When writing about music, we often need to specify which octave a note is in, as well as its name (technically, its pitch class). There are different ways of doing this precisely, of which the most convenient are Helmholtz notation and so-called (ironically so, since Helmholtz was himself the foremost scientific investigator of musical tones) scientific or American notation.

Helmholtz notation

Middle C is notated as c'. Similarly, all the notes above it up to (but not including) the next C are miniscule letters with a single prime superscript: d' e' f' g' a' b'. (Or one can write ci, etc.)

The C an octave below 'middle C' is notated as c -- with d e f g a b lying in between. The pattern is that all notes take the form of their notation from the C below.

Two octaves below 'middle C' we come to C (which is where this explanation gets a bit confusing, for those with unsophisticated browsers). This is where all but the profoundest Russian basses hits gravel and comes to a vocal dead end. One octave below that, the lowest C available on a normal piano (though not the nine-foot Bösendorfer concert grand!), is C, -- again this can be a bit confusing since the subscript can be mistaken for a comma. Alternatively one can write Ci or CC. The Bösendorfer, or the longest pipes on an organ, will be able to give you the (barely audible) C,, or Cii or CCC which vibrates at about 16 and a half hertz (Hz).

Going up, one octave above 'Middle C' is c'' or cii; two octaves above we come to c''' or ciii which is the "High C", the highest note humans are usually called on to sing, and dreaded by operatic sopranos approaching retirement. The so-called Queen of the Night's Aria in The Magic Flute contains several fii 's and requires an unusual type of soprano, specially bred in a secret location just outside Vienna.

The highest C on a bog standard piano (though not a concert grand) is c'''' or ciiii. This note can also be reached by flautists, piccolo players, violinists and cats. Thus, the entire seven-(and-a-bit)-octave range of a piano is as follows:

A,, B,, C, D, E, F, G, A, B, C D E F G A B c d e f g a b c' d' e' f' g' a' b' c'' d'' e'' f'' g'' a'' b'' c''' d''' e''' f''' g''' a''' b''' c'''' d'''' e'''' f'''' g'''' a'''' (b'''' c''''')

missing out the black notes, with 'Middle C' in bold. The notation is simple and elegant, but heavy on the ''s, and of course impossible to pronounce.

Scientific or American notation

Rather than the picturesque sub- and superscripts, this notation just uses numbers. 'Middle C' is C4, one octave below is C3, two octaves below is C2, the lowest C on a piano is C1 (or -- if you paid the extra $10,000 for the Bösendorfer -- the virtually inaudible C0). Going up from 'middle C' are C5, C6, C7, and -- if you've got a concert grand -- C8. If you can only afford a smaller model, your piano stops at A7. As with the Helmholtz notation, pitches that are not C's take their name from the C below.

The first violin part of Eine kleine Nachtmusik begins as follows in American notation:

(D4 B4 G5) D5 G5 D5 G5 D5 G5 B5 D6 C6 A5 C6 A5 C6 A5 F#5 A5 D5

(the first three notes form a chord), while the cello part is

G3 D3 G3 D3 G3 D3 G3 B3 D4 etc.

This notation is logical and easy to format, and can be spoken, but it's ugly, with a distressing tendency to look like hexadecimal machine code.

Wikipedia article on 'piano' (Ack!)