What is Harmony?

Frequencies and Feelings

Twelve. That’s the number of notes that makes up almost all of music. From a mainstream euphoric pop song to a tragic motif for a character’s death in a film score, music sits within the bounds of these 12 notes. But how is that even possible? How can these limited sets of frequencies serve as a conduit for emotion? While the precise connection between these frequencies and human emotions remains largely unexplained, acknowledging this correlation empowers musicians to comprehend and harness harmony in their craft. As we continue to unravel these concepts, grasping how harmony functions is crucial for any composer, producer, performer, or even sound engineer.

Consonance and Dissonance

Harmony is one of the fundamental concepts in music, involving multiple musical notes played simultaneously. Pythagoras, renowned for his contributions to mathematics and the ‘Pythagorean theorem,’ was among the earliest figures to establish and develop a tuning system that closely resembles the modern system. This was developed by assigning specific frequencies (in hertz) to musical notes, named alphabetically.

b — flat

# — sharp

The standard frequency for the ‘A’ note in modern tuning is 440 Hz. Creating this system paved the way for discovery of harmony through the idea of consonance (two notes sounding well with each other). However, to avoid monotony, an essential aspect of harmony is dissonance. This particular concept has to do with how frequencies of different notes relate to each other. To further comprehend how dissonance and consonance manifest themselves within our tuning system, it is crucial to first become familiar with intervals.

Consonance + Dissonance — What makes something sound “bad”?

Intervals

An interval is the distance between two musical notes. The smallest distance between 2 notes is called a ‘semitone.’ (or a half tone) For instance, ‘F’ is a semitone above ‘E,’ and ‘A’ is a semitone below ‘Bb.’ A ‘tone’ (or a whole tone) is essentially equal to two semitones. For instance, ‘F’ is a tone above ‘D#,’ and ‘A’ is a tone above ‘G.’

In addition to the white notes, which are named with standard letters, the black notes derive their names in relation to them. Sharp or # means above (raised), and b or flat means below.

For example, the black note between C and D can be referred to as C# because it is a semitone above C, and it can also be called Db because it is a semitone below D.

What are Semitones and Tones?

Each interval is assigned a specific name. For example, a ‘minor second’ signifies notes that are 1 semitone apart, as heard in the interval between the two notes in the ‘Jaws theme.’ When played together, a minor second interval creates a pronounced dissonance.

Minor 2nd interval (Jaws Theme) #shorts — YouTube

A ‘major seventh’ indicates notes that are 11 semitones apart, such as the interval between the words ‘take’ and ‘on’ in the chorus of ‘Take on me.’

Similarly, a ‘perfect fifth’ is 7 semitones apart, which is also the note we get when we multiply a starting frequency with 3/2 (as discussed before), and is the interval between the first two notes from the Star Wars theme. The ratio of 3:2 (perfect 5th) is one of the most consonant intervals in music, have a listen: [Perfect 5th Interval] Star Wars Overture / Main Title Sequence — YouTube

Here is a fun video (and exercise) that can help beginners associate each interval sound with famous themes/songs:

Songs that will help you identify ascending intervals

Scales — The Building Blocks of Music

It can be observed that a lot of interval names are based on the words ‘major’ and ‘minor.‘ This is because a lot of harmonic concepts are based on the ‘major’ and ‘minor’ scales.

Major scale

Consider the note C. Move up one whole tone to D, then another whole tone to E. Proceed up a semitone to F, followed by two whole tones (G, A, B). Finally, move up a semitone to reach C again, an octave higher. This is the major scale, it can be derived from any note using the following formula: Root — Tone — Tone — Semitone — Tone — Tone — Tone — Semitone (or in whole and half terms — W W H W W W H). The major scale has a quite bright character to it.

What is a major scale? — YouTube

Songs such as ‘Don’t Stop Believing’ by Journey and ‘Let It Be’ by the Beatles use the major scale. Luckily, for the C major scale, we get no sharps or flats (C, D, E, F, G, A, B, C). But for a scale like B major, we get B, C#, D#, E, F#, G#, A#, B; for Ab major, we get Ab, Bb, C, Db, Eb, F, G, Ab.

