Today we are going to wrap up the fundamentals and then move on to discussing diatonicism, which includes chord function, progressions, etc. But first, let's review.
Pitch class space, or the total universe of notes in Western music, is composed of 12 equally spaced pitches. Within those 12, the optimally arranged set of 7 notes is known as the diatonic set. While the specific placement of notes in relation to each other is fixed, the set can be based on any of the 12 pitches, allowing us create 12 unique instances of the diatonic set, called keys. A scale is the set of notes formed by starting on any one note of the diatonic set and naming each successive note. A chord is similar, except we skip every other note. One type of chord is a triad, which is just the first 3 notes of a chord. Within the diatonic set we find that there are only 3 different types of triads - major, minor, and diminished. The difference between these is simply determined by what type of intervals compose the triad, and in which order. (Another type of triad is augmented, although this does not appear within the diatonic set.)
1.5 (cont) Seventh Chords
Alright, so this should be pretty conceptually simple. If a triad is the first 3 notes of a full chord, what kind of chord do we get if we also include the 4th note? The answer is a seventh chord. I have listed below all the seventh chords in the key of F.
Root # | Note (in F) | Triad quality | Seventh Chord | Outside interval | Classification |
I | F | Major | F-A-C-E | Major 7th | Major 7 |
II | G | Minor | G-Bb-D-F | Minor 7th | Minor 7 |
III | A | Minor | A-C-E-G | Minor 7th | Minor 7 |
IV | Bb | Major | Bb-D-F-A | Major 7th | Major 7 |
V | C | Major | C-E-G-Bb | Minor 7th | Dominant 7 |
VI | D | Minor | D-F-A-C | Minor 7th | Minor 7 |
VII | E | Diminished | E-G-Bb-D | Minor 7th | Minor 7 b5 |
Note the different combinations of triad quality with the outside interval, aka the interval formed by the 1st and 4th note of the chord. (For ease of understanding, the 4th note of the chord, which is the 7th note of the corresponding scale, will be referred to as 'the 7th.' In fact, all notes in a chord will be referred to by their placement in the corresponding scale.) We have four that appear; I've listed them below with their common names. Note that the nomenclature doesn't appear consistent with the outside interval. Instead, the "7" in the chord name simply refers to the fact that we added the seventh note of that triad's associated diatonic scale.
Major triad + Major seventh = "Major 7"
Minor triad + Minor seventh = "Minor 7"
Major triad + Minor seventh = "Dominant 7"
Diminished triad + Minor seventh = "Minor 7 flat 5" (Less commonly called half-diminished 7)
So there are 4 distinct types of seventh-chords, whereas there were only 3 distinct types of diatonic triads. Try playing around with seventh chords and hear how they sound compared to triads. You'll feel that they add more 'color' to the sound, perhaps too much in some cases, perhaps only subtly in others. I encourage you to become very familiar with the sounds of the seventh chords, as they can be really beautiful when used in the right way. They are also extremely important in learning theory - you'll see how later.
Can you spell the following chords?
C major 7
E minor 7
F# minor 7 b5
F dominant 7
1.6 The Modes
When we were creating triads, we found that the quality of the triad depended on our starting note. That is, in the key of C, with C = note #1, creating a triad starting on the 2nd note (D) we get a minor triad, but if we start on the 4th note (F), we get a major triad. Out of 7 possible triads, there were only 3 distinct types formed. Does the same property apply to scales?
Scales, much like chords, can be major, minor, etc. Essentially, the scale that corresponds to a chord takes on its quality - so in the key of C, we would call the scale starting on D a 'minor scale,' since the D triad is minor. An F scale would be major, because the F triad is major. Let's analyze all the different scales we can get. For the sake of not getting you confused with things you may have learned elsewhere, I have chosen to use the key of Bb to demonstrate this, instead of C (most everybody uses the key of C to teach this stuff). I've also highlighted in red the 1st, 3rd, and 5th note of each scale to show the quality of the triad, and hence scale.
I - Bb C D Eb F G A (Triad = Bb D F = Bb major)
II - C D Eb F G A Bb (Triad = C Eb G = C minor)
III - D Eb F G A Bb C (Triad = D F A = D minor)
IV - Eb F G A Bb C D (Triad = Eb G Bb = Eb major)
V - F G A Bb C D Eb (Triad = F A C = F major)
VI - G A Bb C D Eb F (Trad = G Bb D = G minor)
VII - A Bb C D Eb F G (Triad = A C Eb = A dinimished)
If we compare two minor triads, for example C minor and D minor, we see that the interval content of each is identical. (Both of them have a m3 between the first two notes, then a M3). But if we look at the SCALES that correspond to those two triads, we will see that they are different! Below, I have spelled out a C minor and a D minor scale (in the key of Bb). Underneath the note names I have labeled the scale degree*, and I also labeled what interval is between each note; minor seconds are red, major seconds are blue.
