Harmony Starts Here

You can hear the Podcast Episode, with all the musical examples at:

March 2024

• Why harmony holds such an important role in music?

• What’s so special about the 5th?

• Why certain notes sound good and others don’t?

To answer these questions we have to dive in the nature of sound itself. This is not a theory class, rather a journey into sound, following a trajectory that extends from strictly musical topics into larger acoustic phenomena. After, the reader will have a more comprehensive understanding of how sound and harmony works. Harmony is relevant in music, but as we shall see it goes beyond music as well.

Let’s start with a statement: The most fundamental brick in the architecture of harmony is an interval.

Musical harmony can be thought of as an architecture: harmony in music is generally referring to chords and chord sequences. When you study harmony you are studying how composers have arranged chords together to create beautiful music: you discover the principles guiding such arrangements and learn how to build nice, interesting sequences of chords yourself, initially by imitation, then following your own creativity. But harmony in the English dictionary relates to concepts like balance, equilibrium, accord, agreement: it is a consistent, orderly, or pleasing arrangement of parts.

In music that balance is accomplished in two dimensions: balance could be found at any given moment, any ‘now’ considered individually (in music they are called vertical harmonies, or chords, because of the way the notes look on a score, stacked up on top of each other), AND the way in which these series of ‘now’ are stringed together on the music timeline, offering a second dimension where we can find balance and harmony, this time a horizontal one.

So ‘architecture of harmony’ is the way we define the complex set of relationships between individual notes to create music, whether they are at one given moment or taken altogether, on the musical timeline. In the same way when we look at an actual architecture, a building, a cathedral, a tower, we can’t avoid focusing on one aspect at the time, walking in and around it, so we can perceive the greater design of a building only as we reconstruct all these individual aspects, the ‘nows’ into a larger system.

With regard to harmony, I say to my students: harmony is neither chords nor sounds, harmony is a relationship: the moment you have more than one sound you have a relationship, you have harmony. The smallest relationship we can find in music is the relationship between two individual notes. The building blocks at the basis of any harmonic architecture is the relationship between two notes. Like the relationship between a proton and an electron holds together and at the same time an atom and the entire fabric of reality, the relationship between two notes holds a chord together, as well as the music.

Our ability to appreciate music stands on this basic phenomenon, the harmonic relationship between two sounds: we can hear two sounds at once. The interesting thing is that we hear them as one sound, one ‘harmony’, in the same way if we put together two colours like red and blue, we don’t see anymore neither red nor blue, but the resultant which is purple. Studying harmony is a way to unpack aggregates of notes into their components and learn to discern the role that each individual sound has in music. The way we have agreed to label the basic relationship between two sounds is by the term ‘interval’.

The term interval suggests a gap, a distance between sounds. In reality there is no distance between sounds, because sounds happen at once in the same space. We see a distance between the notes on a keyboard, but the sounds are not distant at all. The term interval is a shortcut, a simple way to talk about harmonic relationships. We think of music as made of notes, but it would be more appropriate to say it is made of relationships between notes. Harmony in music is made of intervals.

The initial statement is now clearer: ‘The most fundamental brick in the architecture of harmony is an interval’

Here is another statement to unpack: The interval of 5th is the most fundamental interval in harmony.

There are near infinite relationships between any two sounds in the acoustic spectrum. The interval of 5th is just one of them: why would that be fundamental, and why there should be any interval more important or fundamental than any other?

As we enter the core of the argument, let’s take a broader look. Similarly to other creative fields, we humans don’t invent out of nowhere, even though it might be difficult sometimes to trace the origins of what we invent. With regard to the interval of 5th, it is no coincidence that since the beginnings of history, and across cultures and centuries, the interval of 5th has been maintained as a point of reference for musicians. 5ths appear in the very first examples of written music, in modern jazz, in folkloric music from all over the world; musical instruments and entire musical systems are built on the interval of 5th (such as the tonal system, which is the musical system that western culture has adopted and developed since the 16th century onwards). This is no coincidence.

The 5th is not just an interval, or one relationship among others. The 5th belongs to sound itself. How to explain it better: any sustained sound, like a note on the piano, is already an architecture. What we perceive as one tone is actually a combination of frequencies, some stronger some weaker, that align altogether to render this sound, which appears to be ‘one’ to our ears. But we know that the exact same note played on a different musical instrument will sound different: this is because each instrument brings out a frequency or another, among the many that the note is made of. Musical instruments are remarkable technological tools exactly because they allow us to hear the richness of a sound through a sustained tone, which is almost impossible to experience in nature: hearing a sustained tone, like the one you hear by holding a key at the piano, is not a natural phenomenon. Even our voice needs to be educated to produce a sustained tone.

As I was saying, a note is already a harmony, an architecture. This phenomenon is not new to physicists and musicians alike, the components of a note are called ‘harmonics’, and there is virtually no sound in reality that is not a combination of harmonics; there is no pure C or pure D sharp. One note is already a harmony, a relationship. So far, we thought that harmony is what happens when we zoom OUT from single notes and we consider them in aggregates, in groups, chords and sequences, but harmony already happens within a single note, by way of zooming IN an individual sound.

