Octaves start on C with guitar?

Question

I am learning scientific pitch in order to understand the guitar fretboard better, in terms of absolute pitch.

What I was taught, was that A to G, and then back to A up an octave.

When I look at the scientific pitch of the strings, I get this:

E2 A2 D3 G3 B3 E4

At first glance, it makes sense. But wait, B is above G?

The last three strings then become:

open, 1,   2,   3,   4,   5   (fret)  
  G3, G#3, A4,  A#4, B4,  C4
  B3, C3,  C#3, D3,  D#3, E3
  E4, F4,  F#4, G4,  G#4, A5

This blows my brain, so on the fifth fret moving up you get

C4 E3 A5

How does this make logical sense? It goes down an octave yet higher in pitch?

Okay, now I realise like on piano that middle C is C4, and that is an easy reference (being roughly in middle, is the tonic of a scale that involves white keys etc. etc.) but is it really the first note in an octave in scientific pitch despite making sense only on a piano? Should I abandon scientific pitch for guitar and use 'real' octave (whatever that is!?)

In my computer programmer mind-set, where an index might start at 0 instead of 1 (okay, can get used to that), this is like an index starting at 3 and going up from there.

Answer 1

In scientific pitch notation, the octave number increases each time you go up to, or past, another 'C'. In other words, the interval from B3 to C4 is only one semitone. This is true regardless of which instrument you are using.

One problem with your diagram is that you've numbered the open strings using this standard pitch notation (where the octave changes on C), but as you go up the frets, you've used your idea of the octave changing on A - you've mixed two systems.

If you actually go up an octave on C, as you should, the last three strings then become (in the layout of your diagram):

open, 1,   2,   3,   4,   5   (fret)  
  G3, G#3, A3,  A#3, B3,  C4
  B3, C4,  C#4, D4,  D#4, E4
  E4, F4,  F#4, G4,  G#4, A4

And this is fine - A4 is higher than E4, which is higher than C4. Here is another larger diagram from this researchgate article, in a more conventional layout (with the strings ordered the other way):

(Even if you were wanting to use an alternative system where the octave number increased on A, your diagram is already wrong on the open frets, because G3 in 'your system' is actually higher than B3. But it's probably best not to dwell too much on an alternative system - the normal standard is to go up an octave number on C).

What I was taught, was that A to G, and then back to A up an octave.

That's true, and it's true for any letter name. E.g. if you go up from F up to the next F, that's also 'an octave'. In other words, an octave can start on any note at all. But when we say 'an octave' there, we just mean the interval of an octave, not the numbered octave in scientific pitch notation.

Answer 2

Yes, in the scientific notation (regardless of the instrument, of course it works on piano and everywhere else) the octaves start at C. So the order is: ... G3, G#3, A3, A#3, B3, C4, C#4, D4, D#4, E4 and so on.

(By the way, you could have easily found that on Wikipedia: Scientific pitch notation.)

I guess that you could have been tripped up by the fact that if you go A to G, the pitches are sorted alphabetically. This convention dates back to the Middle Ages, and I think it was because they took the A natural minor scale as a reference for naming the pitches (but I'm no music historian). Today, for some reason, we take the major scale as a reference, so the octaves start with C.

Answer 3

It's as simple as C>C. Defying logic somewhat, the numbers don't go from A>A, which we'd expect, but from C>C. So, for example, conecutive notes are A2, B2, C3,D3, E3, F3, G3, A3, B3, C4, D4 etc.

Bear in mind, though, that when you refer to the actual notes written on the treble clef, for guitar, they're written one octave higher than they sound. Also, scientific pitch is for any instrument - it refers to the pitch, not specifically to what an instrument may read or play.

So, the quoted scientific pitch names are correct. That does make B3 above G3, from my list. Accept it, warts an' all, or do like most of us, and be happy that 'middle C' is C4, and be done with it.