# 1

Basic Definitions

## 1.1 Pitches

- A “pitch” is any note that we hear.
- The standard piano can play 88 pitches: A0 to C8, where C4 = middle-C.
- For example, the notes above middle-C are as follows:

C4 (B3), C4(D4), D4, D4(E4), E4(F4),F4(E4), F4(G4), G4, G4(A4), A4, A4(B4), B4(C5)

## 1.2 Pitch Classes

- Pitch classes are used to discuss pitches
*independent*.

of octave displacement and enharmonic spelling - Any two pitches which sound the same on an equal tempered scale (for example, C and D) or are only different due

to octave displacement are said to belong to the same “pitch class”. - For example, the following
*pitches*all belong to*Pitch Class C*: B4, D4 (enharmonic equivalents),

C0, C1, C2, C3, C4, C5, C6 (octave displacements) - There are only 12 pitch classes in a system where each octave has 12 chromatic notes.
- Pitch classes can also be numbered: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11. These numbers are sometimes called “Pitch Class Representatives”.
- For this tutorial, 0 = Pitch Class
**C**(i.e. “fixed Do”). - All other pitch classes will by numbered by counting the half steps from pitch-class C.
- Therefore, C = 0, C = 1, D = 2, D = 3, E = 4, F = 5, F = 6, G = 7, G = 8, A = 9, A = 10, B = 11
- Sometimes the letter ‘T’ (for Ten) or ‘A’ is used instead of the number 10, and ‘E’ (for Eleven) or ‘B’ instead of 11.

## 1.3 Pitch Class Sets

- A “Pitch Class Set” is a list of pitch class numbers: [0, 4, 7, 10] (note the square brackets)
- These are also called “PC Sets”.
- The PC Set for a C minor triad: [0, 3, 7]
- The PC Set for a G major triad: [7, 11, 2]
- In Pitch Class sets, octave doublings and displacements are ignored:
- [0, 3, 7, 12] => [0, 3, 7] (see the section below on modulo math)
- [14, 7, 11] => [2, 7, 11]
- For example, all of the following can be described with Pitch Class Set [0, 1,4]. The only difference in these chords are octave displacements or enharmonic spellings in the pitches.

- Oftentimes PC Set notation is shown without the commas: [037] (here is where A=T=10 and B=E=11 comes in handy, for example: [0,4,7,10] = [047T] = [047A] (note: this is a C dominant 7
^{th}chord)

Copyright © 2004 by Paul Nelson, all rights reserved.