00:00:28

Hello everyone. Today we are going to dive in the nature of sound itself.

00:00:35

And see why harmony functions the way it does.

00:00:40

Often students ask what's so special about the fact and why certain notes sound good and others don't.

00:00:50

As usual, I don't teach theory on this podcast, but I take a larger look at the extended musical phenomenon.

00:00:58

Today I look at Harmony which is relevant in music, but as we shall see, it goes beyond music as well. We are going to answer the questions. What is harmony? What exactly is 1/5 and why is it so important?

00:01:17

What is it?

00:01:18

That makes Harmony Sound one way or another.

00:01:22

So let's get started.

00:01:31

Harmony Starts here.

00:01:34

I'm going to give you a statement.

00:01:37

Which goes.

00:01:39

The most fundamental brick in the architecture of harmony is an interval.

00:01:45

Let's unpack this statement.

00:01:50

Musical harmony can be thought of as an architecture.

00:01:54

Harmony in music is generally referring to chords, chord sequences. When you study harmony, you are studying how composers have arranged courses together to create beautiful music, and so you learn how to build nice interesting sequences of chords yourself.

00:02:15

But harmony in the English Dictionary relates to concepts like balance, equilibrium, accord, agreement.

00:02:23

A consistent, orderly or pleasing arrangement of parts.

00:02:29

In music that balance that agreement.

00:02:33

Has to be accomplished in two dimensions.

00:02:37

Balance could be found at any given moment, any now.

00:02:43

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 vertically.

00:02:56

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.

00:03:10

This time a horizontal one.

00:03:13

So architecture of harmony is the way we define

00:03:19

The often complex set of relationships between individual nodes to create music, whether they are at one given moment or taken together on the musical timeline.

00:03:33

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 a time. Walking in and around it so we can perceive.

00:03:48

The greater design of a building only as we reconstruct all these individual aspects, the nouns into a larger system, a larger design.

00:04:01

With regard to harmony, I say to my students, harmony is neither chords nor sounds. Harmony is a relationship, and the moment you have more than one sound, you have a relationship. You have harmony.

00:04:19

The smallest relationship we can find in music is the relationship between two individual nodes. The building blocks are the basis of any harmonic architecture. Is the relationship between 2 nodes.

00:04:33

Like the relationship between a proton and an electron holds together and at the same time an atom and the entire fabric of reality.

00:04:43

The relationship between 2 notes holds a chord together as well as the music.

00:07:12

We can hear 2 sounds at once. Our ability to appreciate music stands on this basic phenomenon. The harmonic relationship between 2:00 sounds.

00:07:24

The interesting thing is that we hear them as one sound, one harmony, in the same way, if we put together 2 colours like red and blue, we don't see any more, neither red nor blue, but the resultant which is purple.

00:07:42

Studying Harmony is a way to unpack aggregates of notes into their components and learn to discern the role.

00:07:52

That each individual sound has in music.

00:07:56

The way we have agreed to label that relationship is by the term interval.

00:08:04

The term interval suggests a gap, a distance between sounds.

00:08:11

In reality, this is not true. There is no distance between sounds, cause 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.

00:08:30

Harmonic relationships.

00:08:33

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.

00:08:50

Now we understand better what the initial statement meant.

00:08:55

I said the most fundamental brick in the architecture of harmony is an interval.

00:09:02

Here is a second statement to unpack the interval of. 5th is the most fundamental interval in harmony.

00:09:13

The interval 5th is just one of the infinite possible relationships between any two sounds we can find. Why would that be fundamental, and why there should be any interval more important or fundamental than any other?

00:09:33

As we may find, similar 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 come up with.

00:09:46

With regard to the interval of faith, it is no coincidence that since the beginnings of history and across cultures and centuries, the interval of fifths has been maintained as a point of reference for musicians, fifths appear in the very first examples.

00:10:06

Of rhythm music.

00:10:09

In modern jazz, in folkloric music from all over the world.

00:10:13

Entire musical systems are built on the interval of fifth, such as the tonal system, which is the musical system that Western culture has adopted and developed since roughly the 16th century onwards.

00:10:31

This is no coincidence.

00:10:34

The 5th is not just an interval or one relationship among others.

00:10:40

The 5th belongs to sound itself. How to explain it better? Any sustained sound

00:10:49

Like this

00:10:55

Is already an architecture.

00:10:59

What we perceive as one tone in this case, it's G.

00:11:09

Is actually a combination of frequencies, some stronger, some weaker, that align all together to render these apparently one sound.

00:11:22

If the exact same note played on two different instruments sounds different to our ears, that's because.

