The ‘harmonic’ and ‘melodic’ minor scales.

Before we tackle these, a little background information would help understanding them and where they come from.

From the 17th to 19th centuries, music was very structured and bound by some pretty strict rules, guidelines and methods. One of these was the use of something called a 'cadence'. Think of a cadence as a punctuation mark.
There are four types of cadence:
'perfect'
'imperfect'
'interrupted'
and 'plagal'
I'll not go into how why and where these are used as it is a large topic in it's own right [and only useful to folks formally studying music or writing in Baroque, Classical or Romantic style]. For this topic, we are interested in the 'perfect' cadence [a chord progression of chord V to I]. Think of a perfect cadence as a 'full stop' at the end of a section of music [also at the end of the entire piece].
Not only does a chord change from V to I produce a perfect cadence, but V must be major [better still, a dominant 7 chord].
If you cast you mind back to the chords generated by a major scale you'd notice that chord V7 is a dominant 7. So in the key of G major a perfect cadence would be D7 to G.
So let's look at this with respect to a minor key.
The chords of the key of Em are Em, F#mb5, G, Am, Bm, C, D.
So we have a problem because chord V is minor [in this case Bm].
V to I in the key of Em is Bm to Em and it just doesn't sound very 'final'.
Not good for something that wants to behave like a 'full stop' - lol

The solution is to modify chord V from being minor to major [or from a minor 7 to a dominant 7] when executing a perfect cadence in a minor key.
So in the key of Em, the perfect cadence chord progression of Bm to Em becomes B to Em [or better still B7 to Em]. Yummie, this sounds nice and final like a good musical full-stop should.
Now we have a new problem, the scale don't fit with the modified V chord.

The scale of Em is: E, F#, G, A, B, C, D
The modified chord V7 is now B7 which is: B, D#, F#, A - so we can see that the D from the scale and the D# from the chord clash.
Clearly this will sound - in technical terms - totally pants!!!
Ouch!!

The solution is to modify the scale to fit the modified chord [but only during the moment of the cadence - not for the whole piece of music].

This of course gives birth to a new scale that contains E, F#, G, A, B, C, D#…
The spelling of this new scale is:
Tonic
major 2nd
minor 3rd
perfect 4th
perfect 5th
minor 6th
major 7th <- here is the modified note: The major 3rd of chord V7, also the major 7th of the modified minor scale.

This modified scale is called the 'harmonic minor' scale
it sounds very cool too

This is the scale that you'll often hear Malmsteen tearing up and down as fast as he can over chord V of a minor key.

So, back to the 1700's in the key of Em at a perfect cadence.
If you work out the intervals, not with respect to the tonic, but between each note, you'll notice that the interval between the 6th and 7th degrees of the harmonic minor scale is pretty large.
It is an 'augmented major 2nd' - C to D# [not a minor 3rd – C to Eb]
You can also call this interval a "sharpened major 2nd"
and this just happens to 'sound' just like a minor 3rd. This is all well and good for us musicians but there was a problem, choirs hated singing this interval especially with melodies in the ascending direction. It really is pretty tricky to visualise and then sing this interval.
Also, this large interval is particularly 'smooth' when it comes to melody and 'ornamentation' [things like trills].

The solution was to reduce the size of this interval by raising the minor 6th of the scale to a major 6th [during the perfect cadence over chord V7]

Now we have yet another newly modified scale spelt:
Tonic
major 2nd
minor 3rd
perfect 4th
perfect 5th
major 6th <- our new modified note
major 7th
this scale is called the 'melodic minor ascending' scale, and sounds very cool too.

So using E as the tonic we get: E, F#, G, A, B, C#, D# [used over the chord of B7 [V7] in the key of Em]

However, in the descending direction, the 'melodic minor descending' scale is the same as the natural [relative] minor.

For these scales and the perfect cadence, this really is the tip of a huge and incredibly useful / interesting iceberg.

For now, knowing that these modified scales exist and why is good enough, if for no other reason than to de-mystify the 'what' and the 'why'.
In the early stages of playing and learning the neck, concentrate more on the regular major and minor scales.
As you become a more advanced player I'm sure that you'll begin to get into using these scales in anger.

--
--
Frank

and then

here's a piece about minor scales...

Just like the major scale, the minor scale is composed of 7 notes and therefore 7 intervals. It is 'spelt':
Tonic
major 2nd [1 tone/2 frets]
minor 3rd [1 1/2 tones/3 frets]
perfect 4th [2 1/2 tones/5 frets]
perfect 5th [3 1/2 tones/7frets]
minor 6th [4 tones/8 frets]
minor 7th [5 tones/10 frets]

So let's consider this with a real note for a tonic and calculate the notes for a minor scale.
Tonic = E, so here goes:
The major 2nd is two frets above, so is it F# or Gb?
All of the notes have to appear once and in sequence [just like when we looked at the major scale].
The letter F comes after E [not G] so the 2nd has to be 'F' something.
As it is a major 2nd [2 frets] it will be F#.

The 3rd has to be G something. As it is a minor 3rd [3 frets above the tonic] it has to be G natural.
By applying this method as you did with the major scale but using the template of intervals for the minor scale, you should end up with the scale of Em = E, F#, G, A, B, C, D

So, you did this for the major scales so not try it with the minor scale.
Work out the notes of the follows scales:
Am
C#m
Dm
Bbm
Ebm
F#m

Hmmmmm something interesting stands out here.
Notice that the note values look a little familiar?
For example, the notes that create the scale of Em are the same as those that created the scale of G major [G, A, B, C, D, E, F#] but starting from the 6th degree of the scale.
For now, treat this as a very useful coincidence.

