Octave designation

Notes have only seven names, and the piano has more than eighty keys. The sums do not work without repetition: after B comes another C, and then another, and another. A concert grand has eight keys called C.

Hear the notes

On the staff, the clef and the position settle the question: each C sits in a different place. But off the staff, in conversation, in a text, in a table, "C" is not enough. You have to say which C. That is what numbering the octaves is for (Lacerda 1966, ch. XLIV).

The idea: every octave starts on a C

Every system starts from the same decision. The keyboard is cut into slices one octave wide, each slice starts on a C and ends on the next B, and the slice gets a number (Blatter 2007, part 6, appendix I). Every note inside the slice carries its number.

On this site, and in most music software, the numbering is this: middle C is C4, the octave above it starts on C5, the one below on C3.

Hear the passage

Hear the passage

The notes between one C and the next inherit its number. The D just above middle C is D4, the tuning A is A4 too, and the B just below middle C already belongs to the octave below: it is B3.

The rule for finding the number

Lacerda puts the rule in one sentence: a note has the same number as the nearest C below it (Lacerda 1966, ch. XLIV). To find the number of a G, go down to the first C. That C's number is the G's.

Hear the passage

The G above the treble staff is in the same octave as the C in the third space. In this site's numbers, both are in octave 5: C5 and G5.

The rule has a consequence that catches many people out. The number follows the letter, not the sound. B sharp sounds like C but is a B, and stays in B's octave; C flat sounds like B but is a C, and stays in C's octave:

Hear the passage

In the first bar, B♯3 and C4 sound the same. In the second, so do C♭4 and B3. The number changes where the letter changes, not where the key does.

One C, three numbers

So far, so simple. The trouble is that there is no single system. Blatter opens his appendix on the subject lamenting exactly that: it would be good to have a system everyone agreed on, but several have grown up over time, each for its own needs (Blatter 2007, part 6, appendix I).

The three books behind this site give middle C three different numbers.

• Blatter describes the system he calls USA Standard, the same as this site's: the lowest organ C is C0 and middle C is C4 (Blatter 2007, part 6, appendix I). It is also known as scientific pitch notation.
• Lacerda numbers the Cs from 1 to 9, and middle C is dó 5 (Lacerda 1966, ch. XLIV). The octave slices are the same; the numbers are one higher.
• Med divides the whole range of musical sounds into eight octaves from the lowest up, and middle C is dó 3 (Med 1996, ch. XXXVIII). The two lowest octaves get negative numbers, −2 and −1, and there is no octave zero.

Med's negative numbers have a history. Formerly, he says, the lowest note considered was dó 1, the lowest string of the cello. When lower instruments such as the double bass came in, the octaves below had to be numbered with a minus sign (Med 1996, ch. XXXVIII).

None of the three is wrong. Each is consistent within itself, and what matters is knowing which one you are reading. A text that says "dó 3" may mean middle C, if it follows Med, or a C two octaves lower, if it follows Lacerda.

The systems side by side

Blatter compares seven systems in a single chart (Blatter 2007, part 6, appendix I). The most useful to know, with Lacerda's and Med's numbers added:

C	This site	Lacerda	Med	Helmholtz	MIDI	Organ
lowest on the organ	C0	dó 1	dó −2	C₂	12	32 ft
	C1	dó 2	dó −1	C₁	24	16 ft
	C2	dó 3	dó 1	C	36	8 ft
	C3	dó 4	dó 2	c	48	4 ft
middle	C4	dó 5	dó 3	c′	60	2 ft
	C5	dó 6	dó 4	c″	72	1 ft
	C6	dó 7	dó 5	c‴	84	1/2 ft
	C7	dó 8	dó 6	c⁗	96	1/4 ft
highest on the piano	C8	dó 9	dó 7	c′′′′′	108	1/8 ft

Three columns need explaining.

Organ. One of the oldest systems. The pipe organ names each octave after the length of the open pipe that sounds its C: the lowest C, at about 16 vibrations a second, comes from a 32-foot pipe, and each octave up uses a pipe half as long (Blatter 2007, part 6, appendix I). That is why organ stops are still called "8-foot" or "4-foot".

Helmholtz. Devised by the German physicist Hermann Helmholtz, it uses capital and small letters with little strokes or subscripts. Blatter calls it awkward at best and hard to remember (Blatter 2007, part 6, appendix I). It still turns up in German books and in older texts.

MIDI. It numbers keys, not octaves: every semitone is a number, and middle C is 60. It is the system a computer uses internally, which is why 60 shows up in so much music software (Blatter 2007, part 6, appendix I).

What comes next

With an octave number, a note has a full address, letter and floor. That is what makes it possible to talk about the range of a voice, the compass of an instrument, and the difference between the written note and the sounding note on transposing instruments.