* Note that scale degree is different than the 'note number' in the key. For example, the note C is the 2nd note in the key of Bb, but it is the 1st note of the C minor scale. Moving forward, 'note number in the key' will usually be denoted by roman numerals, so usually when you see Arabic numerals associated with notes, they are referring to scale degrees.
Congratulations! Let's move on to ...
Chapter 2 - Diatonicism
Roughly, western (which I will controversially refer to as tonal) music is created out of chord progressions. That is to say, most tonal music is based on chords (either explicitly played or implied) which change over time, usually with some regularity or pattern. Diatonicism refers to the degree to which any given chord or chord progression 'belongs' to the key.
One thing I should mention is that, for now, when I say 'the key of C' I really mean the key of C ionian. This means that my designated 1st note is C and that the scale built on C is an ionian scale. This may seem obvious, but later we will talk about being in the key of, say, A minor, which actually has all the same notes as the key of C but the designated first note is now A.
2.1 Chord Spelling
For now, we are going to focus only on the diatonic chords, that is, the chords that can be formed out of the notes of the key and nothing else. As explained before, each of the diatonic triads corresponds to a certain modal scale. We call this 'taking' a scale: In the key of C, the C triad is major and 'takes' the Ionian scale; the D triad is minor and 'takes' the Dorian scale, etc. But if we don't know what key we're in, it will be impossible to say what scale is appropriate for a given triad. For example, the F major triad exists in three different keys - C, F, and Bb, and it takes a different scale in each (Lydian, Ionian, and Mixolydian respectively).
Therefore we tend to refer to chords not by their actual names, but by their position in the key. This is what was earlier referred to as "note number in the key," and we use roman numerals for it. The numeral I refers to the chord starting on the 1st note of the key; the II refers to the chord starting on the 2nd note, etc. Therefore, I could simply say "the IV chord in C," and I already know a huge amount of information-
1) The chord root (F) Because F is the 4th note in the key: C D E F G A B
2) The triad quality (Major)
3) The mode of the corresponding scale (Lydian)
4) The function (subdominant) will get to this later
Before we move on, see if you can figure out the following chords (and associated scales).
V chord in F
IV chord in G
II chord in A
II chord in F#
I chord in E
VI chord in G
2.2 Chord Roots
The root of a chord is its first note. Finding the root of a chord is simple if the chord is spelled like this: C-E-G. The root is C, and by looking at the other 2 notes inside we know that it's a C major triad. However, often we'll see chords spelled like this: E-G-C. Here, the first note is E... but it has the notes of a C major triad. It is, in fact, a C major triad, but we call it an inversion. No matter how a chord is inverted, its root remains the same. The original spelling, C-E-G, we call root position. The fact that a root-position chord is the same exact thing (from a theoretical standpoint) as any of its inversions is an extremely important concept to understand. In practice, we'll rarely see chords written strictly in root position, so we need to know how to look at a chord and determine its root. As you become more familiar seeing/hearing chords and their inversions, this will become more intuitive.
So how do we 1) tell if a chord is inverted, and 2) determine its root?
Remember much earlier when I described a chord as being the collection of notes formed by going up a scale, skipping every other note? That method will result in a root position chord; and it means that the interval between each successive note MUST be a third. If we look at the note collection G-C-E, we can see that the interval G-C is not a third; there are two notes skipped (A and B), making it a fourth. That's how I automatically know it's an inversion. To find out what this triad is in root position, rearrange the notes until both inside intervals are thirds (another trick is to rearrange the notes until the outside interval a fifth). Thus, C-E-G.
Can you rearrange the following inverted triads into root position?
2.3 Chord progression basics, and Strong vs. Weak Motion
I - Bb C D Eb F G A (Triad = Bb D F = Bb major)
II - C D Eb F G A Bb (Triad = C Eb G = C minor)
III - D Eb F G A Bb C (Triad = D F A = D minor)
IV - Eb F G A Bb C D (Triad = Eb G Bb = Eb major)
V - F G A Bb C D Eb (Triad = F A C = F major)
VI - G A Bb C D Eb F (Trad = G Bb D = G minor)
VII - A Bb C D Eb F G (Triad = A C Eb = A dinimished)
If we compare two minor triads, for example C minor and D minor, we see that the interval content of each is identical. (Both of them have a m3 between the first two notes, then a M3). But if we look at the SCALES that correspond to those two triads, we will see that they are different! Below, I have spelled out a C minor and a D minor scale (in the key of Bb). Underneath the note names I have labeled the scale degree*, and I also labeled what interval is between each note; minor seconds are red, major seconds are blue.
* Note that scale degree is different than the 'note number' in the key. For example, the note C is the 2nd note in the key of Bb, but it is the 1st note of the C minor scale. Moving forward, 'note number in the key' will usually be denoted by roman numerals, so usually when you see Arabic numerals associated with notes, they are referring to scale degrees.
