Download Triads, 7th chords, the roman numeral harmony system, inversions

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What follows are excerpts from Jono Kornfeld’s book, Music Notation and Theory for Intelligent Beginners
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TRIADS
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With an understanding of intervals, we have the basis for understanding harmony–notes
sounding (or at least being heard) at the same time. While the most basic harmonic element is
the interval (two notes), we can go one step further and add a third, simultaneously-sounding
note: now we have a chord. A chord with three notes (for our purposes) is called a triad ("tri" as
in three notes). But these three notes are arranged in a particular way: in vertical 3rds (also
referred to as “stacked” 3rds).
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The four basic triads derive their different qualities from the four possible ways to arrange major
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and minor
thirds. A triad could be Major, Minor, Diminished
or Augmented (just like the
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interval qualities). PLEASE NOTE: A triad will always
be named in terms of its root (the
lowest note in the vertical arrangement of 3rds). The examples below are all different kinds of
“C” triads.
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TRIADS IN THE SCALE
TRIADS IN THE SCALE
Like intervals, triads might be better-understood and/or appreciated when put into a context. We
TRIADS
IN THEfrom
SCALE
can see triads, like intervals, as something
emerging
and belonging to a scale.
Like intervals, triads might be better-understood and/or appreciated when put in a context. We can see
triads,
like
intervals,
as something
emerging
and 3rd
belonging
a scale.
If we
take
a triads
C major
scale
play onlyfrom
the and/or
1st,
and 5thtonotes,
every other
Like
intervals,
might
be and
better-understood
appreciated
whenwhich
put in is
a context.
We note
can see
starting
from
the
tonic,
we
get
a
C
major
triad
(the
intervallic
sequence
of
a
major
3rd
plus
a
triads, like intervals, as something emerging from and belonging to a scale.
If we
take3rd).
a C major scale and play only the 1st, 3rd and 5th notes, which is every other note starting
minor
from the tonic, we get a major triad (the intervallic sequence of a major 3rd plus a minor 3rd).
If we take a C major scale and play only the 1st, 3rd and 5th notes, which is every other note starting
from the tonic, we get a major triad (the intervallic sequence of a major 3rd plus a minor 3rd).
Playing these notes
(every other note in the scale,
Playing
these
notes
or
notes in
thrids
in the scale) gives us
(every other note in the scale,
or notes in thrids in the scale) gives us
WeWe
cancan
apply
thisthis
function
to anytonote
theinscale:
pick apick
notea and
notes
that are
a 3rd
apply
procedure
any in
note
the scale:
notethen
andpick
thenthe
pick
the notes
that
are and
a 5th
above
notes),
and wenotes),
get a triad
builtgetoffa of
every
note
in the
scale
with
these
results:
a 3rd
andita(scalar
5th above
it (scalar
and we
triad
built
from
every
note
in the
scale
with
We can apply this function to any note in the scale: pick a note and then pick the notes that are a 3rd and
these results:
a 5th above it (scalar notes), and we get a triad built off of every note in the scale with these results:
• The triads built off the 1st, 4th and 5th degrees of any major scale are major
• The triads built off of the 2nd, 3rd and 6th degrees of any major scale are minor
The triad
triadsbuilt
builtoff
offofthe
and 5th
degrees
any is
major
scale are major
•• The
the1st,
7th4th
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majorofscale
diminished
• The
builtbuilt
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the 2nd,
3rd4th
andand
6th5th
degrees
of any
major
scale
areare
minor
• triads
The triads
the 1st,
degrees
of any
major
scale
major
•
The
triad
built
off
of
the
7th
degree
of
the
major
scale
is
diminished
•
The
triads
built
from
the
2nd,
3rd
and
6th
degrees
of
any
major
scale
are
minorscale degrees,
As a means of relating these different qualities to the different chords based off the seven
• Thenumeral
triad built
fromis the
7th Upper
degreecase
of the
major scale
is diminished
a roman
system
used.
numbers
represent
major triads (I, IV, V), lower case
As
a
means
of
relating
these
different
qualities
to
the
different
chords
off diminished
the seven scale
degrees,
numbers represent minor triads (ii, iii, vi), and a lower case number based
with the
symbol
(˜)
˜ ). ofUpper
a roman numeral
system
used.
case
numbers represent major
triads (I, IV, V), lower case
Scale
Degree
Triad’s
Root
Quality
represents
a diminished
triadis
(vii
˜
numbers represent minor triads1,(ii,
iii,
vi),
and
a
lower
case
number
with
4, 5
Majorthe diminished symbol ( )
˜
represents
a diminished
triad
(vii2, ).
