Music Notes (摘自维基百科）

One can map a pitch's fundamental frequency f (measured in hertz) to a real number p using the equation

p = 69 + 12log₂(f / 440)

This creates a linear pitch space in which octaves have size 12, semitones (the distance between adjacent keys on the piano keyboard) have size 1, and middle C is assigned the number 60. Indeed, the mapping from pitch to real numbers defined in this manner forms the basis of the MIDI Tuning Standard, which uses the real numbers from 0 to 127 to represent the pitches C_-1 to G₉. To represent pitch classes, we need to identify or "glue together" all pitches belonging to the same pitch class—i.e. all numbers p and p + 12. The result is a circular quotient space that musicians call pitch class space and mathematicians call R/12Z. Points in this space can be labeled using real numbers in the range 0 ≤ x <>

0 = C, 1 = C#/Db, 2 = D, 2.5 = "D quarter-tone sharp"

and so on. In this system, pitch classes which are represented by integers are pitch classes of twelve-tone equal temperament assuming standard concert A.

To avoid confusing 10 with 1 and 0, some theorists assign pitch classes 10 and 11 the letters "t" (after "ten") and e (after "eleven"), respectively (or A and B, as in the writings of Allen Forte and Robert Morris).

PITCH CLASS TABLE
pc	tonal counterparts
0	C (also B sharp, D double-flat)
1	C sharp, D flat (also B double-sharp)
2	D (also C double-sharp, E double-flat)
3	D sharp, E flat (also F double-flat)
4	E (also D double-sharp, F flat)
5	F (also E sharp, G double-flat)
6	F sharp, G flat (also E double-sharp)
7	G (also F double-sharp, A double-flat)
8	G sharp, A flat
9	A (also G double-sharp, B double-flat)
t or A	A sharp, B flat (also C double-flat)
e or B	B (also A double-sharp, C flat)

In music theory, pitch class space is the circular space that results when we ignore the difference between octave-related pitches. Mathematically, it is a quotient space that results from identifying or "gluing together" pitches sharing the same pitch class. In this space, there is no distinction between tones that are separated by an integral number of octaves. For example, C4, C5, and C6, though different pitches are represented by the same point in pitch class space.

Since pitch class space is a circle, we return to our starting point by taking a series of steps in the same direction: beginning with C, we can move "upward" in pitch class space, through the pitch classes C♯, D, D♯, E, F, F♯, G, G♯, A, A♯, and B, returning finally to C. (As Maria puts it in The Sound of Music, "Ti" brings us back to "Do.") By contrast, pitch space is a linear space: the more steps we take in a single direction, the further we get from our starting point.