For instance I have 4 notes in the first octave: C, E, G, B. How to know if it's a Cmaj7 or an Em/C? Can we count C as a bass note?
Edit: What if it were a progression of chords all having one C note in the bass? Like: C, Em/C, Fmaj7/C, Bb/C?
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NOTE/EDIT before you read this, I suggest you make sure you understand the Jazz 2-5-1 progression. Most non-classical or modern songs in some part owe their origin to Jazz; understanding 2-5-1 will help understanding what the chord "really is". In fact, Jazz 2-5-1 is probably the way to "hear" most songs that were not even written as jazz or before the jazz age.
A bass note is the lowest note in a scoring, period. Regardless of what clef it's on.
root note of a chord and the bass note may not be the same. It's that simple. Otherwise life would be very boring for the tuba players.
As to what the chord is, that's more ambiguous and you'll have to learn context (what the key of the song is, how often the chord is used). An Am7
A C E G could also be construed as a C6
C E G A. Diminished 7th chords or Augmented chords are even more problematic as they are really 4 or 3 different chords at once (they are symmetrical). Here, especially with the diminished 7ths, you have to consider context. A standard Jazz progression in C leading home from an F is:
(Play it and you'll recognize it in a lot of songs). You could call the F# dim 7th an C dim 7th if you wanted to; it would be true but most scores won't write it that way. In short, the bass note is what it is but the chord is contextual. C
First, the bass note is the lowest note in the chord voicing.
C E G B no matter how you voice it will be a
Cmaj7. If the
E was the lowest note, in pop-notation it would be
Cmaj7/E, if it were
You are confusing different chords with inversions. You can put any note of a chord in the bass and it will still be the same chord.
Like Tim said, there can be exceptions, like in jazz sometimes they play chords lacking certain notes and you have to use your ear to figure out what note is the root, but
C E G B is a straight forward
We tend to name chords for two potential reasons; to communicate the notes to play to another musician, or to analyse the harmonic progression of the piece.
The bass note is almost always the lowest note in the chord, when you consider all the notes played by everyone. It may not be the root note of the chord.
When you're trying to communicate, it's important to be as clear as possible. So we tend to choose the chord name that's easiest to read. We avoid using the bass note notation (slash chords), if there is a clearer alternative. Here's some examples:
Bb/G[G, Bb, D, F] should be called
Em/C[C, E, G, B] should be called
Fsus2/C[C, F, G, C] should be called
C/B[B, C, E, G] should be called
C/B, because it'll have some horrible name if you try and spell it as a B chord.
The simpler chords are easier to read quickly. There are some exceptions, but they are very much not the norm. Always choose the option that's the easiest to read.
If we're talking about harmonic analysis, we try and name the chord for its function. In that case, you might be a little less pragmatic. I'm not an expert here, and I don't think it's that relevant to your question, so I'm not going to say much here.