A rule of thumb:- if you go to the 6th degree of a major scale, you'll find the tonic of its 'relative minor' scale.
It's called the 'relative' minor because the two scales are related [sharing the same note values]. Consider the major key as the 'centre key' which is the 'birthing place' for the minor.
It simply provides the pool of notes, and nothing more.
And in reverse, you can look at the 3rd degree of a minor scale and find the relative major.

Try a few.
The key of C = C, D, E, F, G, A, B therefore the relative minor key is
The key of E = E, F#, G#, A, B, C#, D#, therefore the relative minor key is
The key of F = F, G, A, Bb, C, D, E, therefore the relative minor key is [saddest of all keys… lol]

and in reverse
The key of Cm = C, D, Eb, F, G, Ab, Bb therefore the relative major key is
The key of Bm = B, C#, D, E, F#, G, A therefore the relative major key is

Note: The relative minor is also known as the 'natural minor'.

So why do the major and minor scales sound different if they are related and made of the same notes?????
This is because the intervals between the notes are completely different thereby giving a totally different tonal relationship with the tonic. This is much easier to see if you look at a major and minor scale side by side with the same tonic.

the key of Em = E, F#, G, A, B, C, D

but the key of E = E, F#, G#, A, B, C#, D#
Very different as you can see.

What about the chords??????
So the chords that you calculated in the key of G major also apply to Em but their position has now changed in exactly the same way as the notes of the minor scale did.

The G major scale produced: I = G, II = Am, III = Bm, IV = C, V = D, VI = Em, VII = F#mb5
So the Em scale produces: I = Em, II = F#mb5, III = G, IV = Am, V = Bm, VI = C, VII = D

This also therefore applies to the 7th chords….. in the key of G, chord V7 is D7. D7 is chord VII7 in the key of Em.
When we look at things like modulation techniques [changing key], you'll begin to understand how powerful this little piece of knowledge can be
very cool stuff

And the main thing to appreciate:
The notes in the key of G and Em are the same [from the same note pool], but the similarity ends there
they are completely different keys with completely different sounds

--
--
Frank

In the beginning

Now we know intervals we can find the notes in a major scale by working them out from a given 'tonic'
First a few simple rules
1 - the letters that represent each degree [each note] of the scale can only be used once
there can only be one A, one B, one C, one D, one E, one F, one G

2 - they will always occur in alphabetical order until you get to 'G' [where the following note is 'A']

3 - You will also need to know the notes of the chromatic scale so here there are. Use them for reference:
A, A#/Bb, C, C#/Db, D, D#/Eb, E, F, F#/Gb, G, G#/Ab, A, and so on
Note that A# and Bb are the some pitch [as in the same key on a piano or same string and fret number on a guitar] but they are not the same note. They are mealy two different names for the same pitch.
Also, you need to know the spelling of a major scale.
The 'spelling' is simply the list of intervals with respect to the tonic.
The major scale is spelt as shown below:
Tonic [where you start from]
Major 2nd [2 frets up]
Major 3rd [4 frets up]
Perfect 4th [5 frets up]
Perfect 5th [7 frets up]
Major 6th [9 frets up]
Major 7th 11 frets up]
Octave [12 frets up]

When the Tonic = C the notes of the scale will be C, D, E, F, G, A, B
Next you need to figure out if the notes are flat [b], natural, or sharp [#]
To do this you use the spelling of the scale, your knowledge of intervals and the list of chromatic notes.
The 2nd note is a major 2nd interval above C [1 tone or 2 frets above the tonic]
Two semi-tones above C [found by looking at the chromatic scale] is D
'C' is the starting point
one semi-tone up is 'C#/Db'
another semi-tone up is 'D'

The 3rd note is a major 3rd interval above C [2 tones or 4 frets above the tonic]
Two tones above C [found by looking at the chromatic scale] is E
'C' is the starting point
one semi-tone up is 'C#/Db'
another semi-tone up is 'D'
the next is 'D#/Eb'
and the next is E

if you follow this through to end, looking at all intervals of the major scale where C is the tonic
you will end up with C, D, E, F, G, A, B, C

Lets look at a major scale where E is the tonic - the scale of E major
When the Tonic = E the order of the notes of this scale will be E, F, G, A, B, C, D and E
but we do not yet know if there are any # or b notes. We need to work them out as we did for C major [above]

The 2nd note is F 'something' and is a major 2nd interval above the E [1 tone or 2 frets above the tonic]
'E' is the starting point
one semi-tone up is 'F'
another semi-tone up is 'F#/Gb' - which do you choose? F# or Gb?
Remember that all the notes have to be in alphabetical order and occur only once
F comes after E so you choose the F#

The 3rd note is G 'something' and is a major 3rd interval above the E [2 tones or 4 frets above the tonic]
'E' is the starting point
one semi-tone up is 'F'
another semi-tone up is 'F#/Gb' - which do you choose? F# or Gb?
The next is G
And the next is G#/Ab
We already have E, F#, and we are looking for G something and have G#/Ab to choose from
So it has to be G#
Try to work out the rest of the scale for yourself
If you get stuck that's ok. Shout and I can show you where you are going wrong and why.
It's much better that you start figuring this out yourself and me nudging you in the right direction rather than me spoon feeding you list after list of scales and you never understanding why
If you think you have the hang of it, try working out the notes in 'F major' and 'A major'
Don't worry about getting it wrong
It's all part of the learning process

--
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Frank