Theory

[kantor1003]

This thread was created to provide Electric Wizard with some basic theory. I figured this would be too long to post in private messages, so I posted it here. Maybe someone else might get something out of it... and I'll be happy to take it further or answer some questions.


Lets take some scale theory:

You have 3 main scales. The normal Ionian/major scale (from C: C D E F G A B), the melodic minor scale and the harmonic minor scale.
Interesting observation: the melodic minor scale is just the same as the Ionian/major scale, only with one note different, flattened 3d, so C, D, Eb, F, G, A, B.
Another interesting observation. The harmonic minor scale is the same as the melodic minor only with the 6th flattened, so C, D, Eb, F, G, Ab, B, C.

Did I mention that you have a scale on each degree of the parent scale?

Maybe you are familiar with these scales derived from the major scale:
1. degree: ionian (major) (C, D, E, F, G, A, B)
2. degree: Dorian (D, E, F, G, A, B, C)
3. degree: Phrygian (E, F, G, A, B, C, D)
4. degree: Lydian (you catch the drift)
5. degree: Mixolydian
6. degree: Aeolian (your normal minor scale)
7. degree: Locrian

You might ask what you can do with all this.
Now, we have to understand the structure of each scale.

Ionian is our starting point, and I hope you already know how that scale is constructed, cause you'll really need to know how the interval relationships in that scale work to understand the rest. Here is the formula:
1, 2, 3 (this is a major 3d), 4, 5, 6, maj7 (this is a raised 7 (major 7th), the note B)

First I take the normal minor scale, aeolian, which is found on the 6th degree. I think that will make it easier to relate to the rest.
1, 2, b3, 4, 5, b6, b7
this is your normal minor scale, as I hope you are familiar with.. it has a b3, hence it being a MINOR scale. It also has a b6 and a b7. If you can remember this formula and the major formula, the rest will go easier.

So, lets take Dorian found on the second degree:
1, 2, b3, 4, 5, 6, b7
The first thing you'll notice is that it's a MINOR scale because of the b3 (by b I mean a lowered, or flattened third). Another interesting observation is that it has a natural 6th unlike the normal minor scale which has a b6. And lastly it has a b7. Basically, the difference between this and the normal minor scale, is the natural 6th.

Phrygian (third degree of major):
1, b2, b3, 4, 5, b6, b7
This is also, as you see, a minor scale (because of the lowered third). This has a b6 as well (just like the regular minor scale. It also has the b7 as a normal minor scale. So what is the difference between this and a normal minor scale? Thats right, the 2. degree. You have a b2 (or b9 as people call it).
So let's make an example.
Here is C minor (aeolian) C, D, Eb, F, G, Ab, Bb
What do you have to do to make this a phrygian scale?
Thats right, lower the 2th degree. Now, let me do that:
C, Db, Eb, F, G, Ab, Bb. Now you have a phrygian.

Lydian (4th degree of major):
1,2,3,#4,5,6,maj7
The first thing you'll notice is that this is a major scale because of the third.
So, whats the difference between this and the normal major scale? thats right, the sharp fourth (or sharp 11th as people call it)
So instead of your C major, or ionian scale, C, D, E, F, G, A, B
you would have; C, D, E, F#, G, A, B

Mixolydian (5th degree of major):
1,2,3,4,5,6,b7
Difference between this and a normal major is the b7. So, Bb, instead of B

aeolian (normal minor) 6th degree of major:
we have already taken this one

locrian (7th degree of major):
1, b2, b3, 4, b5, b6, b7
out of all the scales derived from the major scale this is the strange one this is the only scale where the 5th tone is altered. In this case, it is lowered (b5). The first thing you'll notice is that it is a minor scale because of the b3. Next, we also have the b2, just like phrygian if you remember. Then the b5. So basically, if you play a phrygian and lower the 5th degree, you'll have a locrian.

You can do this with the melodic and harmonic minor scale as well, but forget that for now. You'll have more than enough to remember.

Now where does chords come in?
Chords are constructed by taking a scale and play the 1th 3d and 5th degree at the same time. It could also be arpeggiated of course.
This could be done all the way up to 13th. But for the purposes of this "lesson" I'll only go up to 7.. that will be more than enough I think.
So now, take 1, 3, 5, 7 in the C ionian scale:

1 2 3 4 5 6 maj7
C, d, E, f, G, a, B

the first three tones is C, E and G. This is your basic major chord in all its simplistic beauty. You have 1, 3, and 5. Now, lets add the 7th. Now, we have 1, 3, 5, maj7, or C, E, G, B.
This chord is called Cmaj7. It is called this way because a C chord refers to C major, and the maj7 indicate that the 7th is raised. Now, try to voice that on guitar

Now, let's take 1,3,5,7 in dorian:
1, b3, 5, b7
C, Eb, G, Bb
This is a Cm7 chord.
If you continue to do this with all chords you'll get.

