Apologies if this is a naive question.
If there are 7 natural notes and 12 notes in total, was this originally because only the 7 notes were identified, and later they added some in between notes, giving the sharps and flats?
If each non-natural note is both a sharp and a flat, why use both names? Why not call all of them sharps, or all of them flats?
Thanks if anyone can advise.
Deb
There are no naive or silly questions.
I like this explanation as a potted history and explanation.
I am going to butcher this explanation. I only know just enough about music theory to understand it. There are 7 notes in a scale. Itās easier to remember a scale if we always have the same 7 letters. We then add either a sharp or a flat to determine the 7 notes in each scale. (apologies, I know I didnāt explain that very well, itās all about scales).
Thatās a great video Richard shared. Just to add some additional thoughts around the second part of your question not covered explicitly already.
As noted in the video, each key has each of the letters A, B, C, D, E, F and G once and only once - this makes things easier.
If we look at the key of F, there is one flat - Bb. So we have F, G, A, Bb, C, D, E. If we used all sharps then we would have to write the notes in the key of F as F, G, A, A#, C, D, E - so two types of A and no B.
Conversely, if we used only flats then the key of G would be G, A, B, C, D, E, Gb - two types of G and no F. Instead we use F# and write G, A, B, C, D, E, F#.
So we use a mixture so that we can stick to using each letter once and only once.
A couple quibbles with the video. Overall it was pretty good, but it is specific to western music. He doesnāt really touch on this until the end of the vid when he refers to diatonic scales. It doesnāt address eastern music with microtonal scales.
Also, he refers to the letters used as being the first 7 letters in the English alphabet. But heās talking about things happening during the time period of the Roman empire. Pretty sure English didnāt exist, so it would be the Latin alphabet heās referring to.
I also donāt think it quite touched on Debbieās first question. The video starts out during the time period of the Greeks, but youāll notice that people are already performing music. They just hadnāt been writing it down. So they knew about the notes aka pitches. The intervals between them essentially come down to what āsounds goodā.
The mathematics behind that didnāt come until later (Pythagoras). And, since there are different forms of music, that comes from different groups of people independently deciding what sounded good to them and continuing to use those forms. Then of course notation goes through a whole lot of iterations and refinements until it settled on what we use today because itās logical and it works (and in 1,000 years will probably look a lot different from what we use now). The vid moved through a bunch of that pretty quickly. Iām certain that if you wanted to know the details of those changes, youād probably have yourself a music history degree at the end of it.
Thatās a reasonable whistlestop tour of how western musical notation evolved (even if Iām mildly traumatised, being reminded of how to read the notation for all the years of Gregorian chant in boarding school 
)
It does not however follow that it is a āsensibleā way of musical notation. (Youād never design a nomenclature like this from scratch.)
Iād be surprised if it wasnāt similar to the Imperial system of measurements that so many were reluctant to get rid of, simply because everyone was familiar with it and it worked.
This video is interesting (not that itāll ever catch on! 
)
If you watch the video he starts with the Greek alphabet mentions the fall of the Greek and rise of Rome way before using English letters.