1. What is a consonance or a dissonance?

Have you ever wondered why some sounds go well together and some other not?

Why some sounds can merge beautifully and be consonant, and some others can be less pleasing to the hear and be dissonant?

There are different way to explain that, but we have to go back to what sound is, in its nature.

WHAT IS SOUND?

A sound is a variation of pressure that moves in the air.

Translation: a sound is a vibration of air. 

The particles in the air get all compressed, then stretched out, then compressed, then stretched out, etc... That how sound propagate, like the waves on the surface of water when you throw a rock in a lake for instance. 

That is also why there is no sound in space: if there is no particle of air to be compressed and stretched, there is no sound propagation.

So these vibration will make our ear-drum vibrate inside our ear, and then our brain will be like "hey man, you're hearing a sound"

CONSONANCE / DISSONANCE 

To know if two sounds are consonant or dissonant we can compare their frequency of oscillation. 

Basically, the simpler the ratio is between these frequencies, the more consonant they are.

So if I take a sound that vibrate at 220Hz, the most consonant sound that can go with it is 440Hz which is the double of that frequency. So they have the simplest ratio of 2:1.

The next most consonant to go with our 220Hz is 660Hz, which is triple this frequency, so they have a ratio of 3:1.

And then the next one will be 880Hz with a ratio of 4:1.

If we keep going, we start creating a series that we call the harmonic series.

So the simpler the ratio is between two frequencies, the more consonant they are.

That means that the more consonant they are, the more frequently their waves will sync up.

That is also why when two sounds are dissonant, we can hear a beating in the sound. That are the waves going in and out of sync.

This is how we can define the purity of a consonance : it is the absence of beating when two sounds play together.

We can use that to create our first musical scale and play actual music.

CREATION OF OUR FIRST SCALE

We've settled that the most consonant sound to go with our 220Hz  sound will be 440Hz, so twice as high, with a ratio of 2:1.

They are actually so consonant that they are considered the same note. With different pitches, but if our 220Hz is an A, 440Hz is also an A but one octave higher.

If we take a sounds with fundamental of 220Hz and play it with a sound which the fundamental is 440Hz, so twice as high, so they have a ratio of 2:1. They are so consonant, they are considered the same note. Different in pitch, but if 220Hz would be an A, 440Hz is also an A, but one octave higher.

So that means every time we multiply or divide a frequency by 2, we get the same note an octave higher or lower.


So the most consonant interval between two different notes is when they have a ratio of 3:1. And that is what we'll use to build our scale.

Let's start with our A at 440Hz.

We can add one note above and one note below using this 3:1 ratio. 

440×3=1320 and 440÷3=146,66

Then we can multiply or divide these frequencies by 2 to get the same notes, but closer to our 440Hz note

1320÷2=660Hz and 146,66×2=293,33Hz, 293,33×2=586,66Hz

We can then go one note further with these new notes we just created by multiplying or dividing their frequencies by 3 to get other new notes, and then divide them by 2 to bring them to the narrowest range possible. We can end up with this suite of notes:

391,11 - 440 - 495 - 586,66 - 660

There, we just created our first pentatonic scale, with 5 notes per octave. That is probably the kind of scale that is the most used around the world. it's used a lot in Chinese music, blues, country and folk music for example

The frequencies in our scale actually correspond to the notes G - A - B - D - E, which is the pentatonic scale of G major, or the pentatonic scale of E minor.

And from there we can add two notes again so we can end up with these frequencies that correspond to the notes G - A - B - C - D - E - F# which is the scale of G major.​

And this is how the first scales were created
(precision: up until the XVth century. instruments were tuned from fifth to fifth, so every notes were tuned using this 3:1 ratio. The spacing between each notes of a scale was similar to what is described in this video. This has changed a little since the XVth century. More details on that in the next chapter.)

In this kind of scale, the first note is called the Tonic, then there is the 2nd, the third, the fourth, the fifth, the sixth and the seventh.

And this is why we call the next note the octave, "oct" meaning 8, which is technically the same note than the Tonic.

CONSONANCE IN OUR SCALE

Now back to the harmonic series we made at the beginning of the video, and compare it with the notes we have in our scale.

So the first note, harmonic 1, is our fundamental, and the harmonics 2, 4 and 8 or different octaves.

Then the most consonant notes with the Tonic in our scale would be the fifth and the fourth, as we used the 3:1 ratio of the harmonic 3 to make them. And the fourth is a fifth below the tonic. 

Then the most consonant note with our tonic would be the third and the sixth. if we look the relation between our third and the fundamental, we find a relation of 64/81, which is almost 4/5 (that would be 64.8/81). Which uses the 5:1 ratio of the fifths harmonic in the harmonic series. And the sixth is a third below the tonic.

And finally, the 2 last notes, the 7th and the 2nd are the more dissonant with the Tonic in our scale.

This third that is "almost" exact but not perfect will begin to cause some problems at some point, but we'll see why a bit later.

This is the beginning of a very long road to explore the music theories and to explore how our music is built.

That is a road that I would like to take, slowly, at my own pace in a series of videos.

Starting with the fundamentals, explaining why we use the tools we use today, and then how we can use these tools to create our own music.

So if you'd like to see these videos when they come out, make sure to subscribe and hit the bell button.

In the mean time, thanks for watching and I'll see you next time

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© 2020 Charly Sauret