Have you ever found yourself stuck in a rut, creating chord progressions that seem to wander aimlessly without a clear sense of direction or purpose?
The secret to crafting compelling, meaningful progressions lies in understanding the power of functional harmony.
Progressions that Sound Great and Go Somewhere
Functional harmony is a way of thinking about the purpose of chords in a progression, both in relation to each other and to a central harmony or tonic. By grasping the principles of functional harmony, you’ll gain the ability to create chord progressions that sound great, and have a logical structure and sense of intention.
What You’re Going to Learn
In this comprehensive guide, we’ll demystify functional harmony and show you how to harness its potential to transform your compositions.
We’ll start by exploring the basic concepts of harmony, including the major and minor scales, and then dive deep into the world of functional harmony within the realm of diatonic chords.
Along the way, you’ll learn how to create progressions that effortlessly move to and from the tonic, guiding your listeners on a meaningful musical journey.
But we won’t stop there. We’ll also venture into the exciting territory of chromatic harmony, exploring how to incorporate non-diatonic chords to add color, tension, and interest to your progressions.
By the end of this article, you’ll have a solid understanding of functional harmony and the tools you need to create chord progressions.
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What is Harmony?
Harmony is the sound created by two or more notes being played together.
Triads = 3 Note Chords
Put three notes together and you start to have many possible combinations. These kinds of harmonies are called triads, built on intervals of thirds, and are foundational for understanding diatonic and functional harmony. You may have seen these before:
Sevenths = 4 Note Chords
Add one more note, and the possibilities start to become exponentially greater. Add more notes, and phew… it gets crazy.
Diatonic Functional Harmony
I am a huge fan of Romantic music. I love the way it winds in and out, with extended chromatic passages and dramatic dynamics.
But to understand this type of music, you need a firm grasp on the simpler, diatonic harmony. So what am I talking about when I say diatonic harmony?
Two Scales – Major and Minor
Tonal music is based on two main scales. Major and minor.
Each note in the scale is given a name, such as Tonic, or Dominant. Each is given a roman numeral, representing it’s harmony, such as ii, or IV.
Notice the locations of whole steps and half-steps between the notes in the scales. This is what gives them their unique sound and tonality.
Major
Minor
When we talk about diatonic harmony, we are talking about the harmonies built off of each scale degree in thirds. We have mainly two different types of chords – triads and seventh chords.
When you stack chords on all of the notes, you get the diatonic harmony of that scale. For now, we aren’t going to worry too much about 7th chords, except for the dominant 7th, which is the most common 7th chord.
The Different Ways of Being Minor
One word about minor diatonic harmony. Composers use three different types of minor scales in tonal music – harmonic minor, melodic minor and natural minor (relative minor). The one we are really concerned with right now is the harmonic minor scale, which has a minor 3rd scale degree, a minor 6th scale degree and a raised 7th scale degree. Listen to the difference between the three scales.
Harmonic Minor Scale
Melodic Minor Scale
Natural Minor Scale
The harmonic minor scale is used most often for harmony – hence the name. This is because the raised leading tone allows us to have a major dominant 7th chord.
You can also think of harmonic minor as borrowing the dominant chord from the major scale. This makes it a little easier to understand, especially since the triad built on the third degree, the mediant, is not an augmented chord. It uses a lowered 7th.
Melodic minor and natural minor are used most often in the melody. In the harmonic minor, there is an augmented 2nd between the 6th and 7th tones. This frequently gives the melody an uneven, stilted feeling. Good if you want to write something middle eastern sounding. Bad if you want to write like Mozart or Beethoven. The melodic minor and natural minor get rid of this by either raising both the 6th and 7th or lowering them.
Major, Minor and Dimished
The chords in diatonic harmony only come in a few different flavors. Major, minor and dimished.
In major diatonic harmony, the chords are:
- I – Major
- ii – minor
- iii – minor
- IV – Major
- V – Major
- vi – minor
- vii – diminished
In minor diatonic harmony, the chords are:
- i – minor
- ii – diminished
- III – Major
- iv – minor
- V – Major
- VI – Major
- vii – diminished
You can pick up on a few things from this.
- The Major chords are written in capital roman numerals, minor chords and diminished in lowercase roman numerals. You also frequently see M for major and m for minor.
- The tonality for the most part flip flops for the scales. I becomes i, iii becomes III, vi becomes VI. V and vii don’t really change, and that is because the of the leading tone remaining a half step above. It is also important to to point out that the III uses a lowered 7th tone, also known as the sub-tonic.
Functional Harmony Explained
On to the good stuff. When you first look at the chords that comprise diatonic harmony they don’t mean much. Just a bunch of letters and numbers. But most of them serve specific functions. These functions, just like formal functions, move you along in the harmonic scheme of the music.
The primary harmonic functions are Tonic Function, Dominant Function and Pre-Dominant Function. To help visualize this, we’ll start filling in a chart, that puts everything into clear order. This chart was designed by Dimitri Tymoczko for his book, A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory). An excellent book, and I recommend it to anyone.
Tonic Function
Based off of the name, you can probably guess that the tonic function is fulfilled mostly by the chord built off of the first scale degree.
Tonic serves as “home base” for tonal music. It is both where tonal music starts, and where the music ends. It may not end on the same tonic as it started… but it will end on a tonic.
In addition, the chord built on the 6th scale degree can also serve the tonic function in certain cases. This is not so apparent by it’s name, sub-mediant. Let’s add these both to the chart.
Dominant Function
The dominant function is represented by a chord built off of the fifth scale degree. Hence the name dominant. But like tonic, it also has another chord that can function in the same way – the diminished vii.
