The Harmony Theory thread

by pianohama Sun Jun 01, 2008 6:19 pm

Note: This is not written by me, I found it somewhere Smile

First Lesson: The dominant seventh chord and leading tones in a major scale

This is just an introductory lesson because for the next lessons you have to understand why a dominant seventh chord is so dissonant and tension-filled...

A dominant chord is always the chord which is built on the fifth degree(the dominant) of a scale. To get the dominant seventh chord we just have to add a minor seventh to this dominant triad(1-3-5-7)...
And exactly this added seventh destabilizes the chord so that it needs to resolve in a consonant and stable chord like the tonic. But why is this chord now so instable and dissonant?

It is because this chord contains both leadings tones of the major scale. Leading tones are the tones which define the tension of a chord. In a major scale there exist two leading tones, the harmonic leading tone and the melodic leading tone. The fourth degree of the scale is always the harmonic leading tone and the seventh degree of a scale is always the melodic leading tone...

The special thing about these two leading tones is that they build a diminished(b5) fifth or an augmented fourth(#4) together(that's enharmonically the same). This special interval is called a tritone and it is one of the most dissonant intervals that exist. In the middle ages it was forbidden to play this interval because people belived it would be the interval of satan().
So now we see why the dominant seventh chord is so instable: It contains the tritone which makes this chord so tension-filled...

This dissonant interval needs to be resolved in a consonance. Usually you resolve the dominant seventh chord to the tonic!
To do this you have to resolve the tritone chromatically and with contramotion. That means that you resolve it to a major third: The harmonic leading tone leads a semitone downwards so that it becomes the 3rd of the tonic and the melodic leading tone leads a semitone upwards so that it becomes the root of the tonic!

Example in C-Major:
1. The dominant seventh chord is G7(G-B-D-F)...
2. The harmonic leading tone is F(fourth degree) and the melodic leading tone is B(seventh degree)
3. The dominant seventh chords contains both tones which build a tritone together(interval from B to F = b5)
4. To resolve this instable dominant seventh chord to the tonic you have to resolve the tritone chromatically and in contramotion to a major third:
B -> C(root of the tonic), F -> E(major third of the tonic)
5. Now you have resolved the dissonant tritone to a consonant third...

A small excursus
------------------------------------------------------------------------
- Chords that contain no leading tone like the tonic(without seveth) or the tonic parallel are very stable and consonant. Their desire of exercise is very low...
- Chords that contain just the melodic leading tone(seventh degree) like the dominant parallel are a bit more instable but the melodic leading tone is not enough to destabilize a chord...especially in jazz the tonic with the major seventh(melodic leading tone) is considered to be a stable function...

==> Functions with no leading tone or just the melodic leading tone are called tonic-functions because they are very stable and consonant
These functions are: Imaj7, III-7 and VI-7

- Chords which only conatin the harmonic leading tone like the subdominant or the subdominant parallel are much more instable than the tonic-functions because the harmonic leading tone makes a chord more tension-filled.

==> Functions which just contain the harmonic leading tone are called subdominant-functions which are more unstable and want to be resolved in a stable function
These functions are: II-7, IVmaj7 and V7sus4

- Chords with both leading tones like the dominant and the half diminished seventh degree are the most instable functions.

==>They are called dominant-functions. These functions are: V7 and VII-7(b5)
--------------------------------------------------------------------------

So I hope you understood what I wrote...
It is important to understand why the dominant seventh chord is so instable because otherwise you wouldn't understand why a seconary dominant or a tritone subsitution can have a similiar function...
Later this day or tomorrow I will explain secondary dominants...I hope some people like my thread

Lesson #2: Secondary dominants and the Harmonic-Minor scale

We already know what a dominant seventh chord is and why it is so tension-filled:
- The dom7 chord is a perfect fifth above the tonic
- It contains two leading tones which build a tritone together(destabilization and tension)
- The dissonant tritone needs to be resolved to the tonic(a fifth downwards)
- The leading tones lead a semitone up- or downards to become the root and the third of the tonic!

If you don't know what harmonic-minor is scroll down and read it first.I recognized too late that you need to know about it to understand secondary dominants...^^

The basis of secondary dominants is that you can not only build a dominant to the tonic but also you can create a dominant seventh chord for every other function of a scale. You just have to keep in mind what's the special thing about the dominant seventh chord:
It's a perfect fifth above the chord it wants to resolve to and it consists of a major third and a minor seventh which build a tritone together...

So if you for example would like to create the secondary dominant of A-(in the C-Major scale) you would use "e" as the root of this dominant(a to e = 5).
The major third would be "g#", the fifth would be "b" and the minor seventh would be "d"...
So the secondary dominant of A- is E7(e-g#-b-d). It is a fifth above A- and the major third(g#) and the minor seventh(d) build a tritone together which wants to be resolved to a consonance(here the minor third of A-)...