Harmonics are the molecules that when resonating together give rise to a single note. Earlier we mentioned the structure of an atom, now think of a tree: we can hear the trunk, the main note, which is the connection and the resultant of all its branches, the harmonics.

To me the most fascinating aspect is that there is a world above notes, we are calling it music, harmony, composition: we build systems and explore creative approaches to organize notes, we create splendid architectures and beautiful music, and there is a world within notes, also somehow orderly and organised systematically, with relationships and qualities. Not only one world can map into the other, but the notes seem to be just one level, a degree of resolution at which we look at the phenomenon of sound, above which we have music and harmony, below which we have harmonics.

Through this model notes just seem an arbitrary degree among the many possible: humans like to play with them, most musicians and school are concerned with what happens above the notes, how to aggregate them in larger structures, harmonies and forms, but the world below (harmonics) is what actually governs the way sounds relate to other sounds. Most composers have been inspired by the inner world of harmonics to create music: every time a note is chosen according to a principle of consonance or pleasantness we are referring back to the ground relationships between harmonics. Other composers have arranged notes in a way that mimics how harmonics operate: I am referring to spectral composers, who have been named after writing music that develops from a spectral analysis of sound, which extracts and shows all the harmonics that constitute a sound.

This is a piece called Partiels, by Gerald Grisey from 1975. You can hear these waves of sound springing out those low notes. With a bit of imagination you can almost see the trunk of the tree, splitting into its many branches. Gerald Grisey is a spectral composer, not because he is into ghosts, but because his musical research led him to zoom in the spectrum of sound, discovering and play with harmonics.

Sound is in fact a spectrum. Any note we hear is a combination of several notes, and this is just how nature works. Now, what are these notes and how do they relate to each other? Earlier I mentioned that the frequencies of harmonics align to create a rich and round tone: frequencies of the harmonics from the same sound are mathematically proportioned. Of course harmonics relate to each other in orderly ways: the relationship between them is governed by mathematic proportion and unsurprisingly such proportions determines what we perceive as consonant, harmonic, balanced.

The simplest the proportion,

the more consonant we find the interval.

The strongest relationship you find among the harmonics is the 5th: the frequencies of a note and the one a 5th above match, their proportion is represented exactly by the proportion 3/2. The stability of this relationship, the reason why it sounds so consonant (we call the 5th ‘perfect’) is due to two frequencies mapping proportionally into one the other. There are simplest proportions than 3/2, like 2/1, which is the musical interval of 8ve. While stronger than the 5th, the 8ve does not give rise to very interesting harmony.

If the 5th is so embedded in the nature of sound, we can intuitively conceive how music could just represent this relationship by exploring the two notes, moving for example from 1 to 5. The vertical relationship between two sounds turns into a horizontal relationship, on the timeline of music. It stops being a static architecture and becomes a movement, a trajectory filled with potential. In the west, it’s the perfect opportunity to tell a story. We named it a trajectory between tonic and dominant, and that is what we find at the basis of the tonal system. The interval of fifth is a ground relationship, and as we saw it's a natural one. The 5th is the basic brick of musical harmony, and a typical musical trajectory moves from a note to another a 5th away.

In the west we like to close properly our inventions, so we tend to create music that once goes away it comes back to the initial note. For a few centuries composers have created music that would pretty much always move from the initial note up or down a 5th. Since the 1600 they preferred to move up a 5th, and come back down by the end. Music developed in the 1700 expanding the time spent (and the creative ideas) around each of the two harmonic areas, now called tonic and dominant, structuring entire compositions on this dual principle.

Once composers had become familiar with the duality of Tonic and Dominant they started experimenting and developed music that would string together many subsequent 5ths. This is a musical pattern, almost a trick, that is used everywhere in music, so much that a model has come out of it, which many of my readers will be already familiar with, the Circle of 5ths. Why circle? Because if every note can lead to another one 5th apart, you can organise all the 12 notes around a full circle that sounds like that.

Once you play the notes in either direction, you notice there is nothing musical about it: it is just the acoustic rendition of a geometric model. But the vast majority of composers and music creators have employed at least sections of it. In the Podcast Episode I provide examples from Beethoven, Bach, Frank Sinatra, Gloria Gaynor…

We learned that harmony is an architecture of sound, and that every piece of music is maintained stable by the relationships between sounds, more than the sound themselves. We also learned that the most important, solid relation is the interval of 5th, and the reason why it is so important is because the 5th is embedded in the fabric of sound itself, more than any other interval. And finally, we learned that if our musical system is based in fact on the interval of 5th this is due to the very nature of sound, and that it is possible to think of musical harmony as an extension of what happens within sound.

Some links for more information on the topic.

Harmonics - Wikipedia

Spectral Music - Wikipedia

You can hear the Podcast Episode, with all the musical examples at: