I'm currently in the process of trying to learn to play a keyboard piano (No sustain pedal, no weight sensitive keys), but find that I'll need the help of some more experienced players to answer a few of my questions about how to go about starting. I have a basic knowledge of reading sheet music identifying the proper keys for each note, but I'm pretty much a complete beginner in everything else, having never taken any lessons and having only been practicing with basic 1-note-at-a-time songs for around a week now.
First, I wanted to ask about the proper technique involved when playing above and below a basic scale C to C, for example. I learned through a series of online videos that, using your right hand, a basic scale should be played with your thumb on C, placing your fingers down through G. The first three notes (C, D, E) will be played by your thumb, index finger and middle finger, followed by tucking your thumb beneath your two fingers to strike the F key, then follow with the rest of your fingers to play the remaining 4 notes.
I've been practicing with the technique for a little while and have found that while my finger movements and key identifying are a bit faster, I have no idea how to play a song that would have me switch from the base C up to higher B (last before hitting the next scale).
Any tips on proper hand and finger movements in order to quickly switch between keys?
Second, I've found that, more than anything else thus far, I have absolutely no hand and finger independence at all. I'm able to play a very basic song using both hands, but that's only been the case when the striking of keys with my left hand corresponds exactly with my right hand striking a key. However, if I'm supposed to strike a key off time with my right hand I simply find myself pressing down somewhat randomly with both hands, usually striking with a bit more force than normal as well.
To get straight to the question, what would I be recommended by an experienced player to do in order to train myself in basic hand and finger independence?
P.S. I apologize if I've made some mistake in formatting or in making a question/thread overly similar to another's rather than simply reading their's. I tried looking around for someone asking similar questions, although the answers I found usually involved having experience in basic independence already.