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BASIC MUSIC THEORY

The staff is the foundation upon which notes are drawn. The modern staff comprises 5 lines and 4 spaces. Every line or space on the staff represents a white key on the keyboard.

Clefs assign individual notes to certain lines or spaces. Three (3) clefs are used: the Treble Clef (TC), the Bass Clef (BC) and the Grand Clef (GC).

The Treble Clef (TC) is also called the G Clef. The staff line around which the clef is wrapped is called the G line. Any note placed on this line becomes G. As the musical notes start from A to G, so the note on the space directly above G is A, and the note on the line above A is B and the process continue while placing notes on the staff. But when one runs out of room to place notes then come in the Ledger Lines (LL).

A Ledger Line (LL) is a small line that extends the staff when one runs out of room for placing notes on the original staff. With the LL drawn, one places on the note following the rule explained before.

The Bass Clef (BC) is also called the F Clef. The staff line in between the two (2) dots of the clef is the F line. Everything that is done with the Treble Clef for placing notes on the staff is as well exactly done with the Bass Clef.

The Grand Staff is a theoretical staff consisting of eleven lines where the middle line of all the eleven lines is eliminated giving place to two (2) regular staffs that we talked about before. A Treble Clef is added to the top staff and a Bass Clef added to the bottom staff. The space separating the 2 joined staffs is settled for a C note. This C is commonly called “Middle C” since it corresponds to the middle staff line on the Grand Staff.

Note Duration

The Note Duration is the length of time that a note is played and this length of time is related to the type of note played.

In modern music, the Whole Note (WN) has the longest note duration

The Half Note (HN) has half the duration of a Whole Note. It means that two (2) HN occupy the same amount of time as one WN.

The Quarter Note (QN) is a fourth (or a quarter) the time duration of a WN. It implies that four (4) QN occupies the same amount of time as one WN, and two (2) QN occupies the same amount of time as one HN.

Notes smaller in duration than the QN have flags and each flag halves the value of the time duration of the QN.

An Eighth Note (EN) has one flag. Therefore, two (2) EN occupies the same amount of time as does one QN.

Sixteenth Note (SN) has two flags, the second flag halving again the value of time duration of the privious note (the EN). Therefore, two (2) Sixteenth Notes equal one EN in time duration. Four (4) SN equal a QN in time duration.

It is possible to have notes with three (3) or more flags but they are seldom used so we won’t waste time discussing them here now.

Measures and Time Signature

Vertical bars called bar lines divide the Staff into measures. Staffs are mostly divided into four (4) measures but not only.

Time Signatures define the amount and type of notes that each measure contains.

The first measure is in 4/4 time and the second measure is in 3/4 time.

The first measure (4/4) contains four (4) Quarter Notes.

The second measure (3/4) contains three (3) Quater Notes.

There are also Non-Quarter-Notes Time Signatures like the 3/2 Time Signature that contains three (3) Half Notes, and the 6/8 Time Signature that contains six (6) Eighth Notes.

Rest Duration

Rests represent periods of silence in a measure. Each type of rest shares a duration with a certain type of note. For example, both a Quarter Rest (QR) and a Quater Note occupy the same amount of duration time. While the note would make a sound, the rest stays silent.

To demonstrate this, let’s fill a measure of 4/4 time with quarter notes. When played, all four notes sound. Next, when the third QN is replaced with a quarter rest and all played over again, the third beat is now silent. There are other types of rests too; the whole rest and the half rest

whole rest occupies the same amount of time as a Whole Note and a half rest also equal a Half Note in time duration.

The whole rest is drawn as a dark box descending from the fourth line of the Staff and the half rest is drawn as the same dark box ascending from the middle line of the Staff.

Rests also can have flags as do notes.

An eighth rest has one flag and has the same amount of time duration as does an Eighth Note.

sixteenth rest has two (2) flags and the same time duration as a Sixteenth Note.

Like notes, rests also can have three (3) or more flags; but they are rarely in use.

Dots & Ties

Augmentation Dots and Tenuto Ties are two (2) types of markings used to alter a note duration.

Steps & Accidentals

Half Step (HS) (or Semitone) is the interval or distance from one key on the keyboard to the next adjacent key. From any chosen key on the keyboard to the one next to it is a half step since they are still next to each other.

A Half Step is not always from a white key to a black key on the keyboard. As it happens from the B key (or the B note) to the C note which both are white keys, and from the E key to the F key on the keyboard which both are also white keys.

Whole Step (or a Whole Tone or simply Tone) is the same distance as two (2) Half Steps.

An Accidental is a sign used to raise or lower the pitch of a note. The most common used Accidentals are the Sharp represented as # and the Flat represented as b. The Sharp raises a note by a Half Step while the Flat lowers a note by a Half Step.