You'll see that the intervals between the 1st and 2nd, the 2nd and 3rd, the 5th and 6th, and the 6th and 7th degrees of either scale differ. Therefore, although they are both considered minor scales, they're undeniably different. And so while there is only one type of minor triad, there are multiple types of minor scales. Although we have not done this, you will also find that there are 3 different types of major scales as well. Compare Bb major, Eb major, and F major (all in the key of Bb). Can you find which intervals differ from scale to scale?
To differentiate between the different types of scales, we give them particular names. Unfortunately these are names that you have to memorize, because I will be referring to them often. The column "distinctive feature" refers to a particular and prominent aspect of that mode's interval content, which might come in handy if you are trying to identify the modality of a particular scale. "Interval sequence" describes the intervals between successive degrees; M refers to Major 2nd, m refers to minor second.
So, our naming convention for modes is as follows. If I say "E Dorian," I mean a scale whose
1) 1st, 3rd, and 5th degrees form the E minor triad
2) 2nd degree is a M2 above the 1st
3) 4th degree is a M2 above the 3rd
4) 6th degree is a M2 above the 5th (**distinctive feature of Dorian**)
5) 7th degree is a M2 below the 1st (or, m2 above the 6th, same thing).
Therefore, E F# G A B C# D.
Using the Interval Sequence column in the chart above, can you spell out the following scales? Refer to the original circle diagram if you are unsure of what two notes form a m2 or M2. If you have an instrument handy, I encourage you to play them!
A phrygian
B locrian
F# mixolydian
F ionian
C# dorian
C# aeolian
D lydian
To differentiate between the different types of scales, we give them particular names. Unfortunately these are names that you have to memorize, because I will be referring to them often. The column "distinctive feature" refers to a particular and prominent aspect of that mode's interval content, which might come in handy if you are trying to identify the modality of a particular scale. "Interval sequence" describes the intervals between successive degrees; M refers to Major 2nd, m refers to minor second.
# | Triad quality | Scale name | Distinctive Feature | Interval Sequence |
I | Major | Ionian | m2 between 3 and 4 | MMmMMM |
II | minor | Dorian | M2 between 5 and 6 | MmMMMm |
III | minor | Phrygian | m2 between 1 and 2 | mMMMmM |
IV | Major | Lydian | TT between 1 and 4 | MMMmMM |
V | Major | Mixolydian | TT between 3 and 7 | MMmMMm |
VI | minor | Aeolian | m2 between 5 and 6 | MmMMmM |
VII | diminished | Locrian | TT between 1 and 5 | mMMmMM |
So, our naming convention for modes is as follows. If I say "E Dorian," I mean a scale whose
1) 1st, 3rd, and 5th degrees form the E minor triad
2) 2nd degree is a M2 above the 1st
3) 4th degree is a M2 above the 3rd
4) 6th degree is a M2 above the 5th (**distinctive feature of Dorian**)
5) 7th degree is a M2 below the 1st (or, m2 above the 6th, same thing).
Therefore, E F# G A B C# D.
Using the Interval Sequence column in the chart above, can you spell out the following scales? Refer to the original circle diagram if you are unsure of what two notes form a m2 or M2. If you have an instrument handy, I encourage you to play them!
A phrygian
B locrian
F# mixolydian
F ionian
C# dorian
C# aeolian
D lydian
Congratulations! Let's move on to ...
Chapter 2 - Diatonicism
Roughly, western (which I will controversially refer to as tonal) music is created out of chord progressions. That is to say, most tonal music is based on chords (either explicitly played or implied) which change over time, usually with some regularity or pattern. Diatonicism refers to the degree to which any given chord or chord progression 'belongs' to the key.
One thing I should mention is that, for now, when I say 'the key of C' I really mean the key of C ionian. This means that my designated 1st note is C and that the scale built on C is an ionian scale. This may seem obvious, but later we will talk about being in the key of, say, A minor, which actually has all the same notes as the key of C but the designated first note is now A.
2.1 Chord Spelling
For now, we are going to focus only on the diatonic chords, that is, the chords that can be formed out of the notes of the key and nothing else. As explained before, each of the diatonic triads corresponds to a certain modal scale. We call this 'taking' a scale: In the key of C, the C triad is major and 'takes' the Ionian scale; the D triad is minor and 'takes' the Dorian scale, etc. But if we don't know what key we're in, it will be impossible to say what scale is appropriate for a given triad. For example, the F major triad exists in three different keys - C, F, and Bb, and it takes a different scale in each (Lydian, Ionian, and Mixolydian respectively).
