# 12. Major and minor scales

So are these like weight scales or is it some Scales of Justice from Worms games reference?

## 1. Topics of discussion

In this tutorial we will be taking a look at major and minor scales, what they are and how they are formed. We will also discuss what makes 2 scales relative to each other. So, let’s have some fun.

## 2. Scale formulas

A musical scale is an ordered set of pitches which are found in the same octave. If you remember, we defined an octave as the frequency interval between two notes with the same fundamental pitch of which one has double the frequency of the other.

In an octave we have a total of 12 pitches, including the notes on which the octave is based on. Depending on the direction of the scale, we obtain these 12 pitches by either raising or lowering the pitch of a note by one semitone.

A scale can be played in either an ascending or descending manner and depending on the number of pitches we select to play, can be of different types. In this tutorial we will be focusing on major and minor scales, with the added info that we will be talking only about natural minor scales in this section.

Major and minor scales have a total of 8 pitches and when playing them, you start and end on the same note (with a different pitch of course). This note is known as the root note of the scale. The root note of a scale is the note that gives us its name (e.g. C, A, E etc.) while the quality of the scale (e.g. major, minor etc.) is given to us by the semitone/tone distance between the pitches in the scale.

Since major and minor scales contain 8 pitches, this gives us a total of 7 distances between consecutive pitches. Notes are numbered from 1 to 8, usually using roman numerals and that the formular we’re about to learn contain the semitone/tone difference between two consecutive pitches, in order, starting with the difference between notes 1 and 2, then 2 and 3 and so on. And with this in mind, let’s define the formulas for major and minor scales:

• major scales follow the T-T-S-T-T-T-S formula
• natural minor scales follow the T-S-T-T-S-T-T formula

T and S are short for tone and semitone. With these formulas now learned, let’s apply them in order to create some scales. Since we already know the C major scale, let’s try and build ourselves a G major scale:

Here’s how that sounds like:

Let’s try it again, this time for the E major scale:

Here’s how that sounds like:

Now let’s try and build ourselves an A minor scale:

Here it is played back:

Next up, let’s build the E minor scale:

Here it is played back:

Finally, let’s build the C♯ minor scale:

Here it is played back:

You may notice something interesting about these scales. Especially when you group them two by two: C major with A minor, G major with E minor and E major with C♯ minor. Can’t quite put your finger on it? Let’s move on to the next section.

## 3. Relative scales

The concept of relative scales refers to a major and minor scale which consist of the same notes, albeit played in a different order. All the examples above, grouped in the way we’ve already talked about, are relative to each other. C major and A minor contain the same distinct 7 notes, played in a different order: A, B, C, D, E, F and G. G major and E minor also contain the same 7 notes: G, A, B, C, D, E and F♯. The same goes for E major and C♯ minor.

The simplest way of figuring out a scale’s relative major or minor counterpart is the following:

• for a major scale, the sixth note in the scale gives you the root note of its relative minor scale counterpart (ex: the 6th note in the C major scale is A, therefore A minor is C major’s relative minor scale counterpart)
• for a minor scale, the third note in the scale gives you the root note of its relative major scale counterpart (ex: the 3rd note in the A minor scale is C, therefore C major is A minor’s relative major scale counterpart)

## 4. Harmonic and melodic minor scales

A harmonic minor and melodic minor are both variations of the natural minor scale.

In order to obtain the harmonic variant, we need to sharpen the seventh note of the natural minor scale.

In order to obtain the melodic variant, we need to sharpen both the sixth and seventh notes of the natural minor scale.

Here is the harmonic A minor scale:

And here is what it sounds like:

Now let’s take a look at the melodic A minor scale:

And here is what it sounds like:

As you can see, whenever we play the melodic minor in a descending manner, the previously sharpened notes are restored to their original pitch. This is the way the melodic minor scale is meant to be played.

And that about covers it for this tutorial. Next up, we’ll be discussing music intervals. See you then.

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