3, 6this case, the major scale) are called
Minor
The
triads that
come from
a scale
(in
diatonic triads, meaning that
7
Diminished
they are made up of notes only from that particular scale. Another way to describe these triads is that
The harmonize
triads that come
from(they
a scale
this case,scale
the major
scale) arewith
called
diatoniccapabilities).
triads, meaning that
they
the scale
turn(ina melodic
into something
harmonic
they are made up of notes only from that particular scale. Another way to describe these triads is that
theyparticular
harmonize
the of
scale
(they
turndiatonic
a melodic
scale
intoscale
something
capabilities).
The
order
major
scale
triads
(from
degreeswith
1 – harmonic
7)
The particular order of major scale diatonic triads (from scale degrees 1 – 7)
2 we use. This stands to reason; since the pattern of
is always the same, regardless of which major scale
each major scale is identical, any resulting procedures (such as building triads) should also form
is alwayspatterns
the same,
regardless
major scale we use. This stands to reason; since the pattern of
identical
from
one scaleoftowhich
the next.
THE ROMAN NUMERAL SYSTEM
As a means of relating these different qualities to the different chords based on the seven scale
degrees, a Roman numeral system is used. Upper case numbers represent major triads (I, IV, V),
lower case numbers represent minor triads (ii, iii, vi), and a lower case number with the
diminished symbol ( o ) represents a diminished triad (viio). To represent an augmented triad,
the upper case Roman numeral is followed by a “+” sign.
DIATONIC HARMONIZATION
The triads that come from a scale (in this example, the major scale) are called diatonic triads,
meaning that they are made up of notes only from that particular scale. Another way to describe
these triads is that they harmonize the scale (they turn a melodic scale into something with
81
harmonic
capabilities).
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and melodic
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notes and
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the natural
minor,
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that there
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natural,
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resulting
triads
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the
diatonic
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in terms of their scale degree numbers, the same qualities as their corresponding chords in a
104
3rd
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will become more relevant when we study chord progressions and
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TRIAD TERMINOLOGY
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The notes of a triad are called chord tones. Each chord tone is named in terms of its distance
from the bottom note of the triad, which is called the root.
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Regardless of what quality it is, or which scale degree it is built from, or which key it is in, we
refer to the notes as the root, 3rd and 5th.
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TRIADS SUMMARY
Triads are three note chords whose notes are arranged in 3rds
They are-4named after the bottom note, known as the root
They come in four qualities: Major, Minor, Diminished and Augmented
The particular arrangement of major and/or minor 3rds will determine the quality of the triad
Triads can also be derived from a scale (like intervals) by selecting every other note in the
scale, and any note in the scale can serve as the root
Triads that we associate with a scale are called diatonic triads and they are enumerated with
roman numerals I – VII (uppercase for major, lowercase for minor)
The most often used minor key diatonic triads are a combination of the natural and harmonic
minor scales with the most-important use of the harmonic minor’s V major chord.
•
Major key triads:
I
ii
iii
IV V
Minor key triads:
i
iio
III iv
vi
viio (I)
V VI VII/viio i
6
TRIADS: CONTINUITY AND COHESION
The triad is a basic element in harmony, which is the experience of hearing multiple notes
sounding together. Most western classical, pop, jazz and folk music is based off of this kind of
harmony.
In recalling the issues of continuity and cohesion, it is worth noting that a big point has been
made to understand triads as chords in a diatonic system, meaning that a particular group of
triads can all be related to a single scale. Since a scale can be heard to represent a type of
melodic continuity, a group of diatonic triads can be heard to represent a type of harmonic
continuity. In context, then, a seemingly random collection of chords might be cohesively tied
together by their relationship to a single scale. The chords CM, Am, Dm, GM are all diatonic to
(a part of) the C major scale or the A minor scale.