For instance, the black key between C and D can be called C-sharp (C#) since it is a Half Step above C, or D-flat (Db) since it is a Half Step below D. Also E can be called F-flat (Fb) since it is a Half Step below F and F can be called E-sharp (E#) since F is a Half Step above E.

Whenever a certain pitch has multiple names, it is called an enharmonic spelling.
There is also a Double Sharp and a Double Flat as Accidentals. While Flats and Sharps alter a note by a Half Step, Double Sharps and Double Flats alter a note by a Whole Step.
A Double Sharp is represented by an x while a Double Flat is represented by a bb.
In essence, both D and Ebb have the same pitch since one can reach D by going a Whole Step [or two (2) Half Steps] down from E. D also sounds the same as Cx since D is a Whole Step above C.

Natural cancels out any Accidental and returns the note to its original white key.

RHYTHM AND METER

Simple and Compound Meter

Each time signature can be classified into a certain Meter.

Duple, Triple, and Quadruple are the terms used to refer to the number of beats in a measure. If these beats can be broken into two (2) notes, then the term Simple is used.
For instance, the 2/4 time is classified as Simple Duple; and Duple refers to the two (2) beats per measure, but Simple states that each of these beats can be divided into two (2) notes. 2/2 and 2/8 are also Simple Duple.
3/4 time is classified as Simple TripleTriple refers to the three (3) beats per measure and again, Simple states that each of these beats can be divided into two (2) notes. 3/2 and 3/8 are also Simple Triple.
4/4 time is classified as Simple Quadruple. We understand then that we have here four (4) beats per measure and each beat can be divided into two (2) notes.
We then have 4/2 and 4/8 as Simple Quadruple too.
We can notice that a time signature in the Simple Meter will always have a 2, 3, or 4 for the top number.

While beats in the Simple Meter are divided into two (2) notes, beats in the Compound Meter are divided into three (3) notes. To demonstrate this, we will examine the 6/8 time.
The Six Eighth Notes can either be grouped into two (2) beats (Compound Duple) or three (3) beats (Simple Triple).
Since the Simple Triple pattern already belongs to 3/4 time, 6/8 is a Compound Duple. Therefore each beat in 6/8 time is a dotted quarter note like it is in all Compound Meters.
Any time signature with a 6 on top is a Compound Duple. 6/8 and 6/4 are the most commonly used.
9/8 time is classified as a Compound Triple. There are three (3) beats (three dotted quarter notes), thus making the meter Triple. Since each beat is made up of three notes, the meter is Compound.
Any time signature with a 9 on top is Compound Triple. Although 9/8 is the most commonly used, 9/29/4; and 9/16 can also be used.
12/8 time is classified as a Compound Quadruple. There are four (4) beats thus making the meter Quadruple.
Since each beat is made up of three (3) notes, the meter is Compound.
Any time signature with a 12 on top is a Compound Quadruple, and 12/8 and 12/16 are the most commonly used.

Odd Meter

An Odd Meter is a meter which contains both simple and compound beats.
The first Odd Meter that will be discussed is the 5/8 time. It contains one simple beat and one compound. The order of the beats does not matter. if the compound beat comes first, it is still 5/8 time.
Odd Meters with three (3) total beats.
7/8 time contains two (2) simple beats and one compound beat. Again, the order of the beats does not matter. The compound beat can even be positioned between two (2) simple beats.
8/8 time contains two (2) compound beats and one simple beat. Sometimes, people confuse 8/8 with 4/4, since both have eight (8) notes.
Notice that 4/4 groups the measure into four (4) beats of two (2) eight notes (simple quadruple), while 8/8 groups it into three odd beats.
The last two odd meters have a total of four beats.
10/8 time has two (2) compound beats and two (2) simple beats.
11/8 time has three (3) compound beats and one (1) simple beat.

SCALES AND KEY SIGNATURES

Scale is a selection of certain notes within an octave. The first Scale of discussion is the Major Scale

The MAJOR Scale

The Major Scale is constructed with the following formula:
0-WS-WS-HS-WS-WS-WS-HS
0 = The starting point
WS = Whole Step
HS = Half Step

To build the C Major Scale, the starting point will be the C note.
From the C, a Whole Step (WS) lands on the D note.
From the D, another WS lands on the E note.
From the E now, a Half Step (HS) is landing on the F note.
From the F, the WS brings to the G note.
From the G, another WS lands on the A note.
From the A, the last WS brings to the B note.
And finally, from the B note, a HS returns on the C note.
The C Major Scale is then: C D E F G A B C.

