indicates
I:flattening. Manco changes his pitches more than
I:a little.
N:Parts played in order:123443
Z:Joel Shimberg
M:C|
L:1/8
K:G
"1"{A}BAG=F DC"v"B,C | DE=FG FD C2 | D2GA GFGA | B"+"cdd =fdg2-| ga g=f
d2(3cdc |
BcBG =FD"v"B,2 | DGGA GFGA | {A}B2G2G3 G- || "2" GA"v"Bc d4| _Bcdc _BG=F_B |
GABc dcdc | BcBF G2DF | GA_Bc d4 | _Bcdc =BG=F_B | GAG"v"F DCB,C |
DG2FG2G2 ||"3"A<B G=F DC (3A,B,C | DE=FG FDC2 | D2GA GFGA |
B"+"cdd =fdg2- | ga g=f d2(3cdc | BcBG =FDB,2 | DGGA GFGA |
B2G2G3 "/"G- ||"4" GAB"+"c d4 | de=fg fdc2 | dgga gfd2 |
gagf d^cde | fgaf gfd2 | c2BG F2G2 | GAG=F DCB,C | DG2F G2G2 ||

MOLLY PUT THE KETTLE ON [5]. Shetlands, Shetlands Reel. May be the same as version #2. From the island of Papa Stour, Shetlands.
POLLY PUT THE KETTLE ON [2]. AKA and see "Molly Put the Kettle On," "Granny Will Your Dog Bite?" Old-Time, Breakdown. USA; east Tennessee, western N.C., north Ga. G Major (with flat 7th) {Ford}: D Major {Spandaro}. Standard. AABB. Identified as a common East Tennessee tune. Tune played by Wiley Harper (Monroe, Ga.) in a 1913 Atlanta, Ga. fiddlers' contest.
***
Polly, put the kettle on and slice the bread and butter fine.
Slice enough for eight or nine, we'll all have tea. (Ford).
***
Ford (Traditional Music in America), 1940; pg. 85 (Ford also prints the words to "Molly Put the Kettle On" on page 399). Spandaro (10 Cents a Dance), 1980; pg. 4. In the repertoire of western N.C. fiddler Osey Helton. Biograph 6008, Ebenezer - "Fox Hollow String Band Festival." Folkways FTS 31062, "Ship in the Clouds: Old Time Instrumental Music" (1978). Mountain 310, Tommy Jarrell - "Joke on the Puppy" (1976. Learned from Charlie Lowe).
X:1
T:Polly Put the Kettle On
L:1/8
M:4/4
K:D
|:fg | a2ab afef | gede cAfg | a2ab afef | gfec d2 :|
|: de | dcde fdfa | gfed cBA2 | dcde fefa | gfec d2 :|
X:2
T:Polly Put the Kettle On
L:1/8
M:2/4
S:Howdy Forrester: transcribed by John Hartford
N:Notation for the vocal line appears as the last part, to which is sung:
N:Molly put the kettle on, Katy draw the people in, Molly get the kettle
N:on we'll all take tea.
K:D
A/B/A/G/ F/E/D/F/|E/D/C/E/ F/G/A|A/B/A/G/ F/E/D/F/|E/C/E/F/ D2:|
||A/d/B/c/ d/B/A/d/|B/A/F/A/ d2|A/d/B/c/ d/B/A/d/|B/A/F/G/ A2||
(3A/B/c/||df/g/ a/f/d/f/|e/g/f/g/ a/b/a/f/|df/g/ a/b/a/f/|d/A/B/F/ A2||
||a/b/a/g/ f/d/d/d/|e/d/d/d/ f/d/d/d/|a/b/a/g/ f/d/d/d/|e/d/e/f/ d|]
A/B/A/G/ F/D/D|E/D/D/D/ F/A/A|A/B/A/G/ F/D/D/D/|EC D2||

SALLY PUT THE KETTLE ON. AKA and see "Molly/Polly Put the Kettle On." Old-Time. USA; Arkansas, central Alabama. The title appears in a list of "forgotten" tunes compiled by W.E.G. of Verbena, Alabama, as reported in the "Union Banner" of September 29, 1921. It also appears in a list of traditional Ozark Mountain fiddle tunes compiled by musiocologist/folklorist Vance Randolph, published in 1954.

-Richie