The purpose of the dominant function is to create harmonic instability and at the same time, confirm the tonic. It does this mainly through the use of the leading tone (7th scale degree) moving to tonic (1st scale degree). Sometimes the diminished vii is not a dominant function is certain diatonic sequences, which we will talk about later.
One more thing, the diminished 7th is usually found in first inversion. An inversion is just taking the note on the bottom, and moving it up to the top. For triads there are two inversions and for 7th chords there are three. These are annotated with little numbers to the side of the harmony, called figured bass. I won’t go into too much detail about figured bass for now, this is not a post about part writing.
Pre-Dominant Function
The purpose of the last function, pre-dominant, is to prepare the dominant. It leads us to the dominant. In diatonic harmony, this is represented by the ii chord and the IV chord.
Pre-dominant functions are usually built directly off of the 4th scale degree. This would leave most people to believe that IV is the most common pre-dominant harmony. But ii in first inversion (ii6) is actually more common.
So how do we use this chart? Follow these simple guidelines:
- You can always move rightward from one chord to another by any amount.
- Chords can move leftwards only along the arrows.
- When I moves to vi and back to I, it is normally to a I6.
- The short dash lines represent common neighbor and passing chords for tonic. They usually move back to I.
- vii6 also usually moves back to I, either as a neighbor chord, or as a dominant function.
Listen to this example. The first chord progression just runs straight through the chart. The following chord progressions just remove chords, I don’t add any. It shows you the power of this simple chart. This is not by any means all you can do, just a short example.
What is really cool about this chart, is that is works pretty much the same way in minor.
Introducing Chromatic Harmony
I promised some chromatic harmony, so here it is. The most common types of basic chromatic harmony are pre-dominant functions, either built off of the dominant of the dominant or the 4th scale degree. What does that mean?
Who’s Dominating Who?
Think of it like this. If tonic is C, then it’s dominant is G. Well, if G were the scale being used, it too would have a dominant, which would be D. This is a very common and strong harmony, but is really effective. The reason is because it raises that 4th scale degree, in this case F, to F#. It really makes it want to move to the dominant harmony. Listen to the difference of a ii-V-I progression, and a V/V-V-I progression.
The next type of common chromatic harmony is also pre-dominant, this time using something called modal mixture.
Modal Mixture
Modal mixture sounds mysterious, but it really isn’t. It’s basically just mixing the harmony from the major scale and the minor scale. A very common one is called the Neapolitan 6th. It is a ♭II6 chord. It has a really cool sound. Listen to the example.
That covers a lot of diatonic harmony, but there is still more. We haven’t even talked yet about the types of harmonic progressions. That will have to wait for another day, this article is getting pretty long.
This is your next step!
Your next step is internalizing some of the standard chord progressions. Composer’s don’t just create every element of their compositions. There is a common musical language that we all use.
Here is one of my favorites. It’s the progression Mozart uses in his Lacrimosa. And I have a whole article about how to learn it, internalize it and use it composing. Sometimes it’s best to learn a little theory, and then put it into practice.
Thank you for your great post:) It is so insightful.
However, I have several questions.
1. I(6) and IV(6) are you saying both I and its first inversion are valid?
2. Why we have V7 but not V?
3. What those dashed arrows from vi to I(6) and from vii0 to iii inside the second
and fifth squares, respectively? Can’t both vii0 and V7 (according to the rule “Chords can move leftwards only along the arrows.”) both can go to iii? Do they represent preferences over the other movements?
4. Why secondary diminished chords are not included?
I do appreciate your answers 🙂
Hi. Great explanation. However, I’ve got lost with the iii. Some authors gives it a tonic function. Others a dominant function. But you did not include it in any function. Why?
I feel very stupid because someone else has already asked about the little squares on the chart, but I can’t for the life of me figure out what the little red VII and III represent on the Minor chart. Can we use either VII or III instead of vii°, or maybe III then VII, maybe it can be used before the vii° like the V/ square, or maybe after the vii° because it’s positioned on the right, unlike the V/. Another question, why can’t we use a V/ progression on ii°, is this a property of diminished chords, because this is also the case with vii°? or something else? I have no idea, please help.
Thanks in advance(The explanation as a whole has been a massive help)
Hi Salamander,
No need to feel stupid. I should really add the flat symbols there.
In minor, the most common key to modulate to is actually ♭III. In the case of C minor, this means modulating to Eb major.
Bb is the V/♭III, and it is also the chord that appears in C natural minor.
Therefore, I threw it on the chart, to show that path, but I’ve had so many questions about it, it is clear the chart needs an update.
I was trying to relate the idea that viiº-iii shows up in the descending 5ths sequence in major (C-F-Bº-Em), and in minor (Cm-Fm-Bb-Eb) as a way to modulate.
Hi Jon …
I am very late to this party and hope you are still monitoring this thread … so I can pose my question.
Basically, are there equivalent diagrams of the Dimitri Tymoczko charts for modal progressions?
Or, … put another way … does modal functional harmony exist for any of the modes other than Ionian and Aeolian (natural minor)?
I’m vaguely aware that there tend to be fewer functional chords available with the other modes. As a lover of folk songs, I understand that many are modal. ‘What Do You Do With A Drunken Sailor’ comes to mind. I’d love to see a similar functional harmony chart especially for Dorian and Phrygian.
Thanks for your time and your wonderful articles.
Well, I’m sure you could probably do some statistical analysis on a large corpus of modal music, and come up with some sort of system of modal functions. Not sure if someone has done that.
Considering that most people dive into modal music to specifically break out of the sound of functional harmony, I think it may be more effort than it’s worth.