We proceed on to build the Eb Major Scale, which means our starting point is Eb.
From the Eb, the first WS lands us on the F note.
From the F, the next WS lands us on the G note.
From the G on, a HS is landing us on the Ab note [ not the G# because there can’t be two (2) times G note in the Scale].
From the Ab, the WS brings us to the Bb note.
From the Bb, the next WS lands us on the C note.
From the C, the next WS brings us to the D note.
And finally, from the D note, a HS returns us on to the Eb note.
So the Eb Major Scale is the following: Eb F G Ab Bb C D Eb.
Notice that the Eb Major Scale has three (3) flats [only one (1) Eb is taken to account here]

For a third example, let’s build the D Major Scale.
The first WS takes us from the D note (the starting point) to the E note.
From the E, the next WS takes us to the F# note.
From the F#, the HS lands us on the G note.
The next WS from the G lands us on the A note.
From the A, the WS lands us on the B note.
From the B, the last WS takes us to the C# note.
And finally, the HS from the C# returns us onto the D note.
The D Major Scale is the following: D E F# G A C# D.
D Major Scale has two (2) sharps.

It is possible to build any Major Scale just by starting on the beginning note an follow the formula.

MINOR Scales

While there is only one Major Scale, there are three (3) different variations of the MINOR Scale.

The Natural MINOR Scale

The Natural MINOR Scale is constructed with the following formula:
0-WS-WS-HS-WS-WS-WS-HS

Let’s build the A Natural Minor Scale. The starting point is the A note.
Following the formula, we go a Whole Step (WS) from A to B.
From B, the next step is a Half Step (HS) to C.
Next is a WS from C to D.
From D, we take another WS to E.
Next is a HS from E to F.
Next, from F, we take a WS to G.
And finally, the last WS brings us back from G to A.
A Natural Minor is then the following: A B C D E F G A.
Notice that the A Natural Minor Scale has no notes with the Accidentals.

Second, let’s built the G# Natural Minor Scale with the starting point of course as G#.
The formula makes us go first a WS from G# to A#.
From A#, the next step is a HS to B.
Next is a WS from B to C#.
From C#, we take another WS to D#.
Next is a HS, and it brings us from D# to E.
Next, from E, we take a WS to F#.
And finally, we take the last WS that brings us back from F# to G#.
G# Natural Minor is then as followed: G# A# B C# D# E F# G#.
Notice that the G# Natural Minor Scale has five (5) sharps.

This time let’s built the C Natural Minor ScaleC is the starting point.
Again according to the formula, we go first a WS from C to D.
From D, the next step to take is a HS to Eb (because there can’t be D note twice on the same scale).
Next is a WS from Eb to F.
From F, we take another WS to G.
Next is a HS from G to Ab.
Next, from Ab, we take a WS to Bb.
And in the end, the last WS brings us back from Bb to C.
C Natural Minor is then the following: C D Eb F G Ab Bb C.
Notice that the C Natural Minor Scale has three (3) flats.

The Harmonic MINOR Scale

To convert a Natural Minor Scale into the Harmonic Minor Scale, the seventh (7th) note of the Natural Minor Scale is raised by a Half Step.

Let’s convert the C Natural Minor Scale into Harmonic C Minor Scale.
By simply raising the 7th note (Bb) of the C Natural Minor Scale by a HS resulting in a B note, the Harmonic C Minor Scale is then written as the following: C D Eb F G Ab B.

The Melodic MINOR Scale

To convert a Natural Minor Scale into the Melodic Minor Scale, both the sixth (6th) and seventh (7th) notes of the Natural Minor Scale are raised by a Half Step.

For instance, to convert the C Natural Minor Scale into a Melodic C Minor Scale, we simply raise the Ab and the Bb a HS resulting in A and a B notes.
The Melodic C Minor Scale is as followed: C D Eb F G A B.

Usually, the Melodic Minor is used only when ascending. When descending, composers prefer to use the Natural Minor Scale.

Scale Degrees

Each note of a scale has a special name, called a Scale Degree.
The first (and last) note is called the Tonic.
The fifth note is called the Dominant.
The fourth note is called the Subdominant.
It should be noticed that the Subdominant is the same distance below the Tonic as the Dominant is above the Tonic (a generic Fifth). The prefix Sub is a Latin for “Under” or “Beneath“.
The third note is called the Mediant since it is in the middle between the Tonic and the Dominant.
Likewise, the sixth note is called the Submediant since it is in the middle of the upper Tonic and Subdominant.
The second note is called the SupertonicSuper is a Latin for “Above”.

While the Scale Degrees for the first six (6) notes are the same for both Major and Minor Scales, the seventh (7th) one is special.
If the 7th note is a Half Step (HS) below the Tonic, it is called a Leading Tone. By playing the C Major Scale, one can notice how the 7th note wants to lead into the Tonic.
Leading Tones also occur in Harmonic Minor and Melodic Minor Scales.
In the Natural Minor Scale, the 7th note is a Whole Step (WS) below the Tonic and is called in this case as a Subtonic.
When playing the C Natural Minor Scale, it is to notice how the 7th tone lacks the desire to lead into the Tonic.
A number with a caret may also be used to indicate a Scale Degree. For instance, the Dominant of a scale (like it happens in the C Major Scale with the G note) may be labelled as a fifth (5th) a caret.

