C0

C1

C2

C3

C4

C5

C6

C7

C8

Intervals

Measuring the speed of sound.

Flashing lights.

So music’s got all these Notes, but what do we do with them? When we start to wrap our head around notes and what they represent, we will quickly want to know how to do more with them. At some point we as artists start thinking about how we can combine these notes together to creeate more interesting sounds. This is where the concept of the interval comes in to play.

Definition

Interval

noun

a space between two things; a gap.

An interval is simply the measurment of distance. A mile is an interval of physical distance. A Meter is another measurement of physical distance as well. It is a different length, but it is fundamentally the same concept.

Pitch Distance

In music we are concerned about distance in a different way. We are concerned about the distance between the speed of frequencies. If one frequency is 100 vibrations per second, and another is 200 vibrations per second, then those numbers refer to the speed of vibration of each of those frequencies and the interval is the diffference between those two speeds.

200 - 100 = 100

So, in music, an interval is the measurement of the distance in pitch between two notes.

We can also think of these differences as ratios, through reduction:

2 - 1 = 1

…and we can understand the relative quality of an interval by the simplicity of the ratio. If 100 is the first frequency and 200 is the second, we can reduce those numbers down to a very ratio of 1 to 2, or 1:2. This is the simplest ratio that we can have, and it represents two frequencies, one of which is twice the speed of the other. This is the first interval that we can name, and we are going to refer to it from here on as an octave. Now, you may be wondering why in the world we would call it that, and without any other context you would be very right to question this decision. So, to understand why this choice was made, we first need to talk about note names.

Lines, Spaces, and Letters

In musical notation, we use letters to represent notes on a keyboard. Not all of the letters, I might add. Only a few. We start with the letter A and go through the alphabet to the letter G. If this is new information for you, then I suggest reading all about Notes and how they work in music theory.

Half Step

A Half Step is the distance between two adjacent notes. It is the smallest interval in music. C to Db in this example. We can use the letter H to represent a Half-Step.

C

Db

Whole Step

A Whole Step is simply two half steps added together. It is the second smallest interval in music. C to D in this example. We can use the letter W to represent a Whole-Step.

C

D

Nomenclature

The name of each interval has two parts. This is because there are more notes on a keyboard then there are letters in the musical language.

This is because the “number” in name the interval name does not come from the number of steps.

no no no no no no noooooo.

It actually comes from counting the letters on the keyboard.

The problem is that there are more notes on a keyboard then there are letters in the musical language. We deal with this by introducing a second concept into the naming system

So, naming intervals involves two steps:

Part 1

The first part of the name is derived from the distance, measured in the number of letters, which will give us the “number” in the name of the interval. C to D is a 2nd because there are two letters counted, C and D. From C to E is a 3rd because there are three letters counted, C, D and E. The counting includes the notes of the interval as well as the notes in between.

1st

C

2nd

D

3rd

E

4th

F

5th

G

6th

A

7th

B

Part 2

The second part of the naming system is based on the quality of the interval. We use the terms Major, Minor, Augmented, Diminished, and Perfect.

If we want to create a 2nd we must go from one note to the next, for example, C to D. But the problem we run into is that there are two D’s: D and Db. So we have to devise a way to distinguish between the two D’s.

Intervals

The following is description of each interval in tonality. We start by learning about 2nds, 3rds, 6ths, and 7ths, as they form a logical group.

Color Intervals

Minor 2nd

The interval from C to Db is called a Minor 2nd. It’s a 2nd because there are two letters involved, which are C and D, and it’s minor because it’s the smaller of the two 2nd intervals. Take a listen to how it sounds…

Minor 2nd

C

Db

Major 2nd

The interval from C to D is called a Major 2nd. It’s a 2nd because there are two letters involved, which are C and D, and it’s major because it’s the larger of the two 2nd intervals. Take a listen to how it sounds…

Major 2nd

C

D

Minor 3rd

The interval from C to Eb is called a Minor 3rd. It is a 3rd because there are two letters involved, which are C and E, and it’s minor because it’s the smaller of the two 3rd intervals. Take a listen to how it sounds…

Minor 3rd

C

D

Eb

Major 3rd

The interval from C to E will be a Major 3rd. It is a 3rd because there are two letters involved, which are C and E, and it’s major because it’s the larger of the two 3rd intervals. Take a listen to how it sounds…

