1.3 Half Steps and Whole Steps

Half Steps and Whole Steps

Imagine that you are sitting in front of a piano or a keyboard, and you play every single note, black or white, in order. You might play A-Bb-B-C-C#-D-Eb-E-F-F#-G-G#-A. This is called the chromatic scale. Notice that not all of the transitions have accidentals. For example, B# is enharmonically equivalent to C natural, and E# is enharmonically equivalent to F natural. 

(image via Yamaha)

A chromatic scale is special because all of the notes are a half step apart. In other words, these notes area right next to each other on the keyboard. For example, C is a half step away from C#, and E is a half step away from F. 

A whole step is just two half steps. C is a whole step away from D, and E is a whole step away from F#, for example. 

Intervals

Naming Intervals

Another way to talk about half steps and whole steps is to consider them as intervals. In music, an interval is the distance between two pitches. A half step is a minor second, and a whole step is a major second. 

Intervals can also be described in terms of their quality, which refers to the type of interval (major, minor, etc.) and their size, which refers to the number of pitch classes they span. For example, a "perfect fifth" is a perfect interval that spans seven pitch classes. The number (2nd, 3rd, 4th,...7th) comes from the space between the letters. For example, a C to E is a 3rd, an E to G is a 3rd, etc. Intervals are usually considered as spaces less than an octave, although sometimes, you will hear people talking about a 9th or a 10th. You usually won't hear people talking about a 22nd. 

There are several types of intervals, including major intervals, minor intervals, diminished intervals, augmented intervals, and perfect intervals. 

If you are already familiar with major scales, an easy way to remember whether an interval is minor, major, perfect, etc. is to think about a major scale. A major scale has all major intervals, (e.g. M2, M3, M6, etc.) except for the 4th, 5th, and the octave, which are considered perfect intervals. For example, a C to an E is considered a major 3rd, but a C to a G is a perfect 5th. You usually don't say "perfect octave" or "perfect 8th" -- just "octave" is good enough. 

Once you know the major intervals, a minor interval is one half step less than a major interval. So, if C to E is a major 3rd, then C to Eb is a minor 3rd. These don't necessarily correspond to the minor scale. C to Db is a minor 2nd, but C#/Db is not in the c minor sale. You cannot turn perfect intervals into minor intervals. For example, you will not have a minor 5th or a minor 8th. 

Augmented and diminished intervals are used less frequently than major and minor intervals. You can augment or diminish perfect intervals. When you augment an interval, you add one half step to the major interval. For example, C to E# is an augmented 3rd. When you learn about voice leading in Unit 4, you will most likely talk about augmented 2nds and augmented 4ths as things to avoid in part-writing. 

A diminished interval takes a minor interval and takes away one half step. For example, a C to a E double flat would be a diminished 3rd. The most common diminished chords you will run into are diminished 7ths (for example, C to B double flat) and diminished 5ths (C to Gb). 

Augmented intervals are not as common as major or minor intervals, but they can add tension and dissonance to music and are often used in jazz and other styles of music that incorporate more complex harmonies. Understanding augmented intervals and how they relate to other intervals is an important aspect of music theory.

Singing and Recognizing Intervals

The AP music theory exam will make you recognize intervals in two different contexts. First, you will hear a melody and you will have to notate the melody given a specific starting pitch. This means that you will have to recognize intervals by ear. The second situation is that you will have to sight sing a melody given a score. You will again be given the starting pitch, so you will have to be able to sing intervals with some degree of accuracy. 

Depending on your current background in music, there are a few different ways you can practice for these. My favorite was singing on the do-re-mi scale. It is also helpful to think of specific songs that you are familiar with that use the intervals. Here is a list to start, but you should also do research and make your own! 

Consonant and Dissonant Intervals

Notice that the augmented 4th and diminished 5th are enharmonic to one another, meaning that it sounds the same when you play an augmented 4th and a diminished 5th. This specific interval has a special name in music theory, called the tritone (since the notes are three whole steps apart) The tritone was considered dissonant and unstable by many ancient cultures and was often avoided in music. Historically, many western European considered it the "devil's tone," and it was avoided in any type of religious music (which was most music at the time)

Despite its reputation as a dissonant interval, the tritone has played a significant role in the development of Western music. In the Baroque period, composers such as J.S. Bach and George Frideric Handel used the tritone to create tension and dissonance in their music, particularly in the use of dissonant chords and the use of chromaticism.

In the Romantic and modern periods, the tritone became more widely used and accepted in music, with composers such as Richard Wagner and Igor Stravinsky incorporating it into their music. Today, the tritone is an important interval in many styles of music and is used to create tension, dissonance, and other expressive effects.

Even if you don't have very strong feelings about the tritone, you might notice that some intervals just don't sound good and they feel unsettling, while other notes sound good together - they feel settled and resolved. The intervals that create tension or instability are called dissonant intervals, and the intervals that create a sense of resolution or stability are called consonant intervals. Using dissonance is not always bad. In fact, good music usually requires you to write some dissonance to build tension before you resolve to consonant intervals and chords. 

Consonant intervals are the octave, perfect 5th, and major and minor thirds and 6ths. Dissonant intervals are are the major and minor 2nds, the tritone, major and minor sevenths, and any augmented or diminished intervals. 

What about the perfect 4th? In short, it depends. In some contexts, the perfect 4th is very stable. However, in other contexts, the perfect 4th wants to resolve to the perfect 5th, so it is considered unstable and dissonant. 

It is important to note that these definitions of consonance and dissonance were defined in western Europe, and they are taught here because they are relevant to the AP Music Theory Exam. Different cultures and musical traditions have different ideas about what is consonant and dissonant, and the use of consonance and dissonance can vary widely between different styles of music.