Key Signatures

Key Signature is a collection of every Accidental found in a Scale.
We will use the C Natural Minor Scale which has three (3) flats to demonstrate this.
Instead of writing a flat next to every EA, and B; it’s simply easy to add a Key Signature to the beginning of the measure.
Next, let’s examine Db Major Scale which has five (5) flats.
Again, a Key Signature can be used instead of writing each Accidental next to the appropriate note.
One should notice that the flats are arranged in a special order:
Bb comes first, followed by EbAbDb, and Gb. Next comes Cb and finally Fb.
For remembering this order, one can use the following saying: “Battle Ends And Down Goes Charles’ Father”.

Key Signatures can also comprise Sharps.
Let’s try A Major Scale, which has three (3) sharps to demonstrate this. The C#F#, and G# move into the Key Signature.
Finally, the E Major Scale, with four (4) sharps is another example to try; and we have F#, G#, C#, and D# moving into the Key Signature.
Sharps are arranged in the opposite order of flats.
F# comes first, followed by C#, G#, and D#. Next, A#E#, and finally B#.
One can remember this order by using the following saying: “Father Charles Goes Down And End Battle”.

Key Signature Calculation

30 different Key Signatures exist (15 for Major Scales and 15 for Minor Scales). Most theory students are expected to memorize all 30.
Fortunately, using the Key Signature Calculation Method, one only has to memorize seven (7).
In the calculation method, each Key Signature is assigned a numeric value based on the number and type of AccidentalsSharps are positive (+)Flats are negative (-).

The Key of C Major Scale has no Accidentals; therefore, its numeric value is 0.
The Key of D Major Scale has two (2) Sharps; thus, its numeric value is 2.
The Key of E Major Scale has four (4) Sharps; and, its numeric value is 4.
The Key of F Major Scale has one (1) Flat; and, its numeric value is -1.
The Key of G Major Scale has one (1) Sharp. Its numeric value is 1.
The Key of A Major Scale has three (3) Sharps; with a numeric value of 3.
And finally, the Key of B Major Scale has five (5) Sharps; giving it a numeric value of 5.
These seven (7) values must necessarily be memorized for the rest of the calculation.
Let’s compare Cb Major Scale, C Major Scale, and C# Major Scale.
If we start with C Major and subtract 7, we end up at Cb Major.
If we start with C Major and add 7, we end up at C# Major.
These two numeric relationships can help us calculate the keys that we do not know.
Let’s figure out Eb Major.
We start first with E Major which has a numeric value of 4. To convert it to Eb Major, we subtract 7; and the result gives us -3. Thus, Eb Major has 3 Flats.
Let’s try now with F# Major by starting with F Major with -1 as a numerical value. By adding 7 to convert it to F# Major, we get the result 6. Thus, F# Major has 6 Sharps.

We examine now Minor Scales.
Comparing C Major and C Minor.
To convert a Major Scale to its parallel Minor, simply subtract 3.
Let’s calculate D Minor by starting with D Major with a numeric value of 2.
Next, we simply subtract 3; and the result gives us -1. Therefore, D Minor has 1 Flat.
Let’s try it now with F Minor.
We start with F Major with a numeric value of -1. We subtract 3 and we get -4 as a result. F Minor has then 4 Flats.

Some Key Signatures require two conversions. For instance, let’s calculate C# Minor.
We start with C Major with a numerical value of 0. Next, we add 7 to get first to C# Major, which will give us 7 as numerical value; and then we finally subtract 3 to convert C# Major to the C# Minor.
C# Minor therefore has 4 Sharps.

Using the calculation method, it is possible to calculate Key Signatures which have more than seven (7) Accidentals.
While these exist in theory; in practice, they would not be used.
For instance, let’s calculate the G# Major.
We start with G Major which has a numeric value of 1. Next, we add 7 to convert it into G# Major. And we get the result 8 as a numerical value of the G# Major, meaning that the G# Major has 8 Sharps. A double sharp and six (6) normal sharps.
Again, this key is strictly theoretical. In practice, a composer would use the enharmonic equivalent of Ab Major.

INTERVALS

An Interval measures the distance between two (2) notes.

