Hello, I'm a new one here and I'm french (or belgian) and I speak in "decadent" english.
Some years before, I have written on IORR and other sites. I told about a great version of the concert at Roundhouse in 71 and I have showed that the riff of Under my thumb come from the introduction of "It's the same old song" of the Four Tops, that the melody of Paint it black come from "My world is empty without you" of the Supremes and the "paint it paint it" was inspired by the "baby baby" of Diana Ross on "Where did our love go". I had other ideas. The inspiration of Ron Wood for It's only rock'n'roll (but I like it) is the guitars on Blues Power (Clapton at Rainbow theatre with Wood, Townshend in january 73), the riff of Pinball Wizard comes from London social degree of Billy Nicholls, future producer of the Who. Maybe the riff of Satisfaction come from an acceleration of the horns of Nowhere to run the hit of Martha and the Vandellas. Everytime, the sources come juste a little time before the creation of the Stones (or the Who). Surprise, surprise was sung by Lulu and the Luvers and The Sweet imitates the title with Ballroom Blitz, but in realité the Stones took the riff and structure of Let's stomp, an english merseybeat of 63 by Lee Curtis and the All Stars with a drummer named Pete Best. For Angels in my heart, Mick Jagger took a piece of melody of Would'nt you a song of the very first album of Legend with Mickey Jupp (two albums was intitled "Legend" before Moonshine the third one).
You know that The Last time take a melody  of Maybe the last time (Staple Singers) and I'm alright was a song of Bo Diddley as Charlie Watts said himself on stage at the time (live album Beach Party).
And now, I don't believe in the legend that Bill Wyman creates the riff or the embryo of Jumpin' Jack Flash. Keith is not agree, he writes that the title come from a speech between him and Jagger. Keith saw his gardfener Jack Dyer and said : "Jumpin' Jack", Mick added : "Flash" and they smiled of their rythmic creation.
You will see that Keith hides a part of the truth but he knows better than Wyman the origin of the song.
In reality, Jackie Day is a little bit similar to the name Jackie Dyer. Days goes with "Flash". Jackie was transformed in "Jack". Why a Jumpin' Jackie Day ? Because Keith and Mick was seduced by her song Before it's too late. Mick and Keith transformed "Jackie Day" in "Jumpin' Jack Flash" and "it's too late" in "it's a gas gas gas". Keith transformed the riff of Before it's too late in a riff rock. The riff seems a little bit similar to the music of Otis Redding according to me. But nevermind. It's the same riff with a transformation from soul to rock.
And eventually, Mick and Keith was interested by a particular detail in the structure of the song. After the 2/3 of the song appears a play with saxo and how to say in english a particular sound saturates the song with only one sound. Keith and Mick loved that. They are developped the same thing on Jumpin' Jack Flash with a "organ" who sounded like an harmonica and a big sound saturates the end of the song. They do the same with Street fighting man, you have and indian horn ("hautbois" in french) at the same moment in the structure of the song.

You can find "Before it's too late" on the compilation 4 CD of the catalog of Guy Stevens.
I'm not allowed to publish a link in my first message, but I wanted to say at once all this. I have written in french too in another french site.
I will published the links another time.

A song a little bit similar to Paint it black, but... in 67



The two songs of the Supremes are the origin of Paint it black, but this other song shows how the melody of Paint it black is in a precise period of history of music. Other old titles would be similar to Paint it black for the sad and blue melody. The oriental style hide this fact.

I believe legend has it Mick and Keith were together early one morning after some rain. A gardener named Jack was skipping on the sidewalk to miss puddles and that rhythmic sound was the inspiration of the riff. Jack was the the Jumpin Gardener.

Dude's got some imagination and a lot of time on his hands.

Welcome to the community, GoingDown.  I had never heard that Jackie Day song.  That's it!  The "That's jumpin' Jack" story about the gardener was about the lyric, not the music. 

P.S. You write English excellently.