It’s also important to remember that Ionian is a mode. If you think about a mode as a collection of whole-steps and half-steps, it’s really their relationship to the tonic that defines the sound and therefore the harmony that derives from it.
Thank you …
Yes, I noted that Ionian was a mode.
But then once the root is changed, in Dorian for an example, do the same Tonic, Pre-Dominant and Dominant chord functions persist?
So, for example, if ii is the new tonic chord, is vi (or a variant) the new dominant?
Jon …
Oops! I think may have misspoke. Don’t we name the root chord either i or I, depending on which mode, using the same order of chords as in the major key, but starting on the bespoke chord, i.e., D minor in the key of C is ii, but the same notes in D Dorian are the i?
Yes, that is correct.
DF Tweedie-
There’s a book called THE GUITAR GRIMOIRE by Adam Kadmon (not his real name; not explaining the name here).
That book takes the Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian modes and shows all seven modes created within each mode.
(The seven modes listed above are the modes of the 7 note major scale/ Ionian mode. He gives you the seven modes of the Dorian mode, e.t.c.)
It’s all a matter of moving the tonic to the next step in the mode/ scale you’re looking at.
You also get Harmonic minor, Melodic minor, And you’ll obviously discover Lydian dominant, e.t.c…
For folk music I dont know why you’d want to know all that. However, as a MUSICIAN in general, it’s interesting.
That in conjunction with Ted Greene’s Chord Chemistry (EVERY guitarist should have this open beside their guitar at all times. [That’s where my friend S. Vai says his copy is at all times].
Chords come from scales/ modes, so it might be helpful for you to at least SEE how MODES are created, as in Guitar Grimoire (stay away from the DVD if it’s still available).
I think Ted Greene’s book will open a hundred thousand doors to the fretboard for you, and THEN you can consider what modes can be played over what.
Have fun.
Enjoy!
Those two books made it possible for me to continue writing music after my spinal injury stopped me from playing guitar, drums, bass, keys for over 30 yrs.
So again, enjoy your playing!
Hi Jon. This is an incredibly helpful lesson. Thank you. If the iii chord follows the vii(dim) in a major key, is the next move usually to the V or to the tonic? Thanks again.
Next move is usually to the vi chord. This is part of the sequence of ascending 4ths/descending 5ths.
“In minor diatonic harmony, the chords are:
i – minor
ii – diminished
III – Major
iv – minor
V – Major
VI – Major
vii – diminished”
Hey Jon, really nice work. I have a question. All my reading suggests that that diatonic chord for 7th degree in minor scale is a Major chord. Why do you have it listed as diminished. Also, what do the (6) mean? Is that the bass note?
The natural minor has a flattened seventh, so yes, you are correct. However, in common practice tonal music, we tend to use harmonic minor. We raise the seventh scale degree on chords V and viiº, or you can look at it as borrowing the V and viiº.
In the minor version, do the VII and III at the bottom of the vii° box imply you could move from vii° to either VII or III?
as vii° to iii in the Major version?
Or is it implying a vii° – VII – III – V7 sequence as an option? (I see the line connecting VII and III)
It sounds lovely to do that, but I wasn’t sure if it implies either VII or III, or if vii° moving to VII necessarily requires III follows.
Thanks for putting this together!
Looking at this, I think it would be clearer showing a bVII, with an arrow to III, with III floating off the side maybe. Hard to say.
viiº is a leading tone chord and so it has a strong tonic pull.
VII should really say bVII, and III should say bIII, that would make the movement a little clearer. bVII often ends up becoming the V of the III chord.
None the less, you hit the nail on the head when you said “It sounds lovely to do that”. As long as you like how it sounds its okay.
Thank you for this wonderful article!
Louie, Louie is not diatonic.
You know, I never really listened closely to the song, but now that I have, I see where you’re coming from.
There seems to be a minor V chord. The progression A – D – Em sounds a little strange.
However this would still be diatonic. It’s just a A mixolydian scale, which is really just a D major scale starting on A. Diatonic means within the scale. D, Em, and A are all within the scale, and actually form the backbone of cadential harmony.
But I will grant you that it doesn’t sound like the Major-Minor system – more modal.
1 correction point to you!
Hi Jon,
A question about augmented chords: I’ve written a piece in the key of e minor and I’ve an augmented chord sandwiched between the two chords C (add9) in its second inversion and g minor in root position. The notes of the augmented chord are G flat, B flat and D. Would this be a G flat augmented or B flat augmented chord?
Would I be correct in assuming that this chord wouldn’t have a Roman numeral assigned to it?
Many thanks.
Good question.
With augmented chords it’s best to use the augmented interval as the guide, so Gb -> D would be the augmented interval. If you wanted a Bb augmented, the triad would be Bb-D-F#. Also, it seems like your bass note is Gb.
It can be tricky though, as augmented triads split the octave evenly, and so are ambiguous.
Nice progression by the way.
Thank you! Yes G flat is the bass for that chord. Since the tonic of e minor also has an added 9th (F sharp) a lot of the time, I did wonder if it should be B flat augmented with that F sharp but thanks for making it clear for me. These augmented chords can be so confusing!
Kind regards.
Hi Jon,
First off I want to say your courses are absolutely amazing; designed and structured so well that it’s hard to find an equal out there!
My questions are about cadences and functional harmony.
a) Just how frequently is a cadence really needed? For instance in a canon or fugue it is every statement and phrase that needs a cadence? And how would one choose the type of candences to avoid monotony?
b) If I want the horizontal line of music to be particular way and the notes don’t readiness fit in with the cadences expected, what can we do? Eg: In the opening bars (or even last bars of a piece) I want to end a particular way and when a PAC is expected my horizontal line just doesn’t allow for the perfect cadence chords – should I modify the horizontal line or complete the phrase and simply add the closing chords of the cadence?