00:11:29

Each instrument brings out a frequency or another among the many that the note is made of.

00:11:38

Musical instruments are.

00:11:41

Fantastic. Exactly because they allow us to hear the richness of a sound through a sustained tone.

00:11:49

If you think about it, it's hard to find such phenomenon in nature. I mean, a sustained tone like this.

00:12:02

Even the voice needs to be educated to produce a sustained tone.

00:12:09

As I was saying, a note is already a harmony and architecture. This phenomenon is not new to physicists and musicians alike.

00:12:19

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 sea or pure D sharp.

00:12:34

Perhaps except digitally created sound.

00:12:38

But even there the purity is debatable.

00:12:42

One note is already a harmony, a relationship.

00:12:47

So far, we thought that harmony is what happens when we zoom out from single nodes 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.

00:13:09

Harmonics are the molecules that, when resonating together, give rise to a single node.

00:13:19

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.

00:13:31

Of all its branches, the harmonics.

00:14:31

To me.

00:14:32

The most fascinating aspect of all of this is that.

00:14:36

As we are saying, there is a world above notes. We are calling it music harmony. We build systems and creative approaches to organise notes to create splendid architectures and impressive and beautiful music.

00:14:53

And there is a world within notes also somehow orderly.

00:15:00

And organised systematically with relationships and qualities.

00:15:06

Not only one world can map into the other, as we shall see today, but the notes seem to be just a a level, a degree of resolution at which we look at the phenomenon of sound, above which we have music and harmony below which.

00:15:27

We have harmonics.

00:15:30

Through this model, notes just seem an arbitrary degree among the many possible.

00:15:37

Humans like to play with them. Most musicians and schools are concerned with what happens above the notes, how to aggregate them in larger structures, harmonies and forms. But there is a word below notes, the harmonics that governs the way sound relate to sound.

00:15:59

Composers have been inspired by the inner world of harmonics to create their music as a way to draw a connection between them to expand our perception of what sound is to depart from the level of notes into a more comprehensive view of notes and harmony.

00:16:20

Other composers have arranged notes in a way that mimics how harmonics operate. I am referring here to the spectral composers who have been named after writing music that develops from a spectral analysis of sound.

00:16:41

Which is necessary in order to extract harmonics from a sound.

00:18:27

This was a piece called Partiels.

00:18:31

By the composer Gerald Grisey from 1975.

00:18:36

You could hear these waves of sound springing out of those very low notes.

00:18:46

And you can almost see the trunk of a tree splitting into its many branches.

00:18:53

Gerald Grisey is one of those Spectral composers. Not because they are into ghosts, but because, as I was saying.

00:19:02

Their musical research led them to zoom in the spectrum of sound discovering and play with harmonics.

00:19:11

Sound is in fact a spectrum. Any note we hear is a combination of several notes, and this is just how nature works.

00:19:21

Now, what are these notes and how do they relate to each other?

00:19:28

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 proportional. Of course, harmonics relate to each other.

00:19:49

in orderly ways.

00:19:50

The relationship between them is governed by mathematical proportion and unsurprisingly.

00:19:57

Determines what we perceive as consonant harmonic balanced.

00:20:04

The simplest.

00:20:05

The proportion.

00:20:07

The more consonant we find the interval.

00:20:12

The strongest relationship you find among the harmonics is the 5th.

00:20:17

The frequencies of a node and the one a fifth above match. Their proportion is represented exactly by the proportion 3 / 2.

00:20:30

The stability of this relationship, the reason why it sounds so consonant and perfect as we call such an interval.

00:20:41

It is due to two frequencies mapping proportionally 1 into the other.

00:20:48

There are simplest proportions than 3 / 2.

00:20:52

Like 2 / 1 which is the musical interval of Octave.

00:20:59

While stronger and simpler than the interval of 5th, this interval the octave does not give rise to very interesting harmonies.

00:21:12

So 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 nodes moving, for example, from 1 to 5.

00:21:31

It stops being a stable architecture and becomes a movement, a trajectory filled with potential.

00:21:39

In the West, it's the perfect opportunity.

00:21:43

To tell a story.

00:21:46

We named that trajectory tonic to dominant.

00:21:51

And that is what we find at the basis of the tonal system.

00:21:56

And in general, this is the way we in the West have given birth to a set of fixed tones by virtue of stacking fifths up one onto another. So C

00:22:13

Give us G.

00:22:18

G Now we have 3 notes.

00:22:20

Gives us D.

00:22:33

Gives us A.

00:22:37

A gives us E.

00:22:47

Right.

00:22:50

And so forth.

00:22:52

I'm going to give an example of how this happens in music as well. Going from 1 to 5.

