I've been playing piano for 7 months now. I've decided to formally start music theory. I know the notes, rests and their values. Now, let me start off with 2 bars. The first being a 4/4 and the next one being 4/8.
Also the common time, has 4 beats and with each beat being a quarter/ crotchet. At this point I don't think we have given any absolute tempo to this bar just a relative tempo between the notes, right? What I mean by that is that, I can always play this bar faster by adding a notation like pianissimo or a fortissimo above the bar.
Please correct me if I wrong with my understanding above. Also, is there a standard tempo for a crotchet that people take it for granted? I've seen some sheets where they specify the tempo of a crotchet = 80 and some without. Is this a standard tempo for it which is a priory assumed?
Now, let's consider the second bar. In general, I've seen 4/8 bars being played faster. I understand that there are 4 beats and each beat is an eighth note. But this can always be played EXACTLY as the 4/4 with just change in the tempo in my bar denoted by a semi-crotchet = 80 right? Am I wrong to say this?
My understanding so far has been that 4/8 is faster because it is probably assumed that a crotchet is conventionally always at 80 tempo (unless mentioned) and hence a semi-crotchet is played at 40 tempo as convention and hence the bar is played much faster.
In summary, is it right to say that
If I set the tempo of crotchet = 80 for my first bar semi-crotchet = 80 for my second bar. Is it equivalent to saying 2 4/4 bars instead of 4/4 and 4/8 right?
I know it is simple math but just wanted to get my fundamentals all set :)