C ionian/major: Cmaj7
D dorian: Dm7
E phrygian: Em7
F lydian: Fmaj7
G mixolydian: G7
A aeolian/minor: Am7
B locrian: Bm7/b5

Lesson:
Tell me what scales derived from the major scale I can use over a:
(there is multiple answers to several of these. Try to find all the possibilities)

Cmaj7 chord

Cm7 chord

Cm7b5 chord

C7 chord

Optional:
Cmaj7#11
Cm7b9b13
Cm7 13

 

[Logos]

Thank you soooooooooo much for doing this!

 

[Dormouse]

I have no idea what this is about, but I'm rather charmed by the lovely names of the scales and degrees.

 

[kantor1003]

Thank you soooooooooo much for doing this!

My pleasure. Just hoping you get something out of it

I have no idea what this is about, but I'm rather charmed by the lovely names of the scales and degrees.

Yeah, maybe I should start talking about this when checking out girls... on a second thought, I think I'd better not:P

 

[Hawkeye]

I have no idea what this is about, but I'm rather charmed by the lovely names of the scales and degrees.

hehe

It's basically the basis of Western Music Theory.

I was told everything reverts back to the Major Scale even though the Minor Scale was discovered first.




Anyway... as far as we are concerned there are 12 different notes which are:

...G G# A A# B C C# D D# E F F# G G# A A# B...

These notes repeat forever and ever in both directions

When applying these notes to a piano for example we find that the sharp [#] notes are the black keys (or blue in this case).

The reason the notes start at C on this picture is because Pianos are visually in the Key of C (all the white notes are in the key of C)



What is a Key?

A Key is a collection of notes that form a scale related to a particular note.

The Major Scale contains 7 notes and there are 12 keys of the Major Scale (one for each note).


For example:

The Key of C contains the notes:

C D E F G A B C - the high C is also included as the Octave.



The Key of E contains the notes:

E F# G# A B C# D# E



The Major Scale when played ascending from the first note will produce the familiar Do Re Me Fa So La Ti Do
-------------------------------------------------------------------

To construct a Major Scale you use the following pattern:

Tone Tone Semitone Tone Tone Tone Semitone

or

T T S T T T S for short

A Tone is a transition with a value of 2 notes (C to D for example C - C# - D )

whilst a Semitone is a transition with a value of 1 note (D# to E)

-----------------------------------------------------------

So lets construct the Key of G

• start with G
• The next note is a Tone higher - A
• The next note is also a Tone higher - B
• The next note is a semitone higher- C
• The next note is a Tone higher - D
• The next note is also a Tone higher - E
• The next note is also a Tone higher - F#
  
• The final note is a semitone higher- G (the octave)

So the notes in the Key of G or G Major Scale are:

G A B C D E F#


What are the notes in the Key of A and the Key of B?

 

[kantor1003]

Thanks for the input Hawkeye
Anything else we should cover?

 

[shadowdrums4]

Just throwing out there that because of enharmonic notes there are actually 15 keys not 12. There are 12 unique sounding major scales though. Also we are just now learning modes in my class. I was always taught that they were whole and half steps not tones and semi-tones but from the looks of it, they are the same thing which means I learned something.

I love music theory. How about the basis of maj/min/aug/dim chords? My teacher has made reference to half diminished chords but I don't know what they are yet. Anyone care to explain?

So a major chord is made up of a 1st, 3rd and 5th tone of an Ionian scale but on any starting note. Kantor used C E G as his example of a basic triad. Triads are arpeggios played at once. The intervals that make them up are a root (starting) note a major 3rd to the middle note and a major 5th in between the root and top note. In an Ionian scale, the major chords are on the I IV and V chords.

These chords also make basic progressions although they usually have to be inverted for a smooth sound. Inversions are putting a different note in the base (bottom) of the chord. If the third is in the base, it's a first inversion triad, for example E G C is a first inversion triad because your basic major triad is C E G and the C has been moved up an octave. If the 5th is in the base, for example G C E (which looks more like the 5th has been moved down an octave) then it is a second inversion triad.

Oh and the formal definition of triad is a 3 toned chord so a Cmaj7 chord is not a triad. In most progressions, the V7 (chord on the 5th note of an Ionian scale that contains the 7th) is used instead of the V (chord on the 5th note of an Ionian scale) Interesting: In a V7 the 3rd note in the chord is often ommitted. For example G is the 5th note of the C Ionian scale and it's chord is G B D, which makes G B D the V chord for the C Ionian scale. If a V7 replaced it in a chord progression, the chord would either be G B D F or simply G B F because the D can be ommitted.