Cadences give a very predictable behavior. All of the questions you ask, really come down to you making deliberate choices and weighing them against expectations. If you can’t make a line work with the context of a conventional cadence, there are many other ways to bring closure that don’t require strict adherence to the harmonic scheme.
Dynamics, articulations, rhythm, tempo, liquidation, descending lines, simplifying things in general… these all lead to closure.
Thanks so much Jon for your response and clarification!
Great explanation! Do you happen to have a printable version of the charts? I teach piano and am doing a group class on diatonic harmony in a few days. I’d love to give the students these diagrams for reference! Or, it is ok if I copy and paste the images?
This is from the workbook from my Fundamentals of Music Composition course.
https://www.artofcomposing.com/wp-content/uploads/2018/10/Functional-Harmony-Workbook.pdf
What does the ° mean after certain ones of the chords? Also could you explain exactly what 4th and 6th chords are? Thanks.
The º means the chord is diminished. That means it contains a minor 3rd above the bass, and a diminished 5th above the bass.
The 4th chord is the subdominant, which is a major triad built on the 4th scale degree.
The 6th chord is the submediant, which is a minor triad built on the 6th scale degree.
But you may also be asking about 6/4 chords, which are chords that place the 5th in the bass, and have the root and 3rd above it. It is often seen as a harmony right before the V chord at the end of a theme – the cadence.
I was just wondering if you could also make another one for all the resolves in harmony and how to remember them. That would be really helpful. Thanks!
The best way is to memorize and practice playing them at the piano over and over again.
I feel really stupid because its probally really obvious but what does S and D mean under the dashes?
Subdominant and Dominant.
Here is another definition of the leading-tone effect:
https://www.academia.edu/36495364/What_is_a_Leading_Tone
Bernd Willimek
So I’m curious as to why the III chord isn’t categorized under dominant. In the natural major harmonic field the III chord is the dominant V chord of the relative minor vi position and in a minor harmonic field the III chord acts as the tonic of its relative major field. I’m just curious as to if you could further enlighten me on the subject? Also what’s the point of mediant submediant and all the other names if they fall into only three categories I feel like there has to be more info on the other function types but I can find none.
iii moving to vi
iii naturally wants to move to vi, because of the root movement. If you were to just use the letter names, E moving to A, you can instantly see, this is a descending 5th/ascending 4th. This is one of the most common root movements, and so works very naturally.
iii moving to IV
iii usually wants to lead to IV, because of the half-step from E to F. Notice, that if you play iii moving to IV, it sounds similar to I6 moving to IV. This is actually one of the reasons iii is not considered a functional chord – because it is often aurally confused with I6.
viiº moving to iii
iii follows viiº, once again because of the root movement, a descending 5th. It is frequently found in descending 5th sequences.
Why isn’t it functional?
As I said earlier, it can be confused for a I6 chord. In first inversion, it also tends to sound like a V chord, with an added 6th. But the ultimate reason we don’t call it functional, is because Bach, Mozart, Haydn, Beethoven… pretty much the majority of Baroque and Classical composers, did not use it very often. Usually only in the context of a sequence, or modulation.
As far as why there are names for each chord, even though they fall into three categories. It’s because they are describing two different things. The functions and the actual chord. Unfortunately, the traditional names for functions also match the names of the chords themselves.
Jon….I love your charts but after reading through everything I can’t figure out one thing. What do the the the numbers in the small squares mean? For instance, the brown colored V/ at the bottom of both the major and minor charts, or the blue, red, and green iii on the major chart.
The V/ at the bottom means “applied dominant”. All this really means, is for the main chord in the box (for instance the ii chord) you can precede it with its own applied dominant. To get that, pretend to be in that key for a moment (D minor) and then figure out the dominant in that key (A or A7).
hey there, great stuff, appreciate it.
question, i believe you didn’t really mention how the iii chord fits into all of this. could you notify me on why the iii chord fits into certain groupings (tonic, sub dominant, dominant) as well as its function.
thanks in advance.
Many people ask me, “why isn’t the iii chord a part of the list of functional harmony?”
That question is not a simple one to answer. First, let me point out, that it is, in fact on the chart.
If you notice, the iii is located in the block moving to vi, and iv, and then moving specifically from viiº to iii. There are specific reasons for these placements.
iii moving to vi
iii naturally wants to move to vi, because of the root movement. If you were to just use the letter names, E moving to A, you can instantly see, this is a descending 5th/ascending 4th. This is one of the most common root movements, and so works very naturally.
iii moving to IV
iii usually wants to lead to IV, because of the half-step from E to F. Notice, that if you play iii moving to IV, it sounds similar to I6 moving to IV. This is actually one of the reasons iii is not considered a functional chord – because it is often aurally confused with I6.
viiº moving to iii
iii follows viiº, once again because of the root movement, a descending 5th. It is frequently found in descending 5th sequences.
Why isn’t it functional?
As I said earlier, it can be confused for a I6 chord. In first inversion, it also tends to sound like a V chord, with an added 6th. But the ultimate reason we don’t call it functional, is because Bach, Mozart, Haydn, Beethoven… pretty much the majority of Baroque and Classical composers, did not use it very often. Usually only in the context of a sequence, or modulation.
I’ve read through this and tried to follow all details, but I’m missing why your coloured version of Dimitri Tymoczko’s chart is missing the solid arrow from vii° to I.
Could you please explain?
I just put one big arrow under the red dominant chord section of the chart. I figured Tymoczko’s two arrows were both saying that either dominant could lead back to tonic.