Generic Intervals

When two (2) notes occupy the same line or space, they are first (or a prime) apart.
C to C is an example of a first.
D to D and E to E are also firsts.
Accidentals are ignored when measuring generic intervals; only Staff position matters.
C-C#D-Db, and A#-Ab are still firsts.
As notes become further apart on the Staff, the Interval type increases.
C-DD-E, and E-F are all seconds.
C-ED-F, and E-F are all thirds.
Notice that thirds will always share the same Staff position type (either both on a line or both on a space.
C-FD-G, and E-A are all fourths.
C-GD-A, and E-B are all fifths.
C-AD-C, and E-C are all sixths.
C-BD-C, and E-D are all sevenths.
C-CD-D, and E-E are all eighths.

Specific Intervals

Specific Intervals are measured both on the Staff and in Half Steps (HS) on the Keyboard.
As we learned in the previous lesson, C to D and C to Db are both generic seconds; especially, however, C to D is one HS larger than C to Db.
Let’s learn a few Specific Intervals.

Major second is made up of two (2) HSs.
C to D is a Major second since it is a generic second on the Staff and two (2) HSs on the Keyboard.
E to F# would be another example of a Major second.

Major third is made up of four (4) HSs.
C to E is a Major third.
E to G# is also a Major third.

Perfect fourth is made up of five (5) HSs.
C to F is a Perfect fourth.
F to Bb is also a Perfect fourth.

Perfect fifth is made up of seven (7) HSs.
C to G is a Perfect fifth.
B to F# is also a Perfect fifth.

Major sixth is made up of nine (9) HSs.
C to A is a Major sixth.
Eb to C is also a Major sixth.

Major seventh is made up of eleven (11) HSs.
C to B is a Major seventh.
D to C# is also a Major seventh.

Finally, a Perfect eighth (or Perfect Octave) is made up of twelve (12) HSs.
C to C is a Perfect eighth.

The terms Major and Perfect refer to the Interval‘s quality.
Only seconds, thirds, sixths, and sevenths can have a Major qualityFirsts, fourths, fifths, and eighths use Perfect instead.

Let’s discuss Minor Intervals now.
HSs)
Minor Interval has one less Half Step (HS) than a Major Interval.
For example, since C to E is a Major third (4 HSs), C to Eb is a Minor third (3 HSs).
E to G is also a Minor third (since E to G# is a Major third).
Since Minor Intervals transform from Major Intervals; only seconds, thirds, sixths, and sevenths can be Minor.

An Augmented Interval has one more HS than a Perfect Interval.
Since C to F is a Perfect fourth (5 HSs), C to F# would be an Augmented fourth (6 HSs).
F to B is also an Augmented fourth (since F to Bb is a Perfect fourth).

Major Intervals can be augmented by adding a Half Step.
For instance, since C to A is a Major sixth (9 HSs), C to A# is an Augmented sixth (10 HSs).
Db to B is also an Augmented 6th (since Db to Bb is a Major Sixth).

Diminished Interval has one less HS than a Perfect Interval.
Since C to G is a Perfect fifth (7 HSs), C to Gb would be a Diminished fifth (6 HSs).
B to F is also a Diminished fifth (since B to F# is a Perfect fifth).

Minor Intervals can also be diminished by subtracting a HS.
Recall that C to B is a Major seventh (11 HSs) and C to Bb is a Minor seventh (10 HSs).
C to Bbb is a Diminished seventh (9 HSs).

Writing Intervals

When writing Intervals on the Staff, it is common to confuse Intervals with the same number of Half Steps (HSs).
For example, one may accidentally write C to F# (an Augmented fourth) instead of C to Gb (a Diminished fifth).
Although both Intervals sound the same and look identical on the Keyboard, one is fourth and the other is a fifth.
Fortunately, an easy three-step process exists to reduce the risk of this mistake.

Let’s write a Minor third from C.
First, we write the generic interval on the Staff. For this example, we will write a generic third. Next, we figure out the number of HSs on the Keyboard. Since a Major third is a 4 HSs, our Minor third will be 3 HSs.
Finally, we compare the Staff and the Keyboard results. We add any needed Accidentals to the Staff.
C-Eb is a Minor third.

For our next example, let’s try a Major sixth from F#.
After writing the generic sixth on the Staff, we figure out the HSs on the Keyboard. A Major sixth is 9 HSs.
Finally, we add any needed Accidentals.
F#-D# is a Major sixth.

For our final example, we will write a Diminished fifth from B.
First is writing the generic fifth on the Staff. Next is to figure out the Half Steps on the Keyboard.
Since a Perfect fifth is 7 HSs, our Diminished fifth has 6 HSs. Finally, we add any needed Accidentals.
In this example, no Accidental is needed. B-F is a Diminished fifth.

Interval Inversion

In Music, the verb invert means to move the lowest note in a group an octave higher.
In this lesson, we will be inverting Intervals.

For our first example, let’s invert a Perfect fifthC to G.
To invert this Interval, we move the lowest note (the C) an octave higher, which will result in a Perfect fourthG to C.