Minor triads are the major triads with a b3 as kantor described. When making the chord progressions in minor scales the chords become i (minor first or one) iv (minor four) and V (major 5) This is because the harmonic minor scale is used. (I don't know why this is) Every minor scale has a relative major key to it. Key signatures have not been discussed and if they should be I'm sorry but for the sake of finishing this sometime tonight I will assume you know them. Because of the key sig, you don't have to draw sharps and flats and chords can naturally fall into place when built on certain scale degrees. Since the key sig only covers the natural minor scale (the same as the Ionian 6 notes back as you know or up a minor third) however since chords are made in the harmonic minor (#7) then you have to add an accidental (none key tone) to the 7th note (or the 3rd of the V chord) and this makes the V chord major in chord progressions.

Augmented chords are major triads with a #5 (raised 5th) and diminished are MINOR triads with a b5. (or a major with a b3 and b5). So a C E G# would be the C augmented chord and C Eb Gb would be the C diminished chord. (C Eb G being the minor chord)

Now here is where I ask again what a half diminished chord is. My assumption was that it was C E Gb but I doubt that is right. If it's wrong what would that chord be called?

In an Ionian scale, if you were to put chords on every note, the order would be I (major 1) ii (Minor 2) iii (Minor 3) IV (Major 4) V (Major 5) vi (minor 6th) viio (diminished 7th) (side note: In chords the I IV and V are major not perfect, perfect only occurs in cadences and intervals) (other side note, symbol for augmented is a + at the end of the chord I+ for example)
What about the names of the scale degrees (oh and is this exclusive to Ionian scales?)
1. tonic (starting note of scale where you get the key name)
2. Supertonic (second note)
3.mediant (third note)
4.subdominant (4th)
5. dominant(5th you get it)
6submediant
7 leading tone
Important note: These were named by their distance away from the tonic. The mediant and submediant for example, you go up 2 scale degrees for the mediant and down for the submediant, same with dominant (up) and subdominant (down) which were not named because subdominant comes before dominant.

I'll stop there for now. (Please answer my questions about half diminished chords and exclusiveness of the names to Ionic scales)

No idea if this was actually relevant to teaching electric but it is theory nonetheless. Don't get me started on time signatures. lol

 

[Hawkeye]

lol, I ignored enharmonics to avoid confusion. As for the whole and half step thing. Yeah they are exactly the same only Americani(z)ed. ^^

The Half Diminished chord comes from the tonal spacings of the notes when using 7th chords. It is also known as a Minor Seventh Flat 5 or m7♭5.

It's to do with what diminishing does to a chord. For example, if you have a simple triad C E G or (C Major) and you wanted to make it a diminished chord you flatten the 3rd and 5th (C E♭ G♭). Depending on how you look at this it could be seen as a minor chord whose progressive notes after the root and 3rd are flattened.

So if we had a seventh chord using the formula 1, ♭3, ♭5, ♭7 would it be a diminished chord?

Well, the formula for the minor 7th is 1, ♭3, 5, ♭7 and the rule is to flatten every additional note after the 3rd. This becomes 1, ♭3, ♭5, ♭♭7. The 7th is double flattened (which could also be called the 6th).

So a true diminished chord has the formula 1, ♭3, ♭5, ♭♭7 and so we call the chord 1, ♭3, ♭5, ♭7 a half diminished chord or as I prefer to call it - a minor seventh flat 5.


I've added the other varients of seventh chords below.


1, 3, 5, 7 - Major 7th

1, ♭3, 5, ♭7 - Minor 7th

1, 3, 5, ♭7 - Dominant 7th

1, ♭3, 5, 7 - Minor/Major 7th

1, ♭3, ♭5, ♭7 - Minor 7th (b5) or Half Diminished

1, ♭3, ♭5, ♭♭7 - Diminished 7th

 

[shadowdrums4]

I see but then how can you tell if it's half diminished or fully diminished if it's a 3 toned chord?

 

[Hawkeye]

I see but then how can you tell if it's half diminished or fully diminished if it's a 3 toned chord?

You can't. The half or full bit needs the seventh.

 

[kantor1003]

Minor triads are the major triads with a b3 as kantor described. When making the chord progressions in minor scales the chords become i (minor first or one) iv (minor four) and V (major 5) This is because the harmonic minor scale is used. (I don't know why this is)

The reason why harmonic minor is used has everything to do with resolution.
If you take the good old D T cadence for example:

G B D
C E G

The third B wants to go up a semitone to C. That change is really what makes the whole cadence work and getting the listener to feel a sense of resolution when the D go to T.

Let's take the same cadence in minor, using aeolian minor, not harmonic.

G Bb D
C Eb G

First you'll notice that the dominant now would be minor.. secondly you'll notice that the third (Bb) now is a whole tone away from C.. the whole dominant function is lost.
The sense of resolution created in major between the third wanting to go up a semi-tone to the T is gone.
So what they did, to recreate this in minor, was to raise the third from Bb to B.

So now we would have;

G B D
C Eb G

this is derived from the harmonic minor scale... or, the harmonic minor is derived from this.