Again, we can start to see and hear how at a level of harmony (multiple notes at once), music
theory strives to explain how separate elements (the different chords) are potentially unified
through a fundamental scale. Here, we can liken the notes of a scale as being specific
ingredients for the more complicated chords that emerge from them. Understanding triads (and
therefore, harmony) in this way serves well the basic ideas of continuity and cohesion previously
mentioned. The other basic idea of motion will be taken up in the section on harmonic
progressions later on.
7
&
7TH CHORDS
!
(a major triad
plus a major 3rd
"CM7, C Maj7"
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Major 7th
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maj. 3rd
note chord. The ]triad
is formed by selecting every other note (three ]notes total) in a scale. If we
]
] maj.
add one more note
through
a 7thtriad
chord. The top note
triad the same process (a third higher), we get min.
(a
minor
triad
(a major
triadis an intervallic 7th from the root (bottom note) of the chord.
(the last note
added)
plus a minor 3rd)
plus a major 3rd
"CM7, C Maj7"
"C-7, C min7"
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Minor, Dominant, Half Diminished and Diminished
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min. 3rd
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min. 3rd
]
maj. triad
maj. triad
*also called:
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dim. triad
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"C-7, C"C-7
min7"
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Dominant 7th*
min. 3rd
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maj. triad
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called
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(a diminished triad plus a minor 3rd)
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o
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] its diatonic 7th chords:
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o
(a diminished triad
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plus
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triad
plus a major 3rd)
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superscript symbols for diminished and half diminished are: "C-7 b5, C ø7"
a minor
"C7, Co dom7"
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ww
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from the dominant 7th (V)
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and
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7
7
7
•
•
V7
˜
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vii 7
Vii 7
!
The vii is a half diminished chord.
-5The viio is not a literal diatonic chord because it has a non-scale tone (A flat in the case of C
major), but we allow it the same way we allow similar variations in the minor key triads. In
addition, you will notice that the diminished viio7 sounds very similar to the half diminished
vii 7.
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In more modern music, especially jazz, all the possible diatonic 7th chords are used quite often.
In earlier music (such as from the classical period), the more often used 7th chords were limited
to the V7 (the dominant 7th) and the diminished viio7 and half diminished vii 7ths (i.e. major and
minor 7th chords were seldom used). This was the case for both the major and
?minor keys. In
minor keys, like with their triads, the harmonic minor mode was often used when harmonizing
certain chords that used the leading tone (limited to chords built
off of the 5th and 7th scale o
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GM ii
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Am III
AM V
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The three more-often used 7th chords as they appear in A minor. Like with the diatonic
154
&
minor triads, these chords use the raised 7th scale degree (leading tone) that comes from
the harmonic minor mode (the G sharp).
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&
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c
7TH CHORDS SUMMARY
•
•
•
•
•
•
•
•
•
7th chords are four-note chords
They are essentially triads with another note added on top; this note is a 7th above the root
note
Like triads, the top note is either a major or minor 3rd above the note directly beneath it
There are five 7th chord qualities: Major 7th, Minor 7th, Dominant 7th, Half diminished 7th
and Diminished 7th (although there are other ways to arrange the major and minor 3rds)
Also like triads, 7th chords can harmonize the major and minor scales
When we notate 7th chords, we always include a superscript "7" to the right of the chord
symbol (either a letter name, or a roman numeral)
And also like triads, the seventh chords built off the 5th and 7th scale degrees of a minor key
more often use the harmonic minor mode, which has the raised 7th in the scale
Additionally, the chord built off the raised 7th scale degree in minor could be either a half
diminished 7th chord or a diminished 7th chord
The dominant, half diminished and diminished 7th chords are the ones most frequently used
in classical style music, while jazz will regularly use the major and minor 7th chords as well
Major key 7th chords:
IM7
ii7
iii7
Minor key 7th chords:
i7
iio7
III M7
10
IVM7 V7
iv7
V7
vi7
viio7
(IM7)
VI M7 VII7/viio7 (i7)
INVERTING CHORDS
INVERTING CHORDS
The triads
triads and
and 7th
because
thethe
root of
The
7th chords
chords we
we have
have examined
examinedso
sofar
farare
arecalled
calledroot
rootposition
positionchords
chords
because
the
chord
is
the
lowest
note.