Next, we invert a Perfect fourthF# to B by moving the lowest note (the F#) an octave higher; and we get a Perfect fifthB to F#.

Perfect Intervals will always invert to other Perfect IntervalsFourths and fifths will invert to each other.

Let’s invert a Major thirdC to E by moving the lowest note (the C) an octave higher. The result gives us a Minor sixthE to C.

Let’s invert a Minor thirdE to G by moving the E note an octave higher. The result gives us a Major sixthG to E.

Minor Intervals and Major Intervals invert to each other. Tirths and sixths invert to each other.
Let’s invert a Major seventhC to B by moving the C note an octave higher. The result is a Minor secondB to C.
Seconds and sevenths invert to each other.

Let’s invert finally Diminished and Augmented Intervals to each other.
To demonstrate this, we will invert an Augmented fourthC to F#.
By moving the C an octave higher we get a Diminished fifthF# to C.

CHORDS

Introduction to Chords

Chord is a combination of three or more notes.
Chords are built off of a single note called the root note.
In this lesson, we will discuss Triads. They are created with a root notethird, and fifth.

Triads

Major Triad (or Major Chord) is built with a Major third and a Perfect fifth from the root note.
Let’s write a C Major Triad. First, we write the root (C) on the Staff. Next, we write the generic third and the generic fifth from the root.
We now need to determine the specific intervals on the Keyboard. Since we need a Major third, let’s count up four (4) Half Steps (HSs) from the root. For the Perfect fifth, we go back to the root and count up seven (7) HSs.
As the Chord contains no black keys, we do not need to write any Accidentals on the Staff.
C Major Triad is C-E-G.

Next, let’s try an Eb Major Triad.
We write the generic third and fifth on the Staff. We switch then to the Keyboard and start counting from Eb. For the Major third, we count up four (4) HSs and for the Perfect fifth we count up 7 HSs (still from Eb).
Finally, we write any Accidentals in addition to the already-written Eb; we need a flat next to the B.
An Eb Major Triad is Eb-G-Bb.

Now, let’s try a B Major Triad by writing first the generic third and fifth on the Staff.
Next, we count on the Keyboard, the Major third (4 HSs) and Perfect fifth (7 HSs) starting each time from the B note.
Finally, we write the needed Accidentals on the Staff. We need two (2) sharps, one for the D and one for the F.
B Major Triad is B-D#-F#.

This time, we will discuss the Minor Triad.
It is created with a Minor third and a Perfect fifth from the root note.
Let’s build a C Minor Triad.
We write first the generic third and fifth on the Staff. Then we switch to the Keyboard to count the HSs from C. We count up three (3) HSs for the Minor third, and go back to the C again and count up seven (7) HSs for the Perfect fifth. Finally, we write any needed Accidentals.
C Minor Triad is C-Eb-G.

Let’s build an Eb Minor Triad.
The generic third and fifth are first to write on the Staff. Then we go to the Keyboard for counting the Minor third (3 HSs) and the Perfect fifth (7 HSs), both starting from the Eb.
Finally, we write any needed Accidentals.
An Eb Minor Triad is Eb-Gb-Bb.

Let’s build a B Minor Triad.
We write first the generic third and fifth on the Staff. Then we switch to the Keyboard to count the HSs from B. We count up three (3) HSs for the Minor third, and go back to the B again and count up seven (7) HSs for the Perfect fifth. Finally, we write any needed Accidentals.
B Minor Triad is B-D-F#.

The Augmented Triad is built with a Major third and an Augmented fifth.
Let’s built a C Augmented Triad.
The generic third and fifth are first to write on the Staff. Then we go to the Keyboard for counting the Major third (4 HSs) and the Augmented fifth (8 HSs), both starting from the C.
Finally, we write any needed Accidentals.
An C Augmented Triad is C-E-G#.

Let’s build a B Augmented Triad.
We write first the generic third and fifth on the Staff. Then we switch to the Keyboard to count the HSs from B. We count up four (4) HSs for the Major third, and go back to the B again and count up eight (8) HSs for the Augmented fifth. Finally, we write any needed Accidentals.
B Augmented Triad is B-D#-Fx.

The last Triad that we are going to discuss now is the Diminished Triad.
It is built with a Minor third and a Diminished fifth.

Let’s build a C Diminished Triad.
We write first the generic third and fifth on the Staff. Then we switch to the Keyboard to count the HSs from C. We count up three (3) HSs for the Minor third, and go back to the C again and count up six (6) HSs for the Diminished fifth. Finally, we write any needed Accidentals.
C Diminished Triad is C-Eb-Gb.

Let’s build an Eb Diminished Triad.
The generic third and fifth are first to write on the Staff. Then we go to the Keyboard for counting the Minor third (3 HSs) and the Diminished fifth (6 HSs), both starting from the Eb.
Finally, we write any needed Accidentals.
An Eb Diminished Triad is E-Gb-Bbb.

