# Harmonic Sequences



## Sonic Anomaly (May 21, 2015)

In trying to expand my harmonic horizons, I've used a few Chord sequences, but I feel like I have just scratched the surface of what could be done with them. 
What are some sequences that you might suggest/find useful --
besides the typical cycling up and down fourths/fifths -- and ones that work outside of complex jazz, etc...


For instance, Paul Gilbert's "Olympic" uses the sequence: (he took from Weiss) D/C, G/B, C/Ab, F/A, etc... (which I guess is actually like a cycle of fourths?)

Thanks


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## Mr. Big Noodles (May 22, 2015)

> D/C, G/B, C/Ab, F/A



It looks like a cycle of fifths (or fourths; they are each other's inverted form) if you go by the D G C F progression, but the C/A&#9837; is really A&#9837;+&#8710;, which kind of screws things up. I think you mean D/C G/B C/B&#9837; F/A. And they should all be seventh chords, so what you really are looking for is D7/C G7/B C7/B&#9837; F7/A. This is a chain of secondary dominants. When you use a chain of secondary dominants, you end up with a line of parallel tritones, provided you follow the voice leading correctly. It's quite nice.

You can also do tritone substitution on that progression.

D7/C D&#9837;7/C&#9837; C7/B&#9837; B7/A

Now everything is moving chromatically.

There are some basic things you need to know about progressions. For one, you should memorize these charts for diatonic progressions:

Major keys:







Minor keys:






I'm tired. I'll come back to this in the morning.


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## Sonic Anomaly (May 22, 2015)

Mr. Big Noodles said:


> I think you mean D/C G/B C/B&#9837; F/A.



yes, that's what I meant...


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## Aion (May 23, 2015)

So there are two types of basic harmonic sequences, diatonic and chromatic. There are three of the former, and six of the latter. Let's start with diatonic because there are less of them. Take the I chord in a key. Move it up in seconds, then move it back down. Then move it in thirds. Then move it in fourths. Moving in fifths, sixths, and sevenths are just moving in inverted fourths, thirds, and sixths. While you might want to play with that at some point, don't worry about it for now.

Now we have chromatic sequences. You can move in minor seconds, major seconds, minor thirds, major thirds, perfect fourths, or tritones. Everything else is inversions. Do the same thing. Move the same type of chords by these different intervals. By which I mean, if you're doing major, everything is a major chord.

Now you can get to the fun part. And by fun, I mean several hours of mind straining music time (which I actually do find fun, but you get the point). You are going to move up/down by one interval and then up/down by another. So let's say you move up in thirds and down by seconds. If we're diatonic in the key of C that would be: C-e-d-F-e-G-F-a-G-b0-a-C (capital is major triad, lowercase is minor triad lowercase followed by 0 means diminished) and then backwards C-a-b0-G-a-F-G-e-F-d-e-C. With chromatic intervals you can now mix and match, but keep it so each move up is the same type of movement and down is the same type of movement. By which I mean if you decide you want to move up in minor thirds and down in minor seconds going major to minor then you would have C-eb-D-f-E-g-F#-a-G#-b-Bb-db-C and then back down C-db-Bb-b-G#-a-F#-g-E-F-D-eb-C. If that didn't make sense I can try and clarify. Additional things to think about: you can use the diatonic exercise with any scale (including modes), you can eventually add seventh chords to this, you should occasionally change what key or starting note you are using so that you don't become attached to just one tonal center. There are a lot of possibilities with this exercise. The ultimate end goal of it is that you know how any given chord progression will sound, you'll find some that you like and can use in your work, and you can hear what chord progressions other people are using very easily.


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## Sonic Anomaly (May 24, 2015)

@Aion,
thanks, that makes a lot of sense, I'll try to get some time to work through this.


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## Mr. Big Noodles (May 25, 2015)

Alright, finally getting back to this. Aion, I hope you don't mind if I piggyback onto your post.



Aion said:


> So there are two types of basic harmonic sequences, diatonic and chromatic.



I'm going to take a more functional approach to this, with hopes that with a little bit of further information, you'll know what to expect from your progressions. I'll do this in two posts: the first will be diatonic progressions, the second will be chromatic progressions.