We
call
the
bottom
note
the
bass
note.
But
the
bass
note
of
a
chord
root of the chord is the lowest note. We call the bottom note the bass note. But the bass note of and
rootand
notethe
of root
a chord
always
thing.
athe
chord
noteare
of not
a chord
are the
not same
always
the same thing.
When we
we invert
invert aa chord
chord (just
(just like
like when
When
when we
we inverted
inverted intervals),
intervals), we
we re-arrange
re-arrange the
the order
orderofofthe
thenotes
while
not
actually
changing
the
notes
themselves.
A
step-by-step
approach
to
this
process
looks
notes while not actually changing the notes themselves. A step-by-step approach to this process like
this: like this:
looks
Term
7th Chord
Triad
Root
Position
The root
is in the bass
First
Inversion
The root moves
to the top (inverts),
leaving the 3rd of the
chord in the bass
Second
Inversion
The process repeats:
the bass note (the 3rd)
moves to the top, leaving
the 5th as the new bass note
Third
Inversion
(only for
7th chords)
The process repeats:
now the 7th of the chord
is in the bass
Note: all these inversions are in closed position, meaning that there is never more than an
octave between the lowest and highest note.
In listening to these different inversions, notice that while there is something different-sounding
In
listening
to thesethey
different
inversions,
notice
that Itwhile
is something
about
each chord,
moreover
sound the
same.
is as there
if each
inversion isdifferent-sounding
just a different hue of
about
eachcolor.
chord,Inthey
moreover
sound the
the same
same.notes
It is in
asany
if each
inversion
is merely
a different
the same
music
theory terms,
order
or arrangement
will
always make
hue
of
the
same
color.
In
music
theory
terms,
the
same
notes
in
any
order
or
arrangement
the same harmony, although each unique arrangement of the notes will have its own,will
unique
always
make
the same harmony (since harmony is not defined by the vertical order of the notes),
harmonic
"hue".
although each unique arrangement of the notes will have its own, unique harmonic "hue".
11
LABELING INVERSIONS
When a chord is inverted, the system used to show this with chord symbols is called slash
notation. Take a C major chord. In root position it is spelled C-E-G (or C-G-E) from the bottom
up. As long a C is the lowest note, the chord is in root position.
G
E
C
E
G
C
either of these configurations represents a root position C major chord: C
If the notes are arranged so that E is on the bottom, the chord is in 1st inversion. This would be
represented in a chord symbol as: C/E (described as “C over E”).
C
G
E
G
C
E
either of these configurations represents a 1st inversion C major chord: C/E
It follows the same for a 2nd inversion chord, which would have G on the bottom: C/G
E
C
G
C
E
G
either of these configurations represents a 2nd inversion C major chord: C/G
In Summary:
C
C/E
C/G
=
=
=
Cm =
Cm/Eb=
Cm/G =
Root position C major triad
1st inversion (C is the chord, E is the bottom note)
2nd inversion (C is the chord, G is the bottom note)
Root position C minor triad
1st inversion
2nd inversion
For 7th chords:
G7
G7/B
G7/D
G7/F
=
=
=
=
Root position G7 chord
1st inversion G7 chord
2nd inversion G7 chord
3rd inversion G7 chord
12
HARMONIC PROGRESSIONS
We already know the nuts and bolts of harmony, the origins of diatonic triads and 7th chords in
their possible inversions and how these inversions are represented via roman numeral and
figured bass notation. The next step is to arrange the diatonic chords into some kind of order that
makes “sense” according to common practice standards. To arrange and play chords/harmonies
in a particular order is to create a harmonic (or chord) progression. As the term implies, a
progression should be constructed such that the sequence of chords has a sense of direction and
“progress”, meaning that the progression is not aimless, but directed towards a goal. We can
liken this idea to the natural direction that we hear in a scale as it ascends and descends. While
the idea of direction or “goal-oriented” can be arguably subjective, the western music aesthetic
has some basic and consistent models that inform the notion of what a truly “progressive”
progression is.