Minor scale

Applying the major scale formula (Tone, Tone, Semitone, Tone, Tone, Tone, Semitone), but starting from the sixth step gives us a new formula: Tone, Semitone, Tone, Tone, Semitone, Tone, Tone (W H W W H W W). This sequence results in the minor scale, which is often associated with a more melancholic feel.

Songs like ‘Numb’ by Linkin Park and ‘Heathens’ by Twenty One Pilots use the minor scale. Instead of using the formula, the third, sixth, and seventh notes from the major scale can be flattened to result in the minor scale.

The Natural Minor Scale vs. the Harmonic Minor Scale — YouTube

Chords — The Basis of Harmony

Chords come into existence when multiple notes are played simultaneously. Even if you play notes randomly or slam your instrument, it can still be recognized as some type of chord. While the sheer number of possible chords might seem overwhelming, the majority of harmonic concepts can be grasped by focusing on just four foundational types of chords. These fundamental chords are classified as triads, meaning three notes:

Major Chord

Select a note, like F, for example. Then, take the note located 4 semitones above it (A, in this case), followed by the note 3 semitones above that ©. These three notes played together result in a major chord (F major — F, A, C), characterized by its bright sound.

Comparing the major scale to the major chord reveals that the major chord utilizes notes from the scale itself:

F major chord: F + A + C

F major scale: F, G, A, Bb, C, D, E, F

By using scale numbering, it becomes apparent that the F, A, and C notes are respectively numbered 1, 3, and 5 on the scale. Consequently, the second note of the chord (A in this case) is termed the ‘third’ or the ‘major third’ of F. Similarly, the third note of the chord (C in this case) is referred to as the ‘fifth’ or the ‘perfect fifth’ of F.

Minor Chord

Using the same method as the major scale, but flattening the ‘major third,’ results in a ‘minor third’ interval and a minor chord. For instance, F minor uses F, Ab, and C. As you may have noticed, the ‘fifth’ for both major and minor chords with the same root, remains the same. To form a minor chord without referencing a major chord, simply go 3 semitones above the root for the ‘minor third’ of the chord and then 4 semitones for the ‘fifth.’

In simpler terms, if you opted for 1, b3, and 5, you would end up with a minor chord. The sound of a minor chord is characterized by a relatively more melancholic or somber tone.

Check out this brief overview of Major and Minor Chords:

The BASICS of Major & Minor Chords in 4 MINUTES!

Diminished Chord

Creating a diminished chord involves taking the root note, the note located 3 semitones above it, and the note 3 semitones above that. Alternatively, you can achieve a diminished chord by lowering the fifth of a minor chord by one semitone. This chord brings us to the concept of the ‘tritone,’ the devil in music. As its name suggests, the tritone interval is 3 tones, or 6 semitones apart. The tritone is one of the most dissonant intervals in music, with myths suggesting it was banned from ancient churches for resembling the devil.

What is a Tritone? Tritone Explained in 2 Minutes (Music Theory)

However, it found a prominent place in jazz, where it is utilized to introduce tension before resolution, showcasing the interplay of dissonance and consonance in music. The diminished chord, achieved by flattening the fifth, results in a tritone (also known as a ‘diminished fifth’), contributing to the chord’s ominous feel, especially when combined with the minor third.

Diminished Chords — Why they’re the best!

Augmented Chord

To form an augmented chord, ascend 4 semitones above the root note, and then go another 4 semitones above that. Alternatively, you can create an augmented chord by raising the ‘fifth’ of a major chord by one semitone. The interval between the root note and the #5 (sharp fifth), also called an ‘augmented fifth,’ produces a strange and open feel. This particular chord is frequently employed in film scores to depict outer space. For example, in the soundtrack of Interstellar, Hans Zimmer utilizes the augmented chord as the space shuttle enters a wormhole.

The Bizarre World of Augmented Chords

“Major chords are happy”

A very commonly perceived notion is that major chords are happy and minor chords are sad. This is false… Well, not entirely. It is crucial to understand that the emotions evoked by chords depend significantly on context. If a C major chord follows an F major chord, it is likely to be perceived as “happy.” However, if an F minor chord precedes it, the subsequent C major chord might sound more melancholic or bittersweet, less “happy” in nature. Understanding the context is crucial in determining the emotional impact of chords on the listener.

Quick recap:

Major scale — Root, T, T, S, T, T, T, S