A Survey of Music Theory for the College Classroom: Fundamentals

Pitch, Scales, Keys

Notation of Pitch

Pitch refers to how high or low a note sounds. Pitches are named after the first seven letters of the alphabet, also called the musical alphabet, and are notated on a staff. The treble clef is normally used for higher pitches, and the bass clef is normally used for lower pitches. The grand staff consists of two staves joined by a brace. Ledger lines are used to extend the range above and below the staff.

notes on the grand staff

Octave register designations allow us to name a specific pitch. We say “C4” rather than just “C” when we want to identify middle C. A pitch class includes all the notes with the same name – for example pitch class C.

octave register designations

The concept can also be illustrated on the piano keyboard.

octave registers on the piano

Tenor clef is commonly used by bass clef instruments when playing in their highest registers. Alto clef is used by the viola. This is the note C4 or middle C in the treble, alto, tenor, and bass clefs.

middle C in four clefs

Major Scales

Scales are successions of pitches arranged in half steps and whole steps. Western music from about 1600-1900, which is called the Common Practice Period, primarily uses major and minor scales. Since much of the music we listen to and teach is from this period, we will begin by discussing the major and minor scales.

The half step or semitone is the smallest interval in tonal music. An interval is the distance between two notes. Any two piano keys that are next to one another are a half step apart. This pattern is most commonly a white key to a black key, but the white key notes E to F and B to C are also half-steps. A whole step or whole tone is simply two half steps.

C major scale

The following are the scale degree names in major keys. A number with a caret (^) above it is a short way of writing scale degrees.

\(\hat{1}\) = Tonic
\(\hat{2}\) = Supertonic
\(\hat{3}\) = Mediant
\(\hat{4}\) = Subdominant
\(\hat{5}\) = Dominant
\(\hat{6}\) = Submediant
\(\hat{7}\) = Leading Tone

To construct major scales on other tonics we need to use accidentals.

♯ (sharp) – raises a white key pitch by a half step
(flat) – lowers a white key pitch by a half step
(natural) – cancels an accidental (refers to white keys on the piano)
x
 (double sharp) – raises a white key pitch by a whole step
♭♭ (double flat) – lowers a white key pitch by a whole step

Db major scale

Scales are always named for the tonic note. In this case it is D.

Key Signatures

Key signatures are derived from the accidentals required to make a scale on a given note and are named after the tonic of the scale. While it is important to understand and be able to apply the pattern of half steps and whole steps in creating major scales, it is also essential to memorize all the key signatures for the major and minor scales.

Flats and sharps appear in key signatures in a predictable manner. This order of flats and sharps is as follows:

Order of flats = B E A D G C F 

Order of sharps = F C G D A E B

For example, if a key signature has two flats, they will be B and E, and if a key signature has three sharps, they will be F, C, and G. In modern publications, key signatures appear in a certain way. Below is a graphic that shows how all key signatures should be written in the four most common clefs.

key signatures in four clefs

Enharmonic Equivalence

Some notes on the piano have two names, for example C and D. This is called enharmonic equivalence. Enharmonic notes sound the same because they are the same pitch. Enharmonic notes can share black keys or white keys, such as the notes C and B.

enharmonic notes on the piano keyboard

Minor Scales

There are three forms of the minor scale: natural minor, harmonic minor, and melodic minor. The natural minor scale uses only the accidentals found in that scale’s key signature, while both the harmonic and melodic minor scales use accidentals not found in the key signature. Melodic minor also includes a descending form of the scale in which the scale reverts to natural minor.

This is the a natural minor scale.

a natural minor scale

The names of the scale degrees are the same as they are for major scales with one exception. In natural minor, scale degree \(\hat{7}\) is a whole step below the tonic and is referred to as the “subtonic.” In harmonic and melodic minor, the seventh scale degree is a half-step below the tonic and is called the “leading tone” as it is in major.

This is the a harmonic minor scale.

a harmonic minor scale

This is the a melodic minor scale.

a melodic minor scale

Minor scales can be constructed by counting half-steps, by modifying the parallel major, or by using the concepts of relative major and minor keys. Parallel major and minor scales have the same tonic note but use different key signatures. Relative major and minor scales have different tonic notes but use the same key signature.

Parallel Major Method

Below is a C major scale. If the c natural minor scale is desired, then scale degrees \(\hat{3}\)\(\hat{6}\), and \(\hat{7}\) of the C major scale should be lowered by a half-step or semitone. If the c harmonic minor scale (ascending) is needed, then scale degrees \(\hat{3}\) and \(\hat{6}\) should be lowered by a single half-step, leaving scale degree \(\hat{7}\) untouched. If the melodic minor scale (ascending) is needed, then only scale degree \(\hat{3}\) should be lowered by a half-step. Remember that the descending version of the melodic minor reverts to natural minor.

parallel scales

Relative Key Method

The concept of relative major and minor keys can also be used to build minor scales. For example, if you want to construct a g natural minor scale, you need to know the key signature of its relative major. The tonic notes of relative major and minor keys are a m3 or three semitones apart. The third scale degree of a minor scale is the tonic of its relative major, and the sixth scale degree of a major scale is the tonic of its relative minor.

relative major and minor tonics

B major’s key signature has two flats. The key signature of g minor has the same two flats.

relative major and minor keys

If you want to construct the harmonic minor scale, raise scale degree \(\hat{7}\) by one semitone.

g harmonic minor

If you want to construct the melodic minor scale in ascending form, raise scale degrees \(\hat{6}\) and \(\hat{7}\) by one semitone.

g melodic minor

Circle of Fifths

The circle of fifths is a way of illustrating all the major and minor keys and the concept of relative keys. As you travel clockwise around the circle, each tonic is a P5 above the previous tonic. In other words, each key starts on the dominant scale degree of the previous key. As you travel counterclockwise around the circle, each tonic is a P5 below the previous tonic. Therefore, each key starts on the subdominant scale degree of the previous key. Note the enharmonic keys on the circle of fifths. The major keys are in upper case letters, and the relative minor of each major key is in lower case.

circle of fifths

The Chromatic Scale

The last scale we will discuss in this chapter is the chromatic scale, which consists of only half steps. The ascending chromatic scale is usually written with sharps, while the descending chromatic scale is commonly written with flats.

the chromatic scale

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