DOMINANT TO TONIC MOTION
The most fundamental harmonic gesture in western music is based on the circle of 5ths/4ths
relationship of keys. This gesture (small progression) consists of chords whose roots move up a
4th or down a 5th (ii to V, iii to vi, I to IV, etc.) in the same way that the keys in the circle of 5ths
relate to one and other (G to C, C to F, etc.). The most “important” of these possible
combinations is the V to I progression (or V to i in minor). The V chord (the dominant) moves
up a 4th or down a 5th to the I or i chord (the tonic). This is called dominant to tonic motion. The
larger part of basic diatonic chord progressions is modeled after this 4th/5th root movement
relationship.
V → I/i
This ascending perfect 4th (dominant to tonic) progression informs other chord relationships that,
when put together, allow for larger progressions. If we consider the goal of a progression (like
the goal of a scale) to get back to, or just get to, the tonic (I/i), then we can work backwards from
the V to I/i sequence to see which chord would most typically precede the V chord. Given that
the V is a perfect 4th below the tonic, we can find the chord whose root is a perfect 4th below the
V chord’s root: the ii (we will stay in major for now).
ii → V → I
Likewise, the chord whose root is a perfect 4th below the ii chord is the vi.
vi → ii → V → I
13
A perfect 4th below the vi chord is the iii chord...and the same goes for the IV and viio chords
respectively.
IV → viio → iii → vi → ii → V → I
Remember that these particular chord sequences are derived from a single principal (the
ascending perfect 4th root) that underlies the aesthetic of western “classical” style music in
particular, and also a portion of jazz. As much as this chord progression serves the classical
style, other progressions based on other principals could represent other styles of music. The I –
IV– V – IV progression is something we would be less likely to hear in classical music, but be
very likely to hear in rock. This progression is the basis for Loui-Loui, La Bamba, Twist and
Shout and Good Lovin’, for example.
Based on the information deduced so far, we can construct a chart that shows the basic path that
chords follow in order to sound like a typical classical-style progression:
Major:
(I) → IV → viio → iii → vi → ii → V/V7 → I
Minor:
(i) → iv → VII → III → VI → iio → V/V7 → i
Note that the V7 chord has been added along-side the V triad. The V harmony is the most likely of all to have its 7th
added on
In either the major or minor mode, the ultimate goal of a progression is the tonic (even true in
rock, jazz and pop music most of the time). Because the tonic chord represents maximum
stability (or think of it as the strongest, most-inevitable stopping point: like in a scale), it can be
followed by any chord. In other words, the tonic’s sense of stability and neutrality resets the ear
and allows a progression to start over or resume from any chord. The tonic doesn’t require any
particular chord to follow it.
ADDITIONS AND EXCEPTIONS TO BASIC CHORD
PROGRESSIONS
As much as this up a perfect 4th principal underlies common practice style progressions, there
are exceptions. After all, if this were the only way to allow one chord to follow another, the
music would run out of interesting possibilities rather quickly. In either the major or minor keys,
the IV/iv and the viio chords can also act as substitute chords for the ii/iio and V/V7 chords
respectively. We can relocate these chords to the progression charts:
Major:
(I) → iii → vi → ii/IV → V(7)/viio → I
Minor:
(i) → iv* → VII → III → VI → iio/iv → V(7)/viio → i
14
*In the minor mode, the iv can be used in two different places in the progression chart–that’s
why it’s a “longer” chart.
MORE ADDITIONS AND EXCEPTIONS
Here are a few more alternative progressions (listed for major-key roman numerals, but it is the
same for minor-key chords.