At any given time, you are dealing with chords as they relate to diatonic functions. For the sake of simplicity, we'll refer to the functions in major keys.

I ii iii IV V vi vii°

There are three primary chords and four secondary chords in any given key. The primary chords are I IV V. Notice that these are all major. These give the main color of the mode. The secondary chords are the others: ii iii vi vii°. Notice that these are minor and diminished. These give some slightly more exotic flavors to the mode. I IV V is a very bland, if not incredibly straightforward, diatonic progression. iii IV vii° is a more colorful alternative.

There are three basic groups of diatonic chords: Tonic functions (T), Subdominant functions (S), and Dominant functions (D). Tonic refers to the I chord, Subdominant refers to IV, and Dominant to V. They flow on a continuum that looks like this:


```
T<>S>D<>T
```
Or, with numerals:


```
I<>IV>V<>I
```
The tendency is to go from Tonic to Subdominant to Dominant, back to Tonic, but you can go back and forth between Tonic and Subdominant or Tonic and Dominant. The groups may also be expanded to contain secondary chords.

Tonic group: I vi iii
Subdominant group: IV ii
Dominant group: V vii°

You can choose any one of the chords out of those groups to make a TSDT progression. Examples:

vi ii V I
iii IV V vi
iii ii vii° I

You can also move within the groups, starting with the primary chords and then going through the secondary chords:

I vi IV ii V vii° I

However, since V is such a strong chord, it's preferable to cadence with V. I'll swap V and vii° around:

I vi IV ii vii° V I

(Incidentally, the above progression is a cycle of thirds, up until the V I cadence. Speaking of cadences...)

Eventually, you will have to terminate your phrases. In order to do so, you need something called a "cadence," which is a particular progression that occurs at the end of a phrase. There are two types of cadences: conclusive cadences and inconclusive cadences. Conclusive cadences make a phrase feel harmonically finished, while inconclusive cadences invite further exploration.


```
Conclusive cadences -
Authentic Cadence: V I, vii° I
Plagal Cadence: IV I
```


```
Inconclusive cadences -
Half Cadence: V, vii°
Deceptive Cadence: V vi
```
It would be a good idea for you to familiarize yourself with the sound of each of these cadences, as they determine the overall character of your phrases.

====================

All of the above applies to the other modes as well. Just change the numerals to reflect the mode. For example, the natural minor mode looks like this:

i ii° &#9837;III iv v &#9837;VI &#9837;VII

The primary chords (the main colors of the mode) are i iv v, which you'll notice are minor. The secondary chords (the ones that have a slightly more exotic flavor) are ii° &#9837;III &#9837;VI &#9837;VII, which you'll notice are diminished or major. TSDT is i iv v i. These are the groups:

Tonic group: i &#9837;VI &#9837;III
Subdominant group: iv ii°
Dominant group: v &#9837;VII

These are the cadences:


```
Conclusive cadences -
Authentic Cadence: v i, &#9837;VII i
Plagal Cadence: iv i
```


```
Inconclusive cadences -
Half Cadence: v, &#9837;VII
Deceptive Cadence: v &#9837;VI
```
However, we usually use the harmonic minor when writing minor key music.

i ii° &#9837;III+ iv V &#9837;VI vii°

That changes things slightly, but ends up making the harmony stronger.


```
Conclusive cadences -
Authentic Cadence: V i, vii° i
Plagal Cadence: iv i
```


```
Inconclusive cadences -
Half Cadence: V, vii°
Deceptive Cadence: V &#9837;VI
```
And you get a bonus cadence with the minor mode, called the Phrygian Half Cadence. It has nothing to do with the phrygian mode.


```
Phrygian Half Cadence: iv6 V
```
Everything else is the same. I can talk about the other modes (Lydian, Mixolydian, Dorian, Phrygian) a little later. The concepts are similar though not 100%, and it may end up being confusing.


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## Mr. Big Noodles (May 25, 2015)

Alright, let's talk about chromatic progressions real quick.

