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or lower one note is than another. This distance between two pitches is called the interval between them. In Western music, the small interval from one note to the next closest note higher or lower is called a half step or semi-tone.

Figure 4.8. Half Steps

(a)

(b)

Three half-step intervals: between C and C sharp (or D flat); between E and F; and between G sharp (or A flat) and A.

Listen to the half steps in Figure 4.8.

The intervals in Figure 4.8 look different on a staff; sometimes they are on the same line, sometimes not. But it is clear at the keyboard that in each case there is no note in between them.

So a scale that goes up or down by half steps, a chromatic scale, plays all the notes on both the white and black keys of a piano. It also plays all the notes easily available on most Western instruments. (A few instruments, like trombone and violin, can easily play pitches that aren't in the chromatic scale, but even they usually don't.)

Figure 4.9. One Octave Chromatic Scale

All intervals in a chromatic scale are half steps. The result is a scale that plays all the notes easily available on most instruments.

Listen to a chromatic scale.

If you go up or down two half steps from one note to another, then those notes are a whole step, or whole tone apart.

Figure 4.10. Whole Steps

(a)

(b)

Three whole step intervals: between C and D; between E and F sharp; and between G sharp and A sharp (or A flat and B flat).

A whole tone scale, a scale made only of whole steps, sounds very different from a chromatic scale.

Figure 4.11. Whole Tone Scale

All intervals in a whole tone scale are whole steps.

Listen to a whole tone scale.

You can count any number of whole steps or half steps between notes; just remember to count all sharp or flat notes (the black keys on a keyboard) as well as all the natural notes (the white keys) that are in between.

Example 4.2.

The interval between C and the F above it is 5 half steps, or two and a half steps.

Figure 4.12.

Going from C up to F takes five half steps.

Exercise 4.2.1. (Go to Solution)

Identify the intervals below in terms of half steps and whole steps. If you have trouble keeping track of the notes, use a piano keyboard, a written chromatic scale, or the chromatic fingerings for your instrument to count half steps.

Figure 4.13.

Exercise 4.2.2. (Go to Solution)

Fill in the second note of the interval indicated in each measure. If you need staff paper for this exercise, you can print out this staff paper PDF file.

Figure 4.14.

Note

Thanks to everyone who participated in the survey! It was very useful to me, both as a researcher and as an author, to get a better picture of my readers' goals and needs. I hope to begin updating the survey results module in April. I will also soon begin making some of the suggested additions, and emailed comments are still welcome as always.

Solutions to Exercises

Solution to Exercise 4.2.1. (Return to Exercise)

Figure 4.15.

Solution to Exercise 4.2.2. (Return to Exercise)

Figure 4.16.

If your answer is different, check to see if you have written a different enharmonic spelling of the note in the answer. For example, the B flat could be written as an A sharp.

4.3. Major Keys and Scales*

The simple, sing-along, nursery rhymes and folk songs we learn as children; the "catchy" tunes used in advertising jingles; the cheerful, toe-tapping pop and rock we dance to; the uplifting sounds of a symphony: most music in a major key has a bright sound that people often describe as cheerful, inspiring, exciting, or just plain fun.

How are these moods produced? Music in a particular key tends to use only some of the many possible notes available; these notes are listed in the scale associated with that key. In major keys, the notes of the scale are often used to build "bright"-sounding major chords. They also give a strong feeling of having a tonal center, a note or chord that feels like "home", or "the resting place", in that key. The "bright"-sounding