The important thing about these secondary dominant is that you make a connection to another key. In our example we temporarily regarded A- as our tonic and E7 as the dominant seventh chord of this key. So we swithed from C-Major to A-Harmonic-Minor(I explain what harmonic-minor is at the end of the lesson)...You can regard it as a "fake-modulation" but it's too short so that our ear doesn't recognize it...
You can also see that because the g# in E7 is a non-diatonic tone of C-Major. The g# doesn't exist in C-Major but in A-Harmonic-Minor(where it is the leading tone)...
So the A- chord has two functions: On the one side it is the sixth degree in C-Major and on the other side it is also the chord to which the E7 wants to resolve...

The "g#" is the leading tone of A-Harmonic-Minor(the 7th degree) and so it leads a semitone upwards to "a" where it is the root of the tonic...
After you resolved the E7 chord to A- you can continue playing inthe C-Major scale because A- is a diatonic funtion of this scale...

Note:When you build a secondary dominant of a function you just build a temporarily connection to another key and then you can continue in your original key...
When you build the secondary dominant to a minor-chord you switch to a harmonic-minor-key and when you build the secondary dominant of a major-chord you switch to a major-key. That's because the tonic of a major scale is always a major-chord!

To show that a certain function is a secondary dominant we use a special symbol. We write V7 followed by the function the secondary dominant resolves to. In our example we would write: V7/VI
That means that that this function is the dominant seventh chord of the sixth degree(A-) of our scale...So V7/VI means the chord E7...

Some examples:
The key is C-Major:

V7/II: That's the dominant seventh chord of the second(D-) degree: A7(a-c#-e-g)...
So we temporarily regard the second degree(D-) as our tonic and A7 is the dominant seventh chord of this tonic. A7 resolves to D- whereby the non-diatonic tone c# is the leading tone..."c#" leads to the tonic "d"...
So we made a short connection to D-Harmonic-Minor...
Examlpe chord progression: C-A7-D(-)-F-C...

V7/IV: The dominant seventh chord of the subdominant(F): C7(c-e-g-Bb)...
C7 resolves to F whereby e and Bb are the leading tones...
So we made a short connection to the F-Major scale...

V7/V: This is the secondary dominant of the dominant. The dominant of a dominant is called a double dominant!
So the double dominant of C-Major would be D7(d-f#-a-c)...
f# and c are the leading tones...
Example chord progression: C-F-D7-G-C...

The Harmonic Minor Scale
I'm sure you asked yourself why we switch to a harmonic-minor-key instead of a normal minor key when we talk about secondary dominants...
Therefore we have to regard the intervals of normals minor-key at first:
1-2-b3-4-5-b6-b7....

For example A-Minor would be: a(1)-B(2)-c(b3)-d(4)-e(5)-f(b6)-g(b7)...
The dominant seventh chord in this key would be: E-7(e-g-b-d)...
This chord is not as tension-filled and dissonant as the dominant seventh chord in a major-scale...but why?

It's because this chord doesn't contain any leading tones and so there is no tritone which destabilizes this chord. The melodic leading tone(seventh degree) always leads a semitone upwards to the root of the tonic.
But in a minor scale we play a b7 instead of a 7 and so there is no leading tone because from b7 to 1 it's a whole step instead of a half step...

To get the leading tone in a minor scale we have to alter the seventh degree to a major seventh. Now we have the leading tone and the dominant seventh chord contains a tritone...
The minor scale with altered seventh is called harmonic minor:
1-2-b3-4-5-b6-7
The dominant seventh chord of A-Harmonic-Minor would be: E7(e-g#-b-d)...

So a harmonic minor scale is a normal minor scale with an altered seventh to get the leading tone...without this leading tone the dominant seventh chord wouldn't have enough tension!

Note: In a harmonic minor scale the 6th degree is the harmonic leading tone and the altered 7th degree is the melodic leading tone. The dominant seventh chord just contains the melodic leading tone but that's unimportant because it contains a tritone and leads to the tonic...

So, that's all about secondary dominants. I hope I wrote it understandable...
Would be happy about some comments...

EDIT: The "-" after a chord means it's a minor chord: A- = A-minor chord

by VictorCS Sun Jun 01, 2008 6:40 pm

I play a G7(G-B-D-F), then I play a "B -> C(root of the tonic),
F -> E(major third of the tonic)", and that becomes a C-E?

So I shall play a G7, then a C-E to do it correct?

I barely started experimenting with scales, espesially on the guitar,
but know I need to learn about chords to ^_^

This is just to much, cant I just buy a memorychip and insert it a port in my brain Razz

by Mitsuda420 Thu Jun 25, 2009 4:14 pm

Wow man thanx for posting this.. it helped me and will help alot others!

by Admin Andrew Fri Jun 26, 2009 6:47 am

very nice ^_^ He wrote it out quite well. I actually covered all this several years ago when taking harmony. The thing he doesn't address is the voice leading possibilities. I'm not so great at explaining it though. I would've been interested to hear what he had to say on voice leading Smile

Thanks for the great post!