00:23:30

Did you hear the tonic?

00:23:58

This is the dominant.

00:24:07

The interval of 5th is a ground relationship, and it's a natural one. The 5th is the basic brick of musical harmony and the typical musical trajectory moves from one note.

00:24:23

To another one 5th away.

00:24:26

As we just saw in the West, we like to close properly our invention.

00:24:32

So we tend to create music that once goes away. It comes back, in this case, back to the initial note, the tonic.

00:24:42

Most the most famous example, the simplest that comes to mind is from Beethoven.

00:25:04

This coming and going away from the tonic tonic.

00:25:11

Dominant…

00:25:17

And again.

00:25:27

The relationship between 1 and 5 can be also seen as a kind of an Elastic. It stretches and then comes back like a spring.

00:25:41

For a few centuries, composers have created music that would pretty much always move from the initial note up or down a face.

00:25:52

Since the 1600, they preferred to move up a fifth and come back down by the end. Music developed in the 1700 expanding the two harmonic areas now called Tonic and dominant, making entire compositions around it.

00:26:11

And once composers had become familiar enough with this principle, they started experimenting with it and developed music that would string together many subsequent fifths.

00:26:24

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 you will be already familiar with, called the circle of fifths. Why the circle? Because if every note can lead.

00:26:45

To another one fifth apart, you can organise all the 12 notes around a full circle. That sounds like that.

00:27:09

It is not a musical.

00:27:13

Thing at all. It's just a acoustic rendition of a geometric model you can.

00:27:21

Find all the 12 notes in this manner.

00:27:38

That's the first one I start so.

00:28:00

So it's it's just a geometric model. Too many people, I think, tend to see too much music in it, but there is more in music than just a geometric principle.

00:28:18

Nevertheless, most musicians have employed at least sections of it, and and some examples are actually coming from.

00:28:29

The musical pieces that you heard towards the beginning of this episode I'm thinking of.

00:28:36

Beethoven, Adagio, the passage that goes.

00:28:54

OK, so you hear.

00:29:05

This is a circle of 5th.

00:29:13

Another example still from.

00:29:15

Beethoven is less obvious, but is very much in the ears of any of you who enjoys Beethoven's music. This is from the Moonlight Sonata.

00:29:59

OK, this very last passage is circle of 5th. So we have.

00:30:08

Actually, before that we have C.

00:30:12

Then F#.

00:30:14

Then B.

00:30:16

Then east.

00:30:18

The A.

00:30:20

And the sharp then G#.

00:30:24

And C from the very start we arrive with. I actually continues F. So what we got?

00:30:42

Complete circle of fifths. I'll play it again.

00:31:11

OK so.

00:31:13

Next example is from Bach, who transcribed flute.

00:31:22

A concerto by Benedetto Marcello. You heard it with the second example I played today and at the very beginning we have a circle of fifths. It goes like this.

00:32:11

So you can hear the lowest note of the accompaniment.

00:32:20

The 5th, then again 1/5.

00:32:26

Then again another one.

00:32:32

In the lab.

00:32:39

And the final one.

00:32:45

You see, it's very musical to put to put the circle of faith in this manner.

00:32:52

Couple more examples from more modern music. This is something that I've recently discussed with students student in class and we found out that the song fly me to the Moon has all circles of fifths.

00:33:29

OK.

00:33:34

Another one is less obvious. It's all the things you are a famous jazz standard.

00:34:03

You could.

00:34:03

Here the base part.

00:34:12

And the final example will be absolutely surprising for most of you.

00:34:21

You probably heard this.

00:34:37

What is this? This is I Will Survive Gloria Gaynor and.

00:35:01

Once again.

00:35:02

Circle of fifths.

00:35:13

So what to make of today's journey into the building blocks of harmony, we learn that harmony is an architecture of sound, and that every piece of music is maintained stable by the relationships between those sounds more than the sound themselves.

00:35:33

We also learned that the most important, most solid relation is the interval of faith and the reason why it is so important is because the faith is embedded in the fabric of sound itself.

00:35:49

More than any other interval.

00:35:52

And finally, we learn that if our musical system is based in fact on an interval of 50.

00:36:01

This is due to the very nature of sound and that is possible to think of musical harmony as an extension of what happens in the nature of sound.

00:36:15

Thank you for being with me today. I hope you enjoyed my.

00:36:23

Journey into the fundamentals of harmony. I'm going to provide some links For more information if you're interested regarding this topic and the topics that I have touched throughout this. Thank you again for.

00:36:39

This episode.

00:36:43

Tuning with me and I will see you the next time.