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I noticed that everywhere I read about music in scientific pitch notation, I see the notes in ascending pitch as in:

A2 B2 C3 D3 E3 F3 G3 A3 B3 C4

Instead of what I expected, which was

A2 B2 C2 D2 D2 E2 F2 G2 A3 B3

So why is the octave number changed between B and C instead of G and A?

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Because they probably are based on the Do-Re-Mi. B-> Si, C -> Do – Shevliaskovic Feb 8 at 18:49
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@Shevliaskovic Scientific pitch was proposed by a French physicist and based on C in each octave being a power of two (before A=440), with C4 being exactly 256 Hz. So it seems like the Solfege names are unlikely to be related. Source – Todd Wilcox Feb 8 at 20:02
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@Shevliaskovic do - re - mi is based on scale degrees. So "do" is only a C when you're using a C scale. It's always the tonic, but it's not always C. – AJFaraday Feb 9 at 0:13
    
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@AJFaraday - not exactly. There are countries where do is ALWAYS C. France is one. It's called the fixed do. – Tim Feb 9 at 8:37
up vote 13 down vote accepted

History.

For centuries people just sang, and then somebody came up with a method of writing it down. Our system comes from the Western tradition. In the medieval period, most Western song was in the minor mode. The major key hadn't come into widespread usage. So the first scale they wrote down started with the note "A" and spelled out the A minor scale.

Then in subsequent centuries the major key became more predominant. The relative major key to A minor is C major. So over the centuries they began counting from the "C" note and not the "A" note.

That is why we count from the "C" note today.

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I thought most medieval music was in the Dorian mode (starting on "D") – James Kilfiger Feb 8 at 22:20
    
Maybe so, but what of it? The system of notation (and church organ keyboards) started with "A" and the Aeolian mode, but eventually "C" and the Ionian mode won out as the most popular starting note and mode. Maybe the Dorian mode was quite popular at some point in the middle, but clearly our system of notating octaves is not based on "D". – user1044 Feb 9 at 4:16
    
The note letter names were established before the Aeolian mode was invented, weren't they? If you look at the definitions of the chant modes, the lowest note is a, in the hypodorian mode. – phoog Feb 11 at 20:14

We base most of our notation off of C. Let's put this in the context of the piano. The first scale you learn would be C and most of the first songs you would play would be in C.

In terms of keys, C is made of all the natural letter named notes so it makes sense to base the notation off this especially when it comes to notation.

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I think a follow up to this is "why is the major scale that can be played on the white keys of a piano not called the A major scale instead of the C major scale?" – Todd Wilcox Feb 8 at 19:52
    
@ToddWilcox which is already answered on the site. – Dom Feb 8 at 19:54
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@Dom what's the link for that question? Seems an interesting read – Shevliaskovic Feb 8 at 20:13
    
@Shevliaskovic music.stackexchange.com/q/17760/7222 – Dom Feb 8 at 21:01

The octave numbering was done on the piano keyboard, starting with middle C, which divides the keyboard into left and right sides. Middle C is also the 4th C on the piano, so middle C is C4, and the notes to the right are also numbered 4 up to C5 and then the cycle repeats. Notes to the left of middle C are numbered 3 down to C3 and that cycle repeats.

My understanding is the letter names — A, B, C — were not piano-centric, and that is why they differ conceptually from the octave numbers.

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And presumably if your hypothesisis correct the system was developed before the standard piano range was extended from c down to a. – phoog Feb 11 at 20:20

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