Major 3rd

C

D

E

Minor 6th

The interval from C to Ab is called a Minor 6th. It is a 2nd because there are two letters involved, which are C and A, and it’s minor because it’s the smaller of the two 6th intervals. Take a listen to how it sounds…

Minor 6th

C

D

E

F

G

Ab

Major 6th

The interval from C to A is called a Major 6th. It is a 6th because there are two letters involved, which are C and A, which are six letters arpart, inclding themselves, and it’s major because it’s the larger of the two 6th intervals. Take a listen to how it sounds…

Major 6th

C

D

E

F

G

A

Minor 7th

The interval from C to Bb is called a Minor 7th. It is a 2nd because there are two letters involved, which are C and B, and it’s minor because it’s the smaller of the two 2nd intervals.

Minor 7th

C

D

E

F

G

A

Bb

Major 7th

The interval from C to B is called a Major 7th. It is a 2nd because there are two letters involved, which are C and B, and it’s major because it’s the larger of the two 2nd intervals.

Major 7th

C

D

E

F

G

A

B

There are two intervals that fall out of major minor nomenclature.

Power Intervals

The perfect invtervals are called “Perfect” because of their place in history. They were once known as the most consonant (pretty) intervals by those who created their names, and those people were quite religious (Monks). They felt that 4ths and 5ths were so perfect, they represented God in music. Hence, Perfect 4ths and 5ths.

Perfect 4th

The interval from C to F will be a Perfect 4th. It is a 4th because there are two letters involved, which are C and F, and it’s perfect because, it’s just so pretty.

Perfect 4th

C

D

E

F

Perfect 5th

The interval from C to G is called a Perfect 5th. It is a 5th because there are two letters involved, which are C and G, and it’s Perfect because, well, it’s Perfect.

Perfect 5th

C

D

E

F

G

The Octave

The interval of an octave is 8 letter steps away from itself, and is also known as a Perfect 8th. It comes from the latin word octo, meaning 8. So, from any note to itself will be an ocatave. In this example, we are demonstrating an octave from C3 to C4.

Perfect 8th

C

D

E

F

G

A

B

C

This covers all the intervals within an octave, except for one. There is an interval between the 4th and 5th that is very much not perfect. It is sharp, brash and very dissonant (not pretty). It is known as the

The Tri-Tone

The way we name it is either by Augmenting the Perfect 4th, or Diminishing the Perfect 5th.

Augmented 4th

The interval from C to F# is called a Augmented 4th. It is a 4th because there are four letters involved, which are C, D, E, and F and it’s Augmented 4th because we are raising a Perfect 4th one more half-step.

Tri-Tone

C

D

E

F#

Diminished 5th

The interval from C to Gb is called a Diminished 5th. It is a 4th because there are four letters involved, which are C, D, E, and F and it’s Augmented 4th because we are raising a Perfect 4th one more half-step. The interval from C to F# or Gb will be a either an Augmented 4th or Diminished 5th. It is either a 4th or a 5th based on which note name is used. If F is the target note name then it will be called an Augmented 4th. If G is the target note name then it will be called a Diminished 5th.

Tri-Tone

C

D

E

Gb

There is another name for this interval as well, and that name is the Tri-Tone. This name is derived from the fact that this interval can be found by moving either up or down on the keyboard three whole steps, or whole tones. If I start on C and move up three whole steps I end up on F# / Gb. If I do tha same thing moving down the keyboard to the left, I will end up on the same note.

Tri-Tone

C

D

E

F#

Gb

When all the intervals are combined together in one octave, this is what we get.

All the Intervals

C

D

E

Db

Eb

F

G

A

B

F#

Gb

Ab

Bb

C

The intervals are color coded based on their quality. Strong, powerful perfect intervals are Red. Warm, rich major intervals are Amber. Cold, somber minor intervals are Blue, and dark, unsettling diminished intervals are Purple. Depending on the context however, an interval may also be considered augmented, which are represented by a bright and sharp yellow.

Steps

Here is a chart listing all of the intervals within an octave. You will notice that Half-Steps and minor 2nds are the same. This is true of Whole Steps and major 2nds as well. We will use Half steps and whole steps to measure the distances of each interval.

