Haven’t read the whole thread, but I think you may be looking for the pentatonic scale. The notes in the C pentatonic scale are C, D, E, G, A. All of those notes are also in the F and G major scales, so it will sound OK even when you switch chords.
There are no wrong notes.
It sounds like a pretty radical concept, but it’s one that Kenny Werner puts forward in his book “Effortless Mastery.” He is a jazz pianist himself and he tries to get musicians to look at the concept of soloing a little differently than what most of us would imagine. It’s a fascinating book if you want to give it a read. Here’s a sample.
Sure, I see what you’re saying, but why not have the same notes occupy the same spaces on the staff? You know, F-A-C-E for the spaces between the lines in the treble clef. Why not use that same positioning for the bass clef? Now, I’m sure there IS a reason, but I not-so-secretly think that it’s probably a somewhat archaic one that is kept on by tradition. If the notes were all “in the same place” on the bass clef staff, I could play bass clef no problem.
To me, it’s like having a language where the word “ant” is spelled “bou” because every letter is shifted one space forward. It carries exactly the same information and is just a pain to read.
Biffster, that’s a nice idea, that there are no wrong notes, and I suspect drad_dog’s post, “…you can make a wrong note right by what comes after” is applicable here, but for someone sitting down to “learn” how to improvise at a pretty basic level, there definitely ARE wrong notes. Ask my girlfriend. There are lots of them.
(Not to say I don’t appreciate the link!)
And I’ve been exploring the major pentatonic as well - thanks, jaycat.
Werner’s purpose is mainly to get “trained” musicians to lighten up a bit, and his method really does work. It’s a different way of looking at music though and not everyone is ready for it. My basic advice is trust your ears; if you’re playing in the key of C, for example, the root and the fifth (C and G) are usually your safest notes, with the third (E) working sometimes and not in others (not so good over a IV chord for example). Pentatonic (C D E G A C) is also pretty useful, with the odd Eb and Bb thrown in as blue notes. Really, you just have to experiment and don’t be afraid to make “mistakes.” And if you make a mistake, play it twice.
I don’t know he reason but I suspect you are correct–it’s tradition. The bass clef is an ‘F’ clef, the treble a ‘G’ clef. The shapes are from old ways of writing the letters; the bass clef surrounds the line for ‘F’, the treble the line for ‘G’.
Your idea is a good one. I couldn’t read bass clef until I got to college and had to learn–hell, I could barely read treble clef.
Here’s the video I promised. It’s not the greatest, and I’m being a bit sloppy, but you will get the idea:
I do get the idea, yes - perfect. Thanks for taking the time to make the video!
You can also jazz up existing songs.
Take “Old MacDonald”, for example: Elvis is on the right track with a rockabilly sound.
Too late to expand on that.
I whistle a jazzy version that is similar to his rendition but only up to “E-I-E-I-O”, then it’s like “with a cluck cluck here, and a cluck cluck there, and a cluck cluck everywhere.”
In some thread previously, you made a similar statement. Coming from being a bass player originally, the idea of not moving the scale you were working with around with the root note was an idea that simply hadn’t occurred to me. It’s too common in rock bass and guitar (especially surf) to move the scale around with the root. Plus, it’s easy on stringed instruments to transpose the scale to the current chord.
So, I went over to my keyboard and tried it. I was kind of surprised at how nice it was, but it sounded “corny”. Now that I suck a little bit less, I know that the corny part was my awful playing. I think that staying in the I scale sounds kind of primitive, while moving the scale along with the chord sounds more interesting.
And it was nice to finally see ya play. Even if you were just screwing around, you’re better than I by far. 
And I am in the same camp as the “no wrong notes” guys. Though my favorite version is Victor Wooten’s " You are never more than a half - step away from a right note." That’s pretty much true for any key. Just slide into a note that fits in with some style if you hit a “wrong” note.
I’m not necessarily claiming I do 
but to some extent you do need to know what you are doing (or maybe some geniuses can play everything by ear, who knows). For example, following that link I gave, right after the example of the blues solo in F, the next example is of blues in C minor, and now the advice given is
While a collection of blue notes may serve as a blanket scale in major blues—riding over chord changes without changing—such an approach will not work in minor blues. Generally speaking, minor blues improvisations must follow the chord changes more closely, introducing altered pitches that specifically point to the minor key, not just the blues flavor.
There are some “bass” or “tenor” instruments that are notated using a “treble” clef. The guitar, for example.
Check out some of the clips on this page 
Next installment of my music series:
Well no one ever said you “couldn’t tell” when a player was saving his own bacon after a weird note.
I’m not going to stick around for any length of time, so modes don’t have to worry, but I remember I was somewhat rude to you, pulykamell a few years ago on another board, and I feel bad about that.
You’re a much better man than I am doing very simply things to illustrate at the keyboard.
FWIW, yeah, I mean, you can put some grit in G in a C-blues for emphasis (while still making a melodic statement), but, thanks for putting people right that you don’t actually change scales for a regular, should I say, Chicago blues. You know, just a regular blues.
It’s not like playing some Wayne Shorter tune, you know.
Anyway, that’s pretty brave of you to do just simple stuff, whereas most probably musicians would be running everything they could think of, just for the sake of being fancy.
I have no idea what forum you’re talking about, and I generally don’t get into arguments with people online, but thanks for the good words. Was this on Sound Opinions? That’s about the only board I could think of, but I had a different screen name there.
And I can let shit fly when I need to. In most of the work I’ve done, I’ve always kept it restrained – kept it honest to the song. Add color without taking away attention.
But then I had a friend ask me to do a “wrath of God” solo on this song. It’s also a simple I-IV-I-V progression, and I lean into the gospel organ sound, mostly blues scale, and then, I dunno, something just fucking breaks in me:
It’s not important. I meant to only send you a PM, just to say I liked your demonstrations. It was a while ago, some zoo animal board or something. But I think there’s a threshold above which one must reach in order to do PMs with the new format. I just hang at pianostreet and mellophant now, and I don’t want to cause any more problems for the mods.
Still, it is true that if I or any number of people did a basic illustration of “shuffle blues in C,” probably most people would not have your restraint, so that’s to be respected. IMHO.
And, ad your most recent comment, yeah. Hell, I still listen to Billy Preston’s Vee-Jay recordings on primarily Hammond organ…there is certainly a time to open the gates of hell! Provided one has the chops!