Why Don't We Unite And Simplify Embellishment Notation Once And For All?

This is my idea, but if you have better and more practical ideas just share them. My idea would be to simplify how to write the embellishment, mostly we are all confused often on how the composer wanted us to play. Do we start the trill from the same principal note, above or below, sharp or flat? But why don't we make things more simple? Mostly when we play these ornaments we have only three note: the same principal, the one above, the one below. So, instead of writing symbols why don't we write letters. We just need three letters, s-u-d, and we just combine them. s=same note, u=upper note, d=down. The speed of execution is done simply according to taste, but that's going to be always natural and obvious, the duration of the trill can be prolongued with the usual zig zag sign, and the sharp or flat are just indicated like we do always in a turn symbol. Here are my example pics, let me know what you think, it would be very useful to unite for this.

I changed my mind. Symbols or letters? What's more practical? I don't want to change the original scores, and when the ornaments are open to interpretation, that's also a good thing. On the other hand I am interested on what would everybody would like to read if they had to create a way to write ornaments today from scratch. Language is still a problem, that's true, we are still too territorial, and maybe symbols would be more accepted. So, for example, instead of three letters (s, d, u), we could use three symbols, an up arrow, a down arrow, and an "=" to indicate the principal note? Would it be a good idea? But I am starting to think that it's not that useful, basically I am just reinventing the wheel...

It's a good idea but a little too complex. Most performers even still at a learning level often have enough knowledge to interpret embellishments. As a keyboardist, it's a very natural thing to just see the symbol for an embellishment and to perform it without a second thought. I don't want to have to spend extra time reading letters to figure out an embellishment. 

Also, embellishments were born out of the improvisational styles of the Baroque and Classical periods, and so putting an exact way to interpret it would defeat their purpose. For example, many piano instructors often frown upon improvising on Bach, while Bach actually encouraged improvisation! He left it up to the performer to tastefully decide how to perform embellishments. Putting this kind of system in place would unfortunately take a key part of individual interpretation and musical expression out of music. 

Now, if you as a composer do not wish to leave embellishments up for free interpretation, then it completely fine to dictate exactly how you want them played. That's a choice of your own. 

The good thing about published sheet music nowadays is that if there is an embellishment other than a basic trill in the music, editors will input small footnotes or notes on the margins showing one or more possible interpretations including their fingerings. 

I agree with JaredTC.  Your idea sounds perfectly reasonable, but any time you change the system, you slow down anyone who knows the old system.  So things generally evolve slowly through infinitesimal changes, that everyone can understand immediately, the first time they see, without missing a beat while sight reading.  It's very rare to get a whole new, different system accepted, in music or anywhere else, even if it's better.  This is why the US still uses pounds and miles, instead of kilograms and kilometers.  

Don't forget, students can practice a new piece of music for months, but professionals are often handed the music with only time for one run-through before it is performed, so they have to be able to clearly interpret what you've written correctly every time, including the first time, and when they have a bad page turn and can't read ahead.  It's safest in that situation to stick with the system that all those professionals are already trained in.  

(I get "surprise!  It's a solo for you, and you've never seen this music before in your life!" or "Surprise!  You've never seen this piece before, and you are the only person on your part!" pretty frequently.  Things happen, people get sick, you need an extra person on the descant for balance, the piece you thought would be easy to pull together without a rehearsal turns out not to work well for the group you have... and the director has 15 minutes to come up with a back up plan and run find the music in the library for everyone.)

No, there are already conventions in place to properly notate any possible combination of ornaments, and if ever in doubt it is perfectly acceptable to notate it out instead of relying on an ornament notation.

Perhaps if someone is confused about how to play a trill when coming upon it, instead of developing a new system they should take the time to learn the old one.