Hello Jon,
First, thank you for all your work – I started by wanting to find out about modulation and then ended up here finding our about diminished 7th chords. I know this question has been addressed previously but I too am struggling with the pattern of chords given for minor diatonic harmony:
i – minor
ii – diminished
III – Major
iv – minor
V – Major
VI – Major
vii – diminished
On the page I started on:
https://www.artofcomposing.com/the-art-of-modulation-part-2-common-chord-modulation
the harmonised F minor scale is given as:
i – minor
ii – diminished
III – Major
iv – minor
V – minor
VI – Major
vii – Major
I tried it out on the piano, and it made sense – I just don’t understand the different pattern given on this page. Please could you help?
I think the confusion may be from the fact that one is the harmonic minor scale, and the other is the natural minor, also known as the descending melodic minor scale. In the harmonic minor, we raise the leading tone on the V chord and vii chord so that we can have the half-step movement to tonic.
In the case of C harmonic minor, the V chord is G major and the vii chord is Bº (B diminished). We don’t raise the leading tone on the III chord, because that gives us an augmented chord, which is not all that common in classical functional harmony.
This harmonic minor scale allows us to maintain the same feeling of goal directed tonality that we get in major.
But when modulating in minor, it is very common to go to III. In the case of C minor, this would mean modulating to Eb major. The V chord in Eb major is Bb, which means that we would not raise the leading tone, and instead we call it the subtonic. This allows for easier modulation to III.
It should be written as VII, not vii because it is major.
so the natural minor has a major VII?
Natural minor has a lowered 7th. Harmonic minor has a raised 7th, although recently, I am finding that is more beneficial to think of harmonic minor as actually just borrowing the dominant chord from the major scale. It makes understanding modal borrowing a little easier, and it also takes away any confusion over bIII, which some people want to raise the 7th scale degree on, making it augmented.
Hi Jon I wonder if you can help me. I am an experienced pro songwriter but have encountered a problem with the latest song I have been recording.
I am a guitarist and my song is in D major/B minor. I am using a capo so playing C chords.
Is it ok musically to play a Dm and whilst the notes G and E are still sounding to have a vocal and strings sounding an F#? I am worried about the minor 2nd creating a clash i.e. between the F#and G and also the major 2nd F# and E. The G on the guitar is on the second beat of the bar and then vocal and strings on 3rd beat sounding F#. I have chosen a substitute chord of Fmaj 7 instead of Dm/Dm 9 so that there is no chance of a semitone clash. Or is it ok as the minor 2nd is not sounding on the same beat? Is this ok? Any advice is grea.tly appreciated. (All chords stated are in C, guitar on capo 2
Many thanks
Keith,
What you are basically saying is you want a Dm11 chord. D minor triad has D-F-A. By adding the E and G, you are adding the 9th, and the 11th, which are perfectly acceptable. You can also choose to add the C as well, which adds a softness to the chord (min 7ths are not very harsh to my ears).
The key is paying attention to resolutions. The G wants to resolve to the F, and the E wants to resolve to the D. You can choose to either resolve both, one of them, or none of them. Each will have a slightly different effect on the listener.
Hi Jon thank you for your reply. Don’t think I explained it too well. I just need to point out that the Dm is on capo 2 guitar so it’s really an E minor. Anyway if we take it as an E minor and forget about the capo is it ok to substitute a G maj 7th in place of an E minor 9? I am adding the maj 7th at the top of the chord (on the E string). The vocal seems to belong in the minor and I am singing 2 non-chord tones either side of the maj 7th note. These are both E s so should I use E m/m9 ? Would it be possible to send you an mp3 of my song and I would highlight the relevant places in the song in a message. Explaining it in words is not that easy. I would really appreciate it if you could take a listen and give me your opinion.
Many thanks
Keith
Keith,
The ultimate test is listening. Do you like what you wrote. Theory wise there are no issues with it, which means the only thing that matters at this point is whether you enjoy listening to it.
If you’re interested in sending it, I would suggest trying to make a symposium. Generally they are every Saturday at 8:30am.
Click here for more info on the symposium.
Sorry, In in the first part my previous post I forgot to move from IV to ii: we do it by raising 1^ to 2^ thus giving us the second so-called pre-dominant chord consisting of degrees 2^-4^-6^. This ii chord naturally resolves back to I by moving all natural tendency tones to their rest points: 2^ to 1^, 4^ to 3^ and 6^ to 5^.
This minor addition is just to support the phrase: “This concludes our list of the possibilities with diatonic triads. We tested all of them and none is left out!”. Otherwise it doesn’t change much in the context of further elaboration of the previous post.
Hello Jon! Suppose you want to explain me why IV chord has a pre-dominant function per Functional Harmony Theory. How would you explain that IV tends to progress to V? Let’s stick to triads, right?
IV consists of scale degrees 4^-6^-1^. If we consider tendency tones in a context of Tonality then: 4^ tends to go to 3^, 6^ tends to go to 5^ and 1^ has no tendency. This leads us back to I, 1^-3^-5^ – the tonic. OK, this method doesn’t work. Let’s try another way? By the way, at this point it’s probably worth noticing that we moved 2 notes out of 3 by step to get from I to IV. Does it give us any clue about where else we might get from IV other than returning back to I? Let’s see… (By the way, we haven’t talked about why we got from I to IV but let’s take it for granted.)
So, let’s move some notes of IV by step around and see what triads we might arrive at?
– We can move 1^ to 2^ (against tendencies) and get to ii = 2^-4^-6^ (OK, another so-called “pre-dominant”). Looking at this chord’s degrees we see they are all tendency tones wanting to resolve back to tonic (2^->1^, 4^->3^, 6^->5^). That doesn’t help us either.