Next, let’s built a B Diminished Triad.
We write the root note, the generic third and fifth (the generic Intervals) first on the Staff. Then we go to the Keyboard for counting the Minor third (HSs) and the Diminished fifth (6 HSs), both starting from the B.
Finally, we write any needed Accidentals. No Accidentals are needed.
B Diminished Triad is B-D-F.

Triad Iversion

Like IntervalsTriads can be inverted by moving the lowest note up an octave.
The lowest note, called the bass note, determines the name of the inversion.
When the lowest note is the root of the Chord, the Triad is in root position.

The Chord is now inverted.
The bass note is now the third of the Chord.
This is called First Inversion.

The Chord is inverted again.
Now, the fifth is the lowest note of the Chord.
This is called Second Inversion.

When the Chord is inverted one more time, we notice that the Triad returns to the root position.

Seventh Chords

Seventh Chord is a combination of a Triad and an Interval of a seventh.
Five types of Seventh Chords are commonly in use.

Major Triad and a Minor Seventh combine to form a Dominant Seventh Chord.
Dominant Seventh Chords are abbreviated with a simple 7.

Let’s examine a C Dominant Seventh Chord (C7).
C-E-G is the Major Triad.
C-Bb is the Minor Seventh.
When combined, they form a C Dominant Seventh ChordC-E-G-Bb.

Next, let’s examine an F# Dominant Seventh Chord (F#7).
F#-A#-C# is the Major Triad.
F#-E is the Minor Seventh.
When combined, they form an F# Dominant Seventh ChordF#-A#-C#-E.

Now, let’s examine an Ab Dominant Seventh Chord (Ab7).
Ab-C-Eb is the Major Triad.
Ab-Gb is the Minor Seventh.
When combined, they form an Ab Dominant Seventh ChordAb-C-Eb-Gb.

Major Triad and a Major Seventh combine to form a Major Seventh Chord.
Major Seventh Chords are abbreviated with a capital ‘M‘ and a 7.

Let’s examine a C Major Seventh Chord (CM7).
C-E-G is the Major Triad.
C-B is the Major Seventh.
When combined, they form a C Major Seventh ChordC-E-G-B.

Now let’s examine an F# Major Seventh Chord (F#M7).
F#-A#-C# is the Major Triad.
F#-E# is the Major Seventh.
When combined, they form an F# Major Seventh ChordF#-A#-C#-E#.

Next, let’s examine an Ab Major Seventh Chord (AbM7).
Ab-C-Eb is the Major Triad.
Ab-G is the Major Seventh.
When combined, they form an Ab Major Seventh ChordAb-C-Eb-G.

Minor Triad and a Minor Seventh combine to form a Minor Seventh Chord.
Minor Seventh Chords are abbreviated with a lower-case ‘m‘ and a 7.

Let’s examine a C Minor Seventh Chord (Cm7).
C-Eb-G is the Minor Triad.
C-Bb is the Minor Seventh.
When combined, they form a C Minor Seventh ChordC-Eb-G-Bb.

Now let’s examine an F# Minor Seventh Chord (F#m7).
F#-A-C# is the Minor Triad.
F#-E is the Minor Seventh.
When combined, they form an F# Minor Seventh ChordF#-A-C#-E.

Next, let’s examine an Ab Minor Seventh Chord (Abm7).
Ab-Cb-Eb is the Minor Triad.
Ab-Gb is the Minor Seventh.
When combined, they form an Ab Minor Seventh ChordAb-Cb-Eb-Gb.

Diminished Triad and a Minor Seventh combine to form a Half-Diminished Seventh Chord.
Half-Diminished Seventh Chords are abbreviated with a slashed circle ‘o/‘ and a 7.

Let’s examine a C Half-Diminished Seventh Chord (Co/7).
C-Eb-Gb is the Diminished Triad.
C-Bb is the Minor Seventh.
When combined, they form a C Half-Diminished Seventh ChordC-Eb-Gb-Bb.

Next, let’s examine an F# Half-Diminished Seventh Chord (F#o/7).
F#-A-C is the Diminished Triad.
F#-E is the Minor Seventh.
When combined, they form an F# Half-Diminished Seventh ChordF#-A-C-E.

Now let’s examine an Ab Half-Diminished Seventh Chord (Abo/7).
Ab-Cb-Ebb is the Diminished Triad.
Ab-Gb is the Minor Seventh.
When combined, they form an Ab Half-Diminished Seventh ChordAb-Cb-Ebb-Gb.

Finally, a Diminished Triad and a Diminished Seventh combine to form a Diminished Seventh Chord (or Fully-Diminished Seventh Chord).
Diminished Seventh Chords are abbreviated with an open circle ‘o‘ and a 7.

