Consonances & Dissonances

Question 1

What is sound?

Answer 1

A sound is a vibration of air (or, a variation of pressure that moves in the air).

Question 2

How does a sound vibration function?

Answer 2

The particles in the air get compressed then stretched, then compressed, then stretched, and so on… like the surface of the water when you throw a rock in the lake.

Question 3

Why is there no sound in space?

Answer 3

There is no particle of air to be compressed and stretched, hence no sound propagation.

Question 4

How do we hear?

Answer 4

The sound vibrations in the air vibrate in our ear drum, and we recognise we are hearing.

Question 5

How can we know if two sounds are consonant or dissonant?

Answer 5

We compare their frequency of oscillation - the simpler the ratio between these frequencies, the more consonant they are.

Question 6

Give an example of the simplest oscillation frequency ratio?

Answer 6

If we take one sound that vibrates at 220Hz, the most consonant sound that can go with is 440Hz - double of the original frequency … they have the simplest ratio of 2:1

Question 7

Excluding 440Hz, what is the most consonant frequency that 220HZ can go with?

Answer 7

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

Question 8

If we take 220Hz and pair it with other frequencies, such as 440Hz (2:1), 660Hz (3:1), 880Hz (4:1), 1100Hz (5:1), and 1320Hz (6:1), and combine these in a series… what do we get?

Answer 8

We get a harmonic series

Question 9

The simpler the ratio is between two frequencies, the more _____ they are?

Answer 9

Consonant

Question 10

If two sounds are said to be more consonant than others, do their waves sync up more or less frequently?

Answer 10

More frequently

Question 11

When two sounds are dissonant, why can we hear a beating in the sound?

Answer 11

Their waves are going in and out of sync

Question 12

How can we define the purity of a consonance?

Answer 12

The absence of beating when two sounds play together

Question 13

When two sounds have a ratio of 2:1, do we consider them the same note?

Answer 13

Yes, we consider them the same note, with different pitches e.g., if our 220Hz is an A, 440Hz is also an A but one octave higher.

Question 14

Every time we multiple or divine a frequency by 2, what do we get?

Answer 14

The same note, an octave higher or lower

Question 15

What is the most consonant interval between two different notes?

Answer 15

3:1

Question 16

How are scales created?

Answer 16

They are created using math equations based on the frequencies.

Question 17

What is a pentatonic scale?

Answer 17

A musical scale with five notes per octave

Question 18

What is a heptatonic scale?

Answer 18

A scale which has seven notes per octave (such as the major scale and minor scale).

Question 19

What is the most used scale around the world?

Answer 19

Pentatonic scale (used in Chinese music, blues, country, folk, and more).

Question 20

How can we create a pentatonic scale (example)?

Answer 20

• Let’s start with our A at 440Hz
• We can add note above and one note below using a 3:1 ratio (the most consonant interval between two notes).
• So we have 440×3=1320 and 440÷3=146,66
• We can then multiple or divide these frequencies by 2 to get the same notes, but closer to our 440Hz note (not adjusting our original 440Hz): 1320÷2=660Hz and 146,66×2=293,33Hz, 293,33×2=586,66Hz
• 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:
  1: 391,11
  2: 440
  3: 495
  4: 586,66
  5: 660
• We now have created our first pentatonic scale, with 5 notes per octave

Question 21

What do we get if we add two notes to our two notes to our scale?

Answer 21

We get a heptatonic scale (in this case, G major)

Question 22

What is the first note called in this scale?

Answer 22

The tonic