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24. 7b5 and diminished 7th chords

Hi, I'm woochia, and welcome to music theory is 5 minutes. Today I would like to talk about some very versatile types of chords. They bring a lot of tension, a lot of colour, and they can play several roles at the same time. Let's talk about diminished chords.

BEATS AND BOBS

Diminished chord are often considered as dark sounding, because they are rather dissonant. 
*audio examples*
And this dissonance means tension, which means that they need to be resolved in a way or another. The good thing is that these chords are like actors that can play different roles, so they can be resolved in a lot of different ways. And this versatility makes them excellent tools to do modulations, to go from a tonality to another.

We already saw different ways of making modulations in other episodes.
And one main technique was to utilise the tension of a authentic cadence to lead the progression toward a particular chord, that would then become a new tonality. 

An authentic cadence is a progression from a degree V to a degree I, that means that if I wanted to go to the tonality of Em for example, I could place a B7 chord just before a Em chord to facilitate the transition. Because if E is my degree I, then B is my degree V.
*audio example*

Here the B7 creates a tension that is then resolved by the Em.

Then we've seen in yet other episodes that you could alter this 7 chord in several ways. But one alteration we didn't see is the chord 7b5.
*audio example*

It is made of a root note, a major 3rd, a diminished 5th and a minor 7th. So it's like a dominant 7th chord, but its 5th is lowered by a semi-tone. It's diminished. So when you're using a dominant 7th chord on a Vth degree, you have the option to use a 7b5 chord instead.

For our cadence in Em for example, it would sound like this.
For an example of a major tonality, in G major, it would sound like this.

Now let's take a closer look at this 7b5 as it's getting interesting.
Look at the intervals separating each note, I'll add the root note an octave above, so we see better what's happening.
You see the repeating pattern? 2tone, 1tone, 2tone, 1tone?
If we make an inversion with this C7b5 so we have the Gb at the bass, this is still technically a C7b5, but it is also a Gb7b5: if Gb is the root note, Bb is a major 3rd, C is the diminished 5th (which should be called Dbb here, really, but it's the same note), and E is the minor 7th (again it should be called Fb here, but it's the same note)
So whenever you play 7b5 chord, it can be considered as 2 different chords, which are tritone apart. Which makes it a great pivot point. 
For example, for our cadence in Em, the B7 was transformed into a B7b5. And that would work also to go to the E Major even. but this B7b5 can also be a F7b5, to go to a Bb minor or a Bb major.
*audio example*

Thing is neither Bb major nor Bb minor are in the tonality of Em, nor E major. That's actually a pretty long jump on the circle of 5th. So generally when we do that it's to stay in the new tonality. So a 7b5 chord is a better pivot point for a modulation than for a borrowing.

Now if you like that kind of pivot point, you'll love the diminished 7th chord.
It's made of a root note, a minor 3rd, a diminished 5th and a diminished 7th.
So on a C chord, that'd be a C, a Eb, a Gb and a Bbb (which is the same note than A). 

In this chord, every note is separated by an interval of 1,5 tone. 
Which means you can consider any note as the root, it will always be a diminished 7th. So when you introduce a diminished 7th chord in you progression, you can consider it as 4 different chords, which gives a lot of ways to resolve it.

And that's the best part, there are a lot a ways to introduce and to resolve a diminished 7th chord.

The diminished 7th chord can be found on the VIIth scale degree. It appears naturally in a harmonic minor scale, but it can also be used in a major tonality, as a borrowing. And this resolves well on a first degree.
So in C major or C minor, that would make a Bo7 chord that resolves well on either a C major or C minor.

Note that if you add a G to this Bo7 chord, it becomes a G7b9, which works great on a dominant chord. Which maybe explains better why it resolves well on a C, G being the dominant of C.

In a minor tonality, you can also use it on a IInd to resolve on a I.
In C minor that'd be a Do7 resolving to a C minor.

A diminished 7th chord can also be used on either a raised IInd degree, to resolve on a degree I.
Or on a raised VIth degree, to resolve on a degree V.
In C major, that'd be a D#o7 resolving to a C major and a A#o7 resolving to a G major.
To make it easier to remember, a D#o7 has the same notes than a Co7, so it's like a o7 on the degree I resolving to a degree I.
And the A#o7 has the same notes that a Go7, so it's like a diminished 7 on the degree V resolving to a degree V.

Note that this is generally not used to do modulations, it is generally used in the boundaries of one key, but it is a good way to introduce a diminished 7th chord.
But as always, there no rules set in stone in music, so you can still try it, the best judges would you own ears. 

To sum it up in a simple way, a diminished 7th chord can be resolved on a chord a semi-tone above, either major or minor, or on a chord sharing the same root note, either major or minor.

And to introduce a diminished 7th chord, you can place it on the VIIth degree of your tonality, or the IInd degree if you in minor. These are the best options I think.
But you can also use it on a raised IInd and raised VIth degree.

So you have have a lot of options to introduce a diminished 7th chord, which can be considered as 4 different chords, each of which have several ways to be resolved.

Now to finish this video I'd like to make a little experiment. 
Instead of using this technic for a modulation in the middle of a song, I'd like to use it to raum from chord to chord, using diminished 7th chords for each transition.

Let's focus on a Co7 chord. It is made of the notes C, Eb, Gb and A. So it can be considered as a Co7, a Ebo7, a Gbo7 or a Ao7.
For what we've seen before, each of these chords can be resolves a semi-tone above, so that's C#, E, G and A#. Each of which can be either major or minor.
And they can also resolve to a chord sharing the same root note, so that's C, Eb, Gb and A. Each or which can also be either major or minor. 
That gives a whooping 16 options to resolve 1 chord.

So to test that, I've created clips in ableton with every options, then I've set that up so they play in a random order.
To make it sound more like a proper track, I've sent the midi from that track to another track with and apreggiator, so on top of each chord played, we can have a lead using the same notes.
And then I added some drum patterns for the rhythm.

Right of the bat, we can forsee that the most repeated chord will be Co7, as it's in every clip. So it should make it sound like the tonal center as everything will be moving around that, but it's a non-stable tonal center as it's a diminished chord. 
That should make the thing sound a bit weird, a bit mysterious or haunted. Well it should be interesting.
Let's have a listen.

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