Chromatic chords can be divided into the following categories:

&#8226; Borrowed chords
&#8226; Secondary functions
&#8226; Pre-dominant chords
&#8226; Embellishing diminished seventh
&#8226; Chromatic mediant movements

*Borrowed chords* are easy. All you do with these is take a progression in a major or minor key and slap some chords from the parallel major or minor key into it. For example, this is a major progression with nothing special going on:

I IV V

Here it is with two borrowed chords inserted:

I IV iv &#9837;VII V

The chord progression is essentially major, but now it has some minor flavors thrown in. We can do it the other way around. Here is a minor key chord progression:

i ii° V

And with major borrowed chords:

i IV ii ii° V

It tends to work better when you're borrowing minor key chords into a major key.


*Secondary functions* are next. These are dominant seventh or diminished seventh quality chords that "tonicize" a chord other than the tonic. For example, take the chord progression C F G.

C F G = I IV V

Bread and butter. Now what do you call this one?

C E°7 F D7 G = I ? IV ? V

What's going on here is that E°7 is the vii°7 in the key of F, but since the progression is in the key of C, we will analyze it as being part of a secondary key center. Therefore, in the key of C, E°7 is the vii°7/IV ("seven-diminshed-seventh of four"). Similarly, D7 is V7 in the key of G, but we have to analyze it in the key of C, so it becomes V7/V (five-seven of five).

C E°7 F D7 G = I vii°7/IV IV V7/V V

You can have a chain of secondary functions, as we've already discussed. These will either be V7/x or vii°7/x.

D7 G7 C7 F7 B&#9837;7 E&#9837;7... this can go on. Each chord if the V7 of the next one. This is the same thing, but with diminished seventh chords:

F#°7 B°7 E°7 A°7 D°7 G°7

You can also mix the two:

D7 B°7 C7 A°7 B&#9837;7 G°7

*
Pre-dominant chords* are chords which immediately precede the dominant chord. These tend to be dramatic and depend a lot on voice leading. These work better in the minor mode, because fewer tones have to be altered to accommodate them, but they can also be used in the major mode.

Neapolitan 6th chord: A major triad built on the &#9837;2 scale degree, in first inversion. Has a tritone root relationship with V.






Augmented sixth chords are built on the &#9837;6 scale degree. The augmented sixth chord family includes three chords, the Italian, French, and German augmented sixth, which contain the augmented sixth interval (I'll represent it with F-D# here). The role of the augmented sixth is to expand to an octave (E-E). Therefore, these chords are best treated as contrapuntal devices rather than standalone chords. However, each one of them sounds like a dominant seventh chord.

The Italian augmented sixth is a dominant seventh sonority without a fifth.






The French augmented sixth has a flatted fifth/raised fourth.






The German augmented sixth has a perfect fifth. This causes parallel perfect fifths if it is immediately proceeded by a V chord.






To eliminate the parallel fifth, a cadential 6/4 chord is inserted between them.







*Embellishing diminished seventh* chords are diminished seventh chords that share a common tone with the chord that it is going to. So, if you're embellishing a C major triad, then the common tone diminished seventh is either C°7, E°7, or G°7. If there is a seventh on the chord, like C&#8710;, then B°7 isn't an embellishing chord, because it's plain old vii°7.

*Chromatic mediant movements* are chord progressions that move by thirds, and have the same chord quality. For example, Am Cm E&#9837;m. Or A C# E. These are very colorful progressions. Doubly chromatic mediants are the same thing, except that the chord quality changes too. Am C E&#9837;m, or Am C# Em.


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## Sonic Anomaly (May 25, 2015)

As always, thank you Mr. BNoodles. 
I'm already familiarly with the contents of the first post, but the second was enlightening.

However, perhaps I didn't express my question the right way: (or maybe I'm confused and you did answer it) when I'm talking about chord sequences-- in my imprecise music lexicon--I mean more of what you touched on with the chromatic mediant movements, where one takes two (or more) chords, and cycles through the same pattern/intervallic distance, (modulating?) out of the initial key to a new one or returning after some non-diatonic chords:

The simplest being: C G Bb F Ab Eb, etc...
the "Olympic" sequence being a bit more colorful, where he continues that sequence I showed four or five times (and maybe ending up in a different key?)
So beyond circle of fifths or fourths, or whatever, are there other ways of cycling chords (where there is non-diatonic movement?) that are practically utile?