– We can move 6^ to 7^ and 1^ to 2^ (all against tendencies) and arrive at vii = 7^-2^-4^. Well, that’s something interesting. At least vii has no tendency to go back to IV. With resulting tendencies we have both 7^ and 2^ merge into 1^ and resolve 4^ to 3^ which gives us 1-3. We don’t get a complete tonic triad but we can live with that I guess. So, we could call IV a pre-dominant to vii based on our discovery, provided vii dominates the I (which it does indeed)?
– We can move 4^ to 3^, 6^ to 5^ and 1^ to 7^ which are all good tendency moves except 1^ to 7^. Anyway, let’s see where we got to. It’s 3^-5^-7^, the mediant iii. By moving 7^ back to 1^ we arrive at complete tonic! However the iii is not considered “dominant” so we didn’t find much here.
– We can move 4^ down to 3^ (a good tendency move!) and arrive at 6^-1^-3^ which is vi. vi easily goes back to I with resolving 6^ to 5^ but like in the case with iii above, we don’t have a dominant function in vi. It’s a smooth way to go back to tonic but apart from that we don’t get much benefit from it.
– What else we might do? The only remaining triad we can move to from IV is V: we have to move all tones of the IV against their natural tendencies in order to do that. That’s actually forcing ourselves to make all 3 unnatural moves but let’s be strong and do it! 4^ to 5^, 6^ to 7^, 1^ to 2^. We arrive at the so-called “dominant chord” V consisting of 5^-7^-2^. Continuing with natural tendencies of the scale degrees we can most naturally resolve to an incomplete tonic
triad consisting of 1^-5^ (by resolving both 2^ and 7^ to 1^) but since we successfully arrive at the tonic from the dominant we again can assign the IV the pre-dominant function because we moved from it to the dominant.
– This concludes our list of the possibilities with diatonic triads. We tested all of them and none is left out!
Does it give us any analytic material to make a satisfying conclusion why we consider the IV chord “pre-dominant”? From what I see I can conclude that we can call the IV pre-dominant chord only in the context of it’s ability to move to V which is the dominant.
Wait, wait, wait…. what if we test an ability of some other chord except the tonic to arrive at V? Wouldn’t it automatically give it a pre-dominant function? We exclude I, IV and vii (is this obvious?) and can still test ii, vi and iii for their ability to act as pre-dominants. Here we can actually exclude the ii – a well known pre-dominant thus taking a shortcut.
– iii is a good candidate to test: the tonic I easily moves to iii by dropping 1^ to 7^ (which is however is against the natural tendency). We get 3^-5^-7^. Does iii have a good chance to turn into a pre-dominant? Let’s see. By only dropping one scale degree 3^ to 2^ (which is again a counter-tendency move) we easily arrive at the dominant V: 5^-7^-2^.
This leaves us with a bad feeling that we have one more pre-dominant chord in addition to IV and ii. Should we make ourselves feel even worse by testing the vi? I’m getting nervous… but let’s be strong! We have to make a step forward!
– vi consists of 6^-1^-3^. Ohhhhh, noooooo! We can easily get to vi from the tonic by moving 5^ to 6^ (which is against their tendency by the way but anyway…) . Just as easily we can move all three notes by step to arrive at the dominant V: 6^ back to 5^, 1^ to 7^ and 3^ to 2^ giving us 3^-5^-7^.
What? Another pre-dominant chord? Something must be wrong here.
To make the things even worth we can try to break up our earlier acquisitions. Let’s take vii. We can get from the tonic to vii by a few simple steps: 1^ to 7^, 3^ to 2^ and 5^ to 4^. You can object by saying that all these moves are against the natural tendencies but so are the moves from I to IV except keeping the tonic degree 1^: ^3 to 4^ and 5^ to 6^. In comparison the moves from I to vi are even less painful: we only have to move 5^ to 6^. So back to vii: from vii we can go to V simply by raising 4^ to 5^ which gives us 5^-7^-2^, the dominant triad.
One more pre-dominant? We could probably think so unless we didn’t know of the shorter way to arrive at the tonic: by resolving the vii back to I whether we choose the same way back or merging degrees 7^ and 2^ to 1^ as we did before.
In the end of all this combinatoric test I personally feel stuck. I see that there must exist some fixed criteria that define why IV can have a pre-dominant function and vi and iii cannot.
However, here comes a big question: ARE THESE CRITERIA SELF-DEFINING? If so then we only can believe that IV is a natural pre-dominant and vi and iii are not. Otherwise does it have a mathematical background, the formula that explains why IV is a pre-dominant and vi and iii aren’t?
Of course, we can speculate on theories of Riemann and whatnot but if it’s all speculation on theories is the Functional Harmony including the pre-dominant function of IV only a MATTER OF BELIEF?
Or is there any logic behind calling IV the definitive pre-dominant chord along with it’s minor ii sister?
Viktor,
I think you are over thinking it. The reason IV moves to V, is mainly because over the course of the history of tonal music, composers have moved from IV to V. What our brain interprets as correct harmonic movement is because we have heard music our entire lives that conforms to the schemas we are used to. This is why in Rock music, V can often move to IV. It’s not because there is some inherent reason the frequencies in V resolve to the frequencies in IV, instead, it is because there have been a lot of pieces in that genre where V moves to IV.
In classical music, however, there are many more examples of IV moving to V, or ii6 moving to V. And so, we say that correct harmonic syntax (in the classical style) has IV moving to V.
The terms tonic, predominant and dominant, are also just labels that someone came up with, and others found useful. This allowed them to perpetuate.
Hi there, thank you for the information. I would like to know what you are referring to when you use the term “A2” beginning with the minor scale. Thanks!
