Functional Harmony

Functional harmony is a core aspect of music theory that unlocks a world of vocabulary and experiential changes when listening to music. I’ll discuss intervals, scales, and chords and how they work together to make music compelling.

At the heart of this exploration is the idea of consonance and dissonance.

Consonant means stable and comfortable.

Dissonant means the opposite, uncomfortable, seeking resolution.

Harmony, and music in general, is often constructed around increasing dissonance and then a return to consonance.

Frequency

Sound is a pressure wave: rapid changes from air being compressed to being rarefied. Frequency, denoted in “hertz,” is the measure of how many times the oscillation occurs within a second.

Consider a guitar string - when it is plucked, it moves back and forth very quickly, disrupting the air that immediately surrounds it. This disruption moves outward, and our ears hear that disruption as a different pitch based on how fast the oscillation occurs.

Sound as a pressure wave

Sound waves can be charted on an axis as above, showing the increase and decrease of pressure over time.

Intervals

If two notes are played at the same time, the ratio of their frequencies is called an interval. For example, if one string vibrates at 600 Hz and another at 400 Hz, the ratio is 3:2. This means that in the time it takes for the 600 Hz sound to oscillate three times, the 400 Hz sound oscillates twice.

The “simpler” the ratio, the more consonant we experience the interval as.

The interval 2:1 is the most consonant. From there, the interval 3:2 is slightly less consonant, and then 4:3 is still a bit less, and so on.

Pitch

Pitch is a system of describing frequencies based on the experiential similarity of the ratio 2:1.

We experience these notes as so similar that we give them the same name.

Every “A” on the piano is double the frequency of the A an octave below.

Scales

A scale is a collection of note names (sometimes called “pitch classes”) that fit within one of these 2:1 relationships:

Intervals and frequencies

This is a C Major scale with the ratios of all of the intervals from the lowest note.

2:1 - the octave, C to C

3:2 - the fifth, C to G

4:3 - the fourth - C to F

The names “fourth” and “fifth” come from the number of steps up the scale it takes to get to the second note of the interval.

Chords

Generally when we talk about chords, we mean a collection of three notes made of stacked thirds.

A C major chord, the I chord of the C Major scale is:

C, E, G

The first scale degree, the third scale degree, and the fifth scale degree.

We create such a chord from every note of the scale, giving us:

Seven notes of the scale give us 7 chords. We use Roman numerals by convention to distinguish a chord from other uses of numbers in music

The magic of this is that almost all of the music we love is based on the three chords above with capital letters - the I, the IV, and the V. This corresponds to the three intervals above that were most stable - 3:2, 4:3.

Functional Harmony is based on this math. A move from the I chord (C) to the V chord (G) creates tension, a G to a C gives us the feeling of resolution.

The experience of music is not universal, but in general, we can think of functional harmony as an exploration of the increase in tension created by moving away from the I chord, and the release of tension from resolving back to the I.

This works because we are able to hold onto the tonic chord (the I), as context for experiencing the other moments.

Consider the progression: I, V, vi, IV

• In the key of C this would be C, G, A minor, F, Then C and it continues.

• This progression is extremely popular. Perhaps this is because the harmonic movement creates a pleasing arc of increasing tension to resolution.

I -> V: We move away from tonic, the ratio of our new sonority is 3:2. Tension increased.

V -> vi: We move further away from the tonic, the new ratio is 5:3, more complex.

iv -> IV: New ratio; 4:3, A step back toward consonance as this is less complex

IV -> I: We resolve back to our starting point, tension is released

Tension

There is more nuance to the subject, but this is the gist - the utility of harmony comes from the science of acoustics.

Harmony is the vocabulary of music and learning to think in terms of chords unlocks new worlds of enjoyment and appreciation.