Therefore we tend to refer to chords not by their actual names, but by their position in the key. This is what was earlier referred to as "note number in the key," and we use roman numerals for it. The numeral I refers to the chord starting on the 1st note of the key; the II refers to the chord starting on the 2nd note, etc. Therefore, I could simply say "the IV chord in C," and I already know a huge amount of information-
1) The chord root (F) Because F is the 4th note in the key: C D E F G A B
2) The triad quality (Major)
3) The mode of the corresponding scale (Lydian)
4) The function (subdominant) will get to this later
Before we move on, see if you can figure out the following chords (and associated scales).
V chord in F
IV chord in G
II chord in A
II chord in F#
I chord in E
VI chord in G
2.2 Chord Roots
The root of a chord is its first note. Finding the root of a chord is simple if the chord is spelled like this: C-E-G. The root is C, and by looking at the other 2 notes inside we know that it's a C major triad. However, often we'll see chords spelled like this: E-G-C. Here, the first note is E... but it has the notes of a C major triad. It is, in fact, a C major triad, but we call it an inversion. No matter how a chord is inverted, its root remains the same. The original spelling, C-E-G, we call root position. The fact that a root-position chord is the same exact thing (from a theoretical standpoint) as any of its inversions is an extremely important concept to understand. In practice, we'll rarely see chords written strictly in root position, so we need to know how to look at a chord and determine its root. As you become more familiar seeing/hearing chords and their inversions, this will become more intuitive.
So how do we 1) tell if a chord is inverted, and 2) determine its root?
Remember much earlier when I described a chord as being the collection of notes formed by going up a scale, skipping every other note? That method will result in a root position chord; and it means that the interval between each successive note MUST be a third. If we look at the note collection G-C-E, we can see that the interval G-C is not a third; there are two notes skipped (A and B), making it a fourth. That's how I automatically know it's an inversion. To find out what this triad is in root position, rearrange the notes until both inside intervals are thirds (another trick is to rearrange the notes until the outside interval a fifth). Thus, C-E-G.
Can you rearrange the following inverted triads into root position?
C#-F#-A
Eb-Gb-Cb
C#-F#-A#
Fb-Ab-Db
2.3 Chord progression basics, and Strong vs. Weak Motion
Each instrument has a different way of 'playing' a chord. "Chordal" instruments like the guitar or piano are able to produce all the notes of a chord at once, while low instruments like bass or bari sax usually play the root of the chord in order to further reinforce the sound, and higher instruments (which can only play one note at a time) might play a sequence of notes, or melody, that emphasize the component notes of a chord.
Chord progression is simply the idea of having a series of chords played or implied in some sort of sequence. In the vast majority of music, the sequence of chords and the order in which they appear is predetermined.
The way that we describe a chord progression is by talking about its root motion. Essentially all this means is that we discuss the sequence of chords by the roman numerals of their roots. So, instead of saying "E major, then A major, then F# minor, then B major," we should refer to that same progression as "I - IV - II - V in the key of E." This makes it easier to analyze the chord progression, and if need be, transpose it to another key.
When one chord changes to another chord, some of the component notes may stay the same, while others may change. Let's take a couple examples, in the key of Ab:
I -> II: Ab-C-Eb -> Bb-Db-F (0 notes in common)
I -> III: Ab-C-Eb -> C-Eb-G (2 notes in common)
I -> IV: Ab-C-Eb -> Db-F-Ab (1 note in common)
I -> V: Ab-C-Eb -> Eb-G-Bb (1 note in common)
We hear the most distinction between chords that have fewer notes in common. That is, the I chord and the III chord have 2 out of 3 notes in common, so the two chords are considered more similar than, for example, the I chord and the V chord, which only have 1 note in common. Aurally, the fact that Ab major and C minor are different chords is obvious. However, when it comes to building chord progressions, they have a very similar effect, and are in fact often interchangeable. Thus we can describe two different types of 'motion' between chords: Strong and Weak. Essentially, Strong Root Motionis motion that results in 2 or more notes CHANGING (i.e. a maximum of 1 note staying the same). So, moving from I-II or I-IV would be examples of strong root motion. Weak Root Motion is the opposite, basically any motion that preserves at least 2 of the same notes. Therefore, root motion by a third (or sixth, which is essentially the same distance as a third) is called weak, whereas root motion by a second or fourth/fifth is called strong.
Those of you with instruments, pick any chord from any key. Improvise a melody over that single chord, and then change to another chord in the key via weak motion and sing the exact same melody. You'll see that many of the notes still 'feel' right. Now try moving to another chord via strong motion and doing the same, and listen to the results. While the effectiveness of the melody over the different chords is not a direct function of the type of chord motion, you should start to see that some (weakly related) chords are virtually interchangeable with each other in terms of supporting the melody. Examples: I and VI, II and IV, V and VII, etc.
Alright, this email has gotten long enough. Next time I promise to delve more into Chord Function and Resolution, basically the two factors governing how chord progressions work. Good work today and thanks for reading!
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