A2 refers to an augmented 2nd interval. Intervals tend to come in a few different varieties, perfect, major, minor, augmented, and diminished. Augmented usually refers to a making the major interval a half-step sharper. For instance, from C, a major 2nd would be D, and an augmented 2nd would be D#.
Thank you for the clarification! Growing up I always referred to this interval as “the minor 3rd”.
It’s the same sound(minor 3rd and augmented 2nd), BUT they’re different on how you use them
Hi Jon
I’m trying to understand your chart on Diatonic Harmony (under the “Pre-Dominant Function” header). Below the chart you’ve written the names of the chords. I’m assuming they are named for the root of each chord, starting with I, vi, IV, ii6, etc. First of all, do the chord names under this chart refer to the RH or LH scale? How can it be that the first chord is I in either RH or LH? In RH the first two chords are the same. For LH the roots are different, and it can’t be that you’re referring to the half steps in between (right?).
Thank you so much for your blog posts and your podcast. I am clearly new to music theory (as in I literally started learning 1 week ago) so there is a lot I’m trying to understand at once. Your podcast on harmonics was the most exciting thing I’ve learned thus far.
All the best,
Ryan
Ryan, when using the chart, it shouldn’t matter which hand is playing the chords. The scale in this case is the major diatonic scale for the major chart, and the harmonic minor scale for the minor chart. Each Roman numeral on the chart refers to the root of the chord within the context of it’s function. For instance, I and vi are both considered tonic functioning chords, IV and ii both pre-dominant (meaning they tend to prepare the dominant chord, especially in cadences) and then viiº and V are both dominant functioning chords.
To make things simple for practicing chord progressions, I would play the root in the left hand, and then play a simple triad or seventh chord in the right hand. You don’t have to worry too much about inversions in the right hand, because it is the bass note that determines the chord inversion. Generally you want to keep the right hand moving as little as possible if you are just playing chords.
Hi Jon,
Thanks for the reply!
I’m still a little hazy on the details, but I think I’m starting to understand the basics. Looking forward to more podcasts.
Does the book you mentioned cover even more of this? I can’t get enough. it’s all so beautiful. Playing out through chords using the charts on some string pads and I’m freaking out at how much beauty I’m making over here.
The book focuses more on the geometry of voice leading, so it can be a bit difficult to penetrate, but there is a little more on functional harmony. If you’re really interested in this stuff, I recommend checking out Music Composition 101, because I go into more detail about how to use the charts, including modulation, and modal borrowing.
Awesome. You’re doing a great service to the world with this website, thank you so much. I’ve always had a difficult time trying to understand chords and this is seriously changing my life.
Another quick question, why no use of the III/iii chord in the major/minor tonic function chart?
iii/III, while being a great chord, is non-functional, meaning it doesn’t fall into any of the categories of tonic – pre-dominant – dominant. Sometimes, it can sound like a tonic chord, other times, it gets mistaken for a dominant chord. Most often though, it is used in a contrapuntal way, for instance I-iii6/4-vi, which there the bass line is 1-7-6. Or it is often found leading to vi, or IV, or following viiº in major/VII in minor.
I do have a question … Do all of the harmonized minor scales work in this formula the same way ?
The formula works specifically for harmonic minor, which is the scale used for harmony.
Glad I read the thread before I posted what I was about to ask ! sweet chart !! This is exactly what I’ve been looking for … such beauty can be found in that formula !!
Hi Jon,
I am having a problem understanding some of the information you have posted. The chart or table for Minor Diatonic Harmony does not appear to be correct. You have listed:
i – minor
ii – diminished
III – Major
iv – minor
V – Major
VI – Major
vii – diminished
But in a Minor Key, the V should be minor. In fact, it should be as follows:
i – minor
ii – diminished
III – Major
iv – minor
V – minor
VI – Major
vii – Major
At first I thought, that perhaps you were discussing Harmonic Minor Diatonic Harmony, but that still does not match up with your chart. Harmonic Minor would be as follows:
i – minor
ii – diminished
III – Augmented
iv – minor
V – Major
VI – Major
vii – diminished
So could you please clarify exactly what your chart is expressing because something is not making sense. Thanks much!
Gene,
You are correct in that I am using harmonic minor. Harmonic minor though, is not so much about the scale being used, as it is about the harmony being used. In reality, for traditional classical style music (I am talking 18th century classical, and not a blanket “classical” that covers baroque, classical, romantic, and 20th century), the augmented III is not a part of the harmonic minor scale. The harmonic minor has:
i – minor tonic
iiº – diminished supertonic
III – major mediant
iv – minor sub-dominant
V – major dominant
VI – major sub-mediant
viiº – diminished 7th
The augmented triad, is normally used as a chromatic embellishment, and not considered a part of the harmonic minor scale harmony. You can see this in action, as the majority of minor sonata form movements, will usually confirm tonic through a major V chord, and then modulate to a major III chord.
So maybe it would just be appropriate to label your chart as Harmonic Minor instead of simply Minor. That could help alleviate some confusion. Thanks!
On the whole, this is a very useful article.
However, for the scales that are illustrated with whole steps(W) and half steps (1/2), the total number of half steps (1/2) required to span the chromatic octave is 12: i.e., 13 notes require 12 half step (1/2) intervals –
C(1/2)C#(1/2)D(1/2)D#(1/2)E(1/2)F(1/2)F#(1/2)G(1/2)G#(1/2)A…
(1/2)A#(1/2)B(1/2)C’
So, in any scale that spans an octave and uses the half step (1/2) as its fundamental unit, the total number of half steps (1/2) must be 12.
