Firstly, welcome to the forum @deBachin !   Enjoy your fiddle journey !

In response to your question - I believe that Amazing Grace is a tune and song which has its roots in "American spiritual music".   Many such tunes are often not written using the full 7 note ( 8 if you include the octave ) western diatonic scale - rather, they are written using a subset of only 5 notes from that scale, and is called a pentatonic scale.

You are correct, the key signature (i.e. none shown) assumes the key of C, but you are also correct in that yes, it is a tune in the key of G (pentatonic, that is)

However, the only notes that the tune uses from the key of C ( C being C, D, E, F, G, A, B / C of course ) are five notes - those being G, A, B, D and E - which just happens to be G Maj pentatonic - so - although possibly not immediately obvious - the reason it was scored like that in it's simple way was to remove yet another possible difficulty for beginners (having to think about where any sharp and flattened notes would be - which - in the basic (non-chord) version of this tune - is un-necessary anyway).  The score could quite happily have been explicitly scored showing the key of G Major with the single # on the F stave line.   But - the tune doen't use it ( F# - nor does it use C - ) - so I guess it was an attempt just to keep it simple....

Agreed, the chord version requires the F to be sharpened, and it is shown as such as accidentals where required.  Don't forget, awkward although it may be, even in a score with a key signature (or assumed) of C - using as many accidentals, sharps, flats and naturals as required - the piece could be in ANY key.... (yes, somewhat extreme I agree, but nevertheless, is the case)

It's always difficult to target the level of information at every beginner's level - some arrive (as yourself) with clearly some background musical knowledge, some may arrive with absolutely none - so why burden them with the presence of this # on the F staff line, giving them yet another thing to worry about, when, for this piece, well, it's not necessary

Hope that helps clarify things, and best wishes on your playing journey

ROFL @Gordon Shumway  ( not laughing AT you of course, just a kind of face-palm thing like - oh, no.... something else to investigate!!!  D'Oh !!! )

hahaha, too busy right now to delve into that, stuff to do....  I'll investigate what you wrote later. 

Just out of an enduring sense of interest and general curiosity of course !!!

Just back from cutting some timber - thanks for that @HP

I'll have to go find out more about non-western scales - always been in the back of my mind to research this, but never got around to it....

Of course, there is another minor (no pun intended) possibility - in that in the key of C, its relative minor is Emin.   And of course, Emin pentatonic must be E, G, A, B, D | E

That might just tie it down if I got that correct ?????

Just a thought.....

More timber cut - right - I wrote before I properly thought about it...  I think I was trying to say something like this....

Gordon - you say the key sig was G but the piece was C pentatonic.

I believe what I was trying to say was this (and excuse the stupid slip of the pen two posts above, the relative minor of C Maj is of course A minor, the "key of G thing" was in my mind - the relative minor of which is E min - that's where it came from )

Anyways - how about this - ( LOL - I had to write it down before I confused myself again !!!! )

Key G Maj - G A B C D E F# | G

Key C Maj - C D E F G A B | C

Key A min - A B C D E F G | A

A min pentatonic - A C D E G | A

So, A minor (pentatonic) would "look like" something in the key of C (in the sense it has notes from the scale/key of C) - and of course for Amin the key sig is just C...

Hmmmm LOL

Who needs key sigs anyway, just use accidentals everywhere

pchoppin said
Ye'r a guid jimmy, @BillyG 

  

TY  @Pete_Violin !   Aye, indeed.   A "guid jimmy" - for that sir, I hereby bestow upon you the title of Honorary Scotsman (something not to be taken lightly.. )