  • H will stand for Half Step

  • W will stand for Whole Step

Interval
Letters
Half Steps
Whole Steps
Unison
1
0H
0W
Minor 2nd (Half Step)
2
1H
1/2W
Major 2nd (Whole Step)
2
2H
1W
Minor 3rd
3
3H
1 1/2W
Major 3rd
3
4H
2W
Perfect 4th
4
5H
2 1/2W
Augmented 4th
4
6H
3W
Diminished 5th
5
6H
3W
Perfect 5th
5
7H
3 1/2W
Minor 6th
6
8H
4W
Major 6th
6
9H
4 1/2W
Minor 7th
7
10H
5W
Major 7th
7
11H
6 1/2W
Perfect 8th (Octave)
8
12H
6W

Qualities per Interval

Not all intervals use all the avaiable qualities

2nds, 3rds, 6ths, 7ths - Diminished, Minor, Major, Augmented Unisons, 4ths, 5ths, 8th - Diminished, Perfect, Augmented

…soooo…that’s it…right?

…well…not quite.

You see, there are 12 notes on the piano keyboard. If you are a little heazy about that then read this article about Notes and then come back here. If we think about intervals for a minute we will probably come to the realization that every interval could probably be repeated on every note of the keyboard. For example, the interval that is one note to the immediate next note on the keyboard is called a minor 2nd, or a half-step…but couldn’t we create the same interval starting from every note on the keyboard, rather than just C?

But, of course :-)

C Minor 2nd

C Minor 2nd

C

Db

C# Minor 2nd

D

C#

D Minor 2nd

D

Eb

All three of these intervals are the same type of interval, but not the same exact interval, as they all start on the next note of the keyboard, but they all move up one note to create the interval. You will also notice that in the first interval the second note is Db, but in the very next interval we switch the name to C#.

Reciprocals

All intervals have a reciprocal interval as well. This means that:

  • All 2nds are also 7ths

  • All 3rds are also 6ths

  • All 5ths are also 4ths

…depending on which direction you move on the keyboard, either right (up in pitch), or left (down in pitch).

Here are a few examples:

D

C

D

In this first example the starting, or origin, note is C, and the ending, or target note, is D. If we move up the keyboard in pitch to the right the nthe interval that is created between C3 and D3 is a Major 2nd.

C

D

But if we move down the keyboard to the left to the first D, we end up creating the interval of a Minor 7th.

D

C

No matter which direction we go the ending note is still D, but the interval changes from a smaller interval to a larger interval. The quality will alos be reversed much of the time. In the previous example the interval went from major to minor. This will happen with 3rds and 6ths as well.

E

C

E

So…all good…everything is done…nothing more to discuss…on we go…toooo…

WAIT!!!!!

There is…ummmm…actually one more thing that we should probabaly talk about…

Consance to Dissonance

When we listen to intervals we hear them as being somewhere on a spectrum from completely consonant (sounds really nice) to completely dissonant (sounds completely awful). And it turns that we can kind of understand why this is the case…the way do this is by examining the relationship between each frequency in an interval using the concept of a ratio.

Check out this graphic of two wavy lines:

Now, you may be looking this graph and you might be thining “Da heck? I only see one wavy line…what’s going on?“…and you would be both right and wrong…you see, there is actually two sine waves (the wavy lines) being drawn in the graph, but the ratio between them is 1:1, effectively meaning that they are the exact same thing they are layered on top of each other.

Let’s try a different set of sine waves, shall we?

I hope the difference between them is a bit more clear in this example. The ratio between these two sine waves is 1:2. What this means is that the first wave starts at a position of rest, which is the middle red line, then it moves all the way up, then all the way down past the middle red line, then back to the middle red line to start the process all over again. In audio we call this journy a cycle, or period, which essentially mean the same thing.

If we look at the second wave, we will notice that in the same time that the first wave completes one cycle, the second wave actually completes two cycles. They actually look like they meet right in the middle, and they kind of do, except that each wave is moving in the opposite direction, and that is not what we are looking for. This is what is known as being completely out of phase with each other.

What we are looking for here when we describe the ratio between the two waves is when do they both meet together at 0 again and moving in the same direction. In this particular example, they both end up doing that after one and two cycles, respectively. This is why the ratio between them is 1:2, or 2:1…doesn’t really matter which number is first. I generally put the lower number, as we generally think of frequency in this way, from lowest to highest. So long as you understand what each number means and what it represents then it’s up to you how you want to think of it.

Intervals Tool

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