If the scales that are illustrated above are examined and the whole step (W) is given the value of 2 half steps:
Major: W W 1/2 W W W 1/2
for a sum of 2+2+1+2+2+2+1=12 half steps,
Minor: W 1/2 W W 1/2 W 1/2
for a sum of 2+1+2+2+1+2+1=11 half steps
(Note though that A-flat to B-natural is 3 half steps.),
Harmonic Minor: W 1/2 W W 1/2 W 1/2
for a sum of 2+1+2+2+1+2+1=11 half steps
(Note though that A-flat to B-natural is 3 half steps.),
Melodic Minor Scale: W 1/2 W W W W 1/2
for a sum of 2+1+2+2+2+2+1=12 half steps, and
Natural Minor Scale: W 1/2 W W 1/2 W 1/2
for a sum of 2+1+2+2+1+2+1=11 half steps,
(Note here that B-flat to C-natural is a whole step (W).)
The scales that contain only 11 half steps are improperly illustrated in some fashion; to wit, the minor scale, harmonic minor scale and natural minor scale need to indicate an additional half step somewhere in their respective sequences – lest the octave not close.
This being said, and hoping that I have not made any mistakes in my commentary. The elegance of this site and the amount of work that has been put into this website is a credit to its author, an author who clearly loves music.
Thank you for bringing up “A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice.” It looks like a must read as does your site.
You are correct, and it has been pointed out a few times in the past to me. Thank you though for the thorough proof-reading, it goes a long way to making the site better. I have now updated the images so it should be reading correct amount of half-steps and whole-steps.
Thanks
great article, but I find it a serious misleading mistake the presentation of the natural minor scale where you say W, H, W, W, H, W, H instead of W, H, W, W, H, W, W
Good catch. I’ll make a note of it just below. It is an image, so it’s a little more difficult to correct quickly.
Interesting stuff! So how would you define ‘non-functional harmony’ in a nutshell?
Non-functional harmony is harmony that doesn’t follow normal resolution path of functional harmony chords. They tend to feel like floating harmonies that can sometimes be unconnected.
No mention of the Everly Bros.
Why I came here.
I’ll wait for the 3D or 4D visual to describe all these charts.
I show harmony with moving LEDs.
Sorry, no Everly Bros here.
The Everly brothers sang wonderful duets in a country rock style. Like many duet styles the harmonies are more or less straight thirds. This is a simple but very effective harmony type. It’s essentially the melody, but up a third, very easy to sing or play once you’re “on it”.
Great article! Well written, informative and insightful.
I think the difficulty associated with music theory lies largely with the design of the piano keyboard and the 5-line staff, which are essentially designed to make the C Major scale easy to work with, while screwing up every other scale. The Janko keyboard (an isomorphic keyboard) would have made things easier, because chord shapes are all the same in every key, so even individuals with no musical training can quickly spot logical patterns. There exist alternative musical notation systems (e.g. 3-line Muto notation) that closely mirror the isomorphic layout and completely remove the need for key signatures, accidentals, sharps, and all that nonsense.
Great points Manuel, but you also have to realize that the system, clunky as it can be, has still allowed the creation of amazing music and amazing performers of that music. I’ve looked into other kinds of notation, but I came to the point that it is not worth my time to learn them, and just to focus on traditional music theory and notation.
thank you for all jon but I find it hard to understand the numbers at the top of the table( to VI,IV6 or iv6) could explain
thank you again
André
Thank you very much.
Thanks Jon. The chart is good; however I always thought the chord on III in the harmonic minor was augmented (to take account of the sharp 7th)? eg in A minor, III would be C-E-G# = Caug.
Thanks for the course – loved it!
Augmented chords are really looked at as modified major or minor triads. In most cases, when you see a III in minor, it is a major chord. Glad to hear you liked the course.
Jon
Thank you for your excellent website. I discovered it through your YouTube videos.
I have a question. I noticed in Dimitri Tymoczko’s chart that the iii is missing. Does the iii chord have a function?
iii actually doesn’t have it’s own function, but it can prolong tonic.
According to Riemann, it can also replace the Dominant in some instances, although rarely used.
I think a I-iii progression can sound “dreamy”, “wistful”, “bittersweet” and is common in pop and ballads.
I agree with Jon that it can “prolong the tonic”. A Cmaj7 and Em share the same notes except for B and it doesn’t change the tone of the harmony as much as the OTHER diatonic chords. (Maybe it’s like a leading chord because of the leading tone, for emphasis on the next chord?)
I-iii Examples:
Toto – Africa
Come on Eileen
Al Stewart – The Year of the Cat (is actually I-ii-iii but uses a Imaj7)
This will probably be covered in a future lesson, but if you want your iii to sound more important, then you can embellish. I have been studying Latin theory, where the iii is a very common chord. In C, a sharp 5th makes E become major and then add a Dom7, which gives it a Latin flavor. (I would play E phrygian with the G# and a nat. 7 over this chord for a tense Latin melody.)
I-III7 Examples:
Build me up buttercup – the foundations
Streetlight Manifesto – Somewhere in the Between
Stray Cat Strut (resolves to III7)
(Sorry for the lengthy post! Love the podcast!)
Great examples.
Awesome! very well explained.
thanks
Thank you very much.
Your explanations gave me a clearer grasp of those things. You’re great !!! Thanks
Glad I could help.
I have never had the time or money to take real music theory lessons making my search for this imformation very difficult before I read this post. I feel like I have a much better grasp now because of that chart!
Thanks. Most music theory tends to complicate things… not because its necessarily wrong (or right for that matter) but just because its written so confusing. I am just trying to untangle the ideas, and put them down in as clear a way as possible.