Let’s examine a C Diminished Seventh Chord (Co7).
C-Eb-Gb is the Diminished Triad.
C-Bbb is the Diminished Seventh.
When combined, they form a C Diminished Seventh ChordC-Eb-Gb-Bbb.

Next, let’s examine an F# Diminished Seventh Chord (F#o7).
F#-A-C is the Diminished Triad.
F#-Eb is the Diminished Seventh.
When combined, they form an F# Diminished Seventh ChordF#-A-C-Eb.

Now let’s examine an Ab Diminished Seventh Chord (Abo7).
Ab-Cb-Ebb is the Diminished Triad.
Ab-Gbb is the Diminished Seventh.
When combined, they form an Ab Diminished Seventh ChordAb-Cb-Ebb-Gbb.

More Seventh Cords

Additional types of Seventh Chords can occur in POPular Music and Jazz.
Let’s learn about three of these additional types of Seventh Chords.

Minor Triad and a Major Seventh combine to form a Minor-Major Seventh Chord.
Minor-Major Seventh Chords are abbreviated with a lower-case ‘m‘, capital ‘M‘, and a 7.

Let’s examine a C Minor-Major Seventh Chord (CmM7).
C-Eb-G is the Minor Triad.
C-B is the Major Seventh.
When combined, they form a C Minor-Major Seventh ChordC-Eb-G-B.

Now let’s examine an F# Minor-Major Seventh Chord (F#mM7).
F#-A-C# is the Minor Triad.
F#-E# is the Major Seventh.
When combined, they form an F# Minor-Major Seventh ChordF#-A-C#-E#.

Next, let’s examine an Ab Minor-Major Seventh Chord (AbmM7).
Ab-Cb-Eb is the Minor Triad.
Ab-G is the Major Seventh.
When combined, they form an Ab Minor-Major Seventh ChordAb-Cb-Eb-G.

An Augmented Triad and a Major Seventh combine to form an Augmented-Major Seventh Chord.
Augmented-Major Seventh Chords are abbreviated with a plus (+), capital ‘M‘, and a 7.

Let’s examine a C Augmented-Major Seventh Chord (C+M7).
C-E-G# is the Augmented Triad.
C-B is the Major Seventh.
When combined, they form a C Augmented-Major Seventh ChordC-E-G#-B.

Now let’s examine an F# Augmented-Major Seventh Chord (F#+M7).
F#-A#-Cx is the Augmented Triad.
F#-E# is the Major Seventh.
When combined, they form an F# Augmented-Major Seventh ChordF#-A#-Cx-E#.

Next, let’s examine an Ab Augmented-Major Seventh Chord (Ab+M7).
Ab-C-E is the Augmented Triad.
Ab-G is the Major Seventh.
When combined, they form an Ab Augmented-Major Seventh ChordAb-C-E-G.

Finally, an Augmented Triad and a Minor Seventh combine to form an Augmented Seventh Chord.
Augmented Seventh Chords are abbreviated with a plus (+), and a 7.

Let’s examine a C Augmented Seventh Chord (C+7).
C-E-G# is the Augmented Triad.
C-Bb is the Minor Seventh.
When combined, they form a C Augmented Seventh ChordC-E-G#-Bb.

Now let’s examine an F# Augmented Seventh Chord (F#+7).
F#-A#-Cx is the Augmented Triad.
F#-E is the Minor Seventh.
When combined, they form an F# Augmented Seventh ChordF#-A#-Cx-E.

Next, let’s examine an Ab Augmented Seventh Chord (Ab+7).
Ab-C-E is the Augmented Triad.
Ab-Gb is the Minor Seventh.
When combined, they form an Ab Augmented Seventh ChordAb-C-E-Gb.

Seventh Chord Inversion

Like TriadsSeventh Chords can be inverted by moving the lowest note up an octave.
Root position is the same as a Triad – the root is the lowest (bass) note.

Let’s invert the Chord.
The First inversion is also the same as in Triad – the third is the lowest note.

Let’s invert the Chord again.
The Second inversion is also the same as in Triad – the fifth is the lowest note.

Let’s invert the Chord another time.
Now, the Seventh is the lowest note of the Chord. This is called the Third inversion.

Let’s invert the Chord one more time.
It is to notice that the Chord returns to the root position.

DIATONIC CHORDS

Diatonic Triads

Every Major and Minor Scale has seven (7) Special Triads, called Diatonic Triads, which are formed from that Scale‘s notes.
To discover the Diatonic Triads, a three (3) step process must be used.

First, the Scale must be constructed.
For our first example, we will be using the C Major Scale.
Next, we stack two (2) generic thirds on top of each note.
And finally, we analyze the resulting Triads.

The First Triad is C-E-G, a Major third, and a Perfