Standard 2: The Major Scale

2.1 Half Steps and Whole Steps

2.11 The Keyboard

The keyboard is great for helping you develop a visual, aural, and tactile understanding of music theory. On the illustration below, the pitch-class letter names are written on the keyboard.

Try this exercise to name the white keys on the piano keyboard

2.12 Half Steps and Whole Steps

One of the reasons why we use the keyboard is to help you visualize how pitches are organized on the chromatic scale, a series of pitches arranged by ascending or descending half steps.

What's a half step?

A half step describes the distance between a key and the next adjacent key on the piano. For example, the distance between a white key and its next adjacent black key is a half step. However, there are two pairs of white keys on the piano that have no black keys in between them (E and F, B and C). Since they describe two adjacent keys, these are examples of half steps as well.

What's a whole step?

A whole step is equivalent to two half steps. For example, the distance between C and D is a whole step because it includes two half steps (C to C#, C# to D).

Before you move on to the next section, review this online lesson, which illustrates the half step, whole step, and introduces accidentals.

2.13 Accidentals

Accidentals are used to indicate when a pitch has been raised or lowered by one or two half steps. When described as as words, they are written after the note name (e.g. "C-sharp"). When they are placed next to a note on a staff, they are written before the note.

Lowering Pitches

• When you lower one of the white notes of the piano by a half step, you add a flat.
• When you lower a note that is already flat by a half step, you add a double flat.
• When you lower a note that is already sharp by a half step, you add a natural.

Raising Pitches

• When you raise one of the white notes of the piano by a half step, you add a sharp.
• When you raise a note that is already sharp by a half step, you add a double sharp.
• When you raise a note that is already flat by a half step, you add a natural.

The example below shows the symbols for flat, natural, sharp, double sharp, and double flat, respectively.

Try this exercise to name all the keys on the piano keyboard

And also try this exercise to review how to name notes on the grand staff by using the correct accidentals

2.14 Enharmonic Equivalence

Notice that some of the piano keys have two names (see the illustration below). When two note names share a key on the keyboard, they are said to have enharmonic equivalence. Theoretically, each piano key could have several names (the note C could also be considered D♭♭, for instance), but it's usually not necessary to know more than two enharmonic spellings.

2.2 The Scale

A scale is a succession of pitches ascending or descending in steps. There are two types of steps: half steps and whole steps. A half step (H) consists of two adjacent pitches on the keyboard. A whole step (W) consists of two half steps.

2.21 The Chromatic Scale

The chromatic scale consists entirely of half steps, and uses every pitch on the keyboard within a single octave. Here is the chromatic scale that spans the pitches C4 through C5.

2.22 The Major Scale

A major scale, a sound with which you are undoubtedly familiar, consists of a pattern of whole steps and half steps in a given pattern:

W - W - H - W - W - W - H

Notice that 1) there are seven steps in the above pattern, and 2) the pattern consists of two "W - W - H" patterns connected together with an extra "W" in the middle. This smaller pattern of "W - W - H" is called a Tetrachord. By connecting two tetrachords together with an additional whole step, we can form the pattern for the Major Scale.

The first pitch of the scale, called the tonic, is the pitch upon which the rest of the scale is based. When the scale ascends, the tonic is repeated at the end an octave higher and thus completes the scale.

Here is the D major scale. It is called the "D major scale" because the pitch D is the tonic and is heard at both ends of the scale.

2.23 Scale degrees and solfège

While ISO notation (e.g. C4, D4) allows us to label a pitch in its specific register, it is often useful to know where that pitch fits within a given scale. For example, the pitch D is the first (and last) note of the D-major scale. The pitch A is the fifth note of the D-major scale. When described in this way, we call the notes scale degrees, because they're placed in context of a specific scale.

Solfège syllables, a centuries-old method of teaching pitch and sight singing, can also be used to represent scale degrees (when used in this way, this system is specifically called movable-do solfège).

Scale degrees are labeled with Arabic numerals and carets (^). The illustration below shows a D-major scale and corresponding ISO notation, scale degrees, and solfège syllables.

2.24 Writing the Major Scale

We can create a major scale starting with any note on the piano keyboard by simply following the pattern of whole steps and half steps.

To write a major scale:

1. Start with the first pitch (also called the “tonic”).
2. Write out the letter names in order by using the musical alphabet. Use all of the letters and end with the tonic again.
3. Starting with the first tonic, evaluate the interval between each succeeding pair of notes (e.g. C-D, D-E, E-F), and use either sharps or flats to adjust the notes so that they match the W-W-H-W-W-W-H pattern.
4. If you successfully completed the above steps, if you needed to add accidentals, you should have used either sharps or flats, but not both. In addition, the 7th scale degree will always be a half-step away from the tonic that ends the scale.

Before you move on, review this online lesson on how to write a major scale.

Now try your hand at writing a major scale using a given note as the "tonic" (e.g. the first note). Use the buttons on the lower-lefthand corner to select the notes that need an accidental, and add accidentals as needed. Always use a piano keyboard when you are working on this exercise.

2.3 Key Signatures

2.31 What is a key signature?

When you're writing a piece of music that uses a specific major scale for an extended period of time, it gets tedious to write out the same accidentals over and over again.

For example, here is a simple melody in D major, written without a key signature.

To avoid adding so many accidentals to the notation, composers use a key signature at the beginning of each staff to remind performers to always use flats or sharps for certain pitches in the major scale. A key signature is a collection of every accidental found in a scale.

In this case, since this piece is written using the D major scale (e.g. it's in the "key" of D major), all F's and C's will always be played as F#'s and C#'s. Hence, instead of writing a # next to all F's and C's, we can use a key signature at the beginning of the staff to remind the performer that F and C will always be played as F-sharp and C-sharp, regardless of octave.

2.32 Reading Key Signatures

What do key signatures look like? Here is an example of seven different key signatures, all using sharps, and all on the treble clef.

When you see a key signature in notated music, it will always be placed at the beginning of each line of staff (also known as a "system"). The key signature is always placed directly to the right of the clef.

Here is an easy way to identify the major key of a piece of music by just looking at the key signature:

• For sharp key signatures, take a look at the final sharp in the signature. When you raise the pitch one half-step above the pitch indicated by the final sharp, you will arrive at the major key associated with this signature.

• For flat key signatures, take a look at the second-to-last flat, which indicates the major key associated with this signature. If there is only one flat, you'll need to remember that this is the key of F major.

Remember: there is a total of 15 major scales, and each major scale is associated with a unique key signature. These signatures tell you 1) the major scale that the piece uses; and 2) which sharps or flats are associated with that major scale.

Review this lesson that introduces key signatures. Note that the lesson refers to a minor scale (which will be covered in Standard 3), but the concept of key signatures is the same for both major and minor scales.

Try your hand at identifying these key signatures.

2.33 The Circle of Fifths

The circle of fifths is an illustration that has been used in music theory pedagogy for hundreds of years. It conveniently summarizes the key signature needed for any key with up to seven flats or sharps.

But which notes are flat or sharp in a key? To properly use the circle of fifths to figure out a key signature, you'll need to also remember this mnemonic device, which tells you the order of flats and sharps in a key signature:

Father Charles Goes Down And Ends Battle.

For sharp keys (clockwise on the circle of fifths), the order of sharps will always be F-C-G-D-A-E-B. You can arrive at this order by reading the mnemonic device forwards. For example, if there are three sharps in a key signature (as in the key of A major), the three sharps will always be the first three sharps in this pattern: F-sharp, C-sharp, and G-sharp (i.e. Father, Charles, and Goes).

For flat keys (counter-clockwise on the circle of fifths), the order of flats will always be B-E-A-D-G-C-F. You can arrive at this order by reading the mnemonic device backwards. For example, if there are four flats in a key signature (as in the key of A-flat major), the four flats will always be the first four flats in this pattern when read backwards: B-flat, E-flat, A-flat, D-flat (i.e. Battle, Ends, And, Down).

2.34 Writing key signatures

When you need to write a key signature for a given key, remember the following:

1. Identify the major scale (or key) that you are trying to find the key signature for.
2. If it's a scale that uses sharps, find the note that's a half-step below the key. This will be the final sharp in the key signature. Write all the sharps in order (F-C-G-D-A-E-B) until you reach the final sharp.
3. If it's a scale that uses flats, the key will be the second-to-last flat in the key signature. To find the key signature, write all the flats in order until you reach the key, and then add one more flat according to the pattern (B-E-A-D-G-C-F).

Finally, remember the sharps and flats on a key signature need to be placed on a specific line or space. For example, the "F-sharp" in a sharp key signature in treble clef will always be placed on the fifth line. Below is a reference that shows how all of the key signatures should be written on treble and bass clefs.

Take a look at this exercise to construct a key signature that uses sharps.

Now try your hand at this exercise to construct a key signature that uses flats.

The most important thing is to keep practicing writing and identifying key signatures. With consistent practice, you will improve your speed and accuracy with writing major scales and key signatures.