I don't know if that makes any sense, but maybe you can divine what I'm trying to ask.


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## Mr. Big Noodles (May 25, 2015)

So you're asking about "sequences" in the contrapuntal sense, meaning the same thing transposed up or down either diatonically (tonal sequence) or chromatically (real sequence), not "sequence" as a mere succession of chords. I'm doing Memorial Day stuff with my family, so I'll get back to this later, if nobody else covers it beforehand.


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## Mr. Big Noodles (May 26, 2015)

I had a look at what Bach does. Check it out:






The progression of this sequence is C#m/E F#7, B/D# E, A#°/C# F#7(&#9837;9). It's a cycle of fifths (C# F# B E A#), and on the third time it changes (F#7 breaks the cycle). Very typical. I want to point out what is going on contrapuntally though: notice that the model is two measures long, and that each time the entire thing is transposed down by a second. I think this is important for how the sequence functions, because then it has the sense of moving down in a melodic fashion rather than something overtly harmonic. In other words, use whatever chord progression you want for the model, but then transpose it down or up by an interval that works. In this case, the transposition is by second, but it does not necessarily need to be so. As an example, I wrote a model and (tonal) sequence that goes down by third.






This works because of the melodic motion. Of course, you want good harmonic progression, but the process of sequence is fundamentally melodic.

Here is a special kind of real sequence, called a "modulating sequence," because it moves from one tonal center to another:






I'm just doing iv V i in one key and then moving the whole progression to the next key. The chord progression in the model can be whatever you want; it doesn't have to conform to a cycle of fifths or any other single interval scheme. Feel free to use those chromatic mediants, if you want to, as well as any other type of root movement. The only thing that I would caution you is that sequences usually happen pretty quickly. One or two measures per sequence is common. Maaaybe you could do three, probably not more. These are just chunks of a phrase, not phrases in and of themselves.


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## Sonic Anomaly (May 26, 2015)

This definitely helps. Thanks again!


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## All_¥our_Bass (May 29, 2015)

A cool thing to keep in mind with chromatic mediant or tritone progressions, is that even though the chords are distant key-wise, they are (usually) close in a voice-leading sense.


```
Am  Fm  C#m  Am

A   Ab  G#   A
E   F   E    E
C   C   C#   C
A   Ab  G#   A



Cm  Ebm  Am

C   Bb   A
Gb  Gb   E
Eb  Eb   C
C   Bb   A
```


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## Mr. Big Noodles (Jun 11, 2015)

Chapter 5 helped me earlier today: Guide to the Practical Study of Harmony (Tchaikovsky, Pyotr) - IMSLP/Petrucci Music Library: Free Public Domain Sheet Music


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## All_¥our_Bass (Jun 13, 2015)

Some of this might be a little over your head, but here's a bit more on the thought behind my previous post.

https://en.wikipedia.org/wiki/Neo-Riemannian_theory


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## Mr. Big Noodles (Jun 14, 2015)

This dissertation on Neo-Riemannian theory is a good introduction. The basic idea is that chords may be related to each other by transformations that change them a step at a time. Going from C, for example, you can get the following transformations:

Parallel: C > Cm (C E G > C E&#9837; G, the third goes down a half step)
Leading tone exchange: C > Em (C E G > B E G, the root goes down a half step)
Relative: C > Am (C E G > C E A, the fifth goes up a whole step)

All of the transformations are between major and minor chords. For example, from Am:

P: Am > A (A C E > A C# E)
L: Am > F (A C E > A C F)
R: Am > C (A C E > G C E)

Those are then used to make compound transformations, so to go from C to E, you need two transformations.

C (C E G) --L--> Em (B E G) --P--> E (B E G#)

This compound transformation would be abbreviated "LP".

There are other neat things, like PL cycles.

B > Bm > G > Gm > E&#9837; > E&#9837;m > B > Bm...

or PLPLPLPL...

Such triadic cycles produce a special kind of hexachord. In this case, the only pitches that are being used are B D D# F# G A# (and their enharmonic equivalents, of course). Interesting stuff. Might be inspiring.


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