Lesson 1.2 - ScalesClick here to Print


The twelve possible pitch classes (one for each of the twelve white and black keys within an octave on the keyboard) are known as the chromatic system. These pitch classes form the chromatic scale when arranged in order, as shown in Example 1.6.


Example 1.6: The Chromatic and Diatonic Scales
Example 1.6: The Chromatic and Diatonic Scales


The chromatic system is a collection of all twelve possible pitches. Most composers have preferred to use pitch-class scales that mix seven half and whole steps in various orders.

Consider the pitch classes E-F-G-A-B-C-D— these seven pitches are notated as unfilled pitches in Example 1.6. Notice that there are five whole steps (W) and two half steps (H) within these pitches, the latter occurring between G/A and D/E.

This scale, using the seven different letter names (A – G), is the foundation for western music. A composition based on such a seven-note pitch-class scale is considered to be in a particular key. For example, a composition in the key of E is based on a scale generated from the pitch class E.

A scale uses each letter of the musical alphabet only once and so is called a diatonic (or “through the tones”) scale. A diatonic scale can begin on any of the twelve different pitch classes, and can either ascend or descend.

To return to Example 1.6 above, pitches that are members of the seven-pitch class scale are called diatonic (shown as unfilled pitches), and pitches that lie outside the diatonic scale are called chromatic (from the Latin chroma, or “color”).

Half steps have two different names:

  • Diatonic half steps involve two different letter names (e.g., G and A, as in the E scale above)

  • Chromatic half steps share the same letter name (e.g., A and A).

Notice in Example 1.5B that pitches such as Cand B, and B and C are played on the same physical key on the keyboard, and therefore sound the same. Despite their different names, these pitches are enharmonically equivalent. How a pitch functions in the overall musical context determines its specific name or “spelling.”

Most western composers have drawn most of their pitch material from the diatonic scale, but they also freely include elements from the chromatic scale.


Scale-Degree Numbers and Names

As shown in Example 1.7, each of the seven members of a scale can be numbered in ascending order, beginning with the tonic. Each numbered scale member is called a scale degree.


Example 1.7: The E Scale with Scale Degree Numbers and Names
Example 1.7: The E Scale with Scale Degree Numbers and Names


Scale degree numbers are designated using the caret, or cap, placed above each number. They are also identified by names that indicate their relationship to the tonic pitch class:

In order of importance, the next scale members are the dominant and mediant.

  • If the tonic is the first step, the dominant lies four steps above the tonic (on 5^).
    • The mediant lies two steps above the tonic (on 3^).
    • The subdominant (4^) lies four steps below the tonic, just as the dominant lies four steps above.
  • The submediant (6^) lies two steps below the tonic, just as the mediant lies two steps above.

  • The supertonic lies immediately above the tonic.

  • The leading tone (7^), which usually leads to the tonic, lies one step below the tonic.


Specific Scale Types: Major

To memorize scale patterns, arrange the pitch classes in ascending order. This ordering uses every pitch letter name once and only once. The designations major or minor refer to the mode of the piece.

  • A major scale consists of a succession of seven different pitch classes with the intervallic order w-w-h-w-w-w-h.

  • A minor scale consists of a succession of seven different pitch classes with the intervallic order w-h-w-w-h-w-w.

It’s important to memorize the pattern of intervals that makes up a major scale, especially the location of the half steps: between 3^ and 4^ and between 7^ and 1^. The name of a key provides two kinds of information:

  • it identifies the tonic pitch

  • it identifies the mode (major or minor)

Each of the remaining eleven pitch classes becomes the tonic of a major scale by imposing the same pattern of half and whole steps as found in the E major scale shown in example 1.7. Transposition means moving any pitch pattern so that it begins on a different set of pitches. For example, let’s build a major scale on A.

  1. Because a scale consists of stepwise motion, you’ll use every letter name in turn, and you’ll end the scale by repeating the tonic pitch one octave higher: A-B-C-D-E-F-G-A.

  2. You’ll refine the scale and create the sound of the major mode by using the pattern of half and whole steps you used in the context of E major (w-w-h-w-w-w-h).

    • A to B, the first interval, is a whole step.

    • The second interval should also be a whole step. However, B to C is only a half step, so you must increase the size of this interval by adding a sharp to C, raising the pitch a half step (C). B to C is a whole step, so you can move on to the next interval, which should be a half step.

    • D lies a half step below C, so you can move on.

      Continuing this process until you reach the octave A, the resulting pitches of the major scale on A are A-B-C-D-E-F-G-A (see Example 1.8). Because the scale of A major contains three sharped pitches, we say that “the scale of A major has three sharps.”


Example 1.8: The A-Major Scale
Example 1.8: The A-Major Scale


Key Signatures and the Circle of Fifths

The key signature, a pattern of either sharps or flats, is a helpful musical symbol or shorthand for indicating the pitch classes of a key. Example 1.9 shows the key signature (four sharps) for E major.

Note that there is only one F, one C, one G, and one Dshown in the E major key signature. When you include a sharp or flat in a key signature, this accidental applies to the entire pitch class. For example, if you write a sharp for one F, then all Fs become Fs).


Example 1.9: The Key Signature for E Major
Example 1.9: The Key Signature for E Major



  • G major has one altered pitch (F), so its key signature has one sharp.

  • D major has two altered pitches (F, C), so its key signature has two sharps.

The complete list of major keys with sharps is: G (1 sharp), D (2), A (3), E (4), B (5), F (6), C (7). The tonic note for each key on the list follows a pattern of fifths: it is four steps (or a “fifth”) higher than in the previous key. When read from left to right, the sharps in a key signature are also a fifth apart: F, C, G, D, A, E, B.

The flat keys follow the same pattern of fifths, but in the opposite direction from C: F, B, E, A, D, G, C. Similarly to the ascending sharps, you add flats in a specific order of descending fifths: B, E, A, D, G, C, F.

Using the circle of fifths, you can represent the opposing process of flat and sharp key relations:

  • Each key on the circle lies a fifth above the preceding key if you move clockwise around the circle.

  • Each key on the circle lies a fifth below the preceding key if you move counterclockwise around the circle.

The circle of fifths contains fifteen keys, even though there are only twelve chromatic pitches. This is because of three enharmonic keys that occur at the bottom of the circle: B/C, F/G, and C/D.

Example 1.10: The Circle of Fifths
Example 1.10: The Circle of Fifths