•
•
•
•
V/V7 can go to vi (this is called a “deceptive” progression
IV can go to I (this is called a “plagal” progression)
viio can go to V, vi can go to IV and IV can go to ii (these are “descending 3rd”
progressions)
iii can go to IV
These addition combinations allow for each chord to have numerous options for “travel”. Still,
the main circle of 5ths style progression (iii – vi – ii – V(7) – I) is considered the most typical.
FUNCTION
The reason some chords can substitute for other chords is due to the notion of function. As long
as certain chords are fulfilling the proper function, the sense of progression is maintained. If we
liken function to food, consider the function of an appetizer, whether it be cheese and crackers,
fancy shrimp cocktail, or caviar. The appetizer functions as a pre-dinner food. It has its place in
an organized stage of events. If dessert immediately followed the appetizers, convention and
expectation would tell us that the order of events was “abnormal” (or in musical terms, “not
progressive”).
DOMINANT AND PRE-DOMINANT FUNCTION
In music, the idea of function is important because it identifies the purpose of something or a
group of things. In earlier examples, we recognized the function of the leading tone in the major
scale (it’s all in the scale!) to “lead” up to the tonic; it announces the imminent arrival of the
tonic note (which is why the harmonic and melodic minor modes add the leading tone; to
function like a major scale). Similarly, on a harmonic level, the V/V7 chord (the dominant) leads
to the I/i chord (tonic), as we learned in the first section about chord. So in other words, the
function of dominant harmony is that it leads to tonic harmony. In fact, this will be our new
definition of dominant harmony: harmony that wants to be followed by tonic harmony (the I or i
chord). Likewise, because the IV can substitute for the ii (or in minor keys, the iv for the iio), we
can call that group of chords “pre-dominant” because their usual purpose is to be followed by
dominant-functioning (V/viio) chords.
Pre-Dominant
→
Dominant
15
→
Tonic is the same as
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WHY THE viio FUNCTIONS
AS
A
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(V
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&
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In terms of function, the viio chord can be considered dominant. One reason for this is that the
notes in the viio chord are the same as the upper three notes of a V7 chord.
&
&
w
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7
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The top three notes of the G7 chord are the same as the notes of the Bo.
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In this sense, the pre-dominant, dominant and tonic relationships can be heard as an inevitable
process: each fulfilling a certain function that progresses to the next. Certainly these functions
could be re-ordered, but then they would be perceived as not adhering to the standard style of a
progression; like dessert following the appetizer. A re-ordering of the functions would simply
yield a type of progression that fits into a different style of music, perhaps folk, rock or pop.
Such progressions are not inherently “bad”, they are just stylistically different from the classical
sound much in the same way cubism is stylistically different from impressionism in the world of
painting.
16
HARMONIC PROGRESSIONS SUMMARY
•
•
•
•
•
•
•
•
A harmonic progression is a series of chords arranged in an order that makes “sense” and
suggests the feeling of progressing towards a goal
Harmonic progressions in the common practice style are based on chords whose roots move
up a perfect 4th or down a perfect 5th
This intervallic relationship is connected to the relationship of keys in the circle of 5ths
The most fundamental of all these possible progressions is the dominant to tonic (V/V7/viio to
I/i) because the ultimate goal of a progression is the tonic
We can work backwards from the up a perfect 4th/dominant to tonic relationship to find other
chords that fit the progression
In addition, there are some chords whose roots do not fit into the up a perfect 4th model, that
substitute for other chords
When chords can substitute for one and other, they fulfill the same harmonic function
On top of these other chords acting as functional substitutes, there are still other exceptions to
the basic progression model; where the up a perfect 4th root movement principal is not
adhered to – this allows for a wide variety of possible progressions
Major:
(I) → iii → vi → ii/IV → V(7)/viio → I
Minor:
(i) → iv* → VII → III → VI → iio/iv → V(7)/viio → i
Common Exceptions:
•
•
•
•
V/V7 can go to vi (this is called a “deceptive” progression
IV can go to I (this is called a “plagal” progression)
viio can go to V, vi can go to IV and IV can go to ii (these are “descending 3rd”
progressions)
iii can go to IV
*In the minor mode, the iv can be used in two different places in the progression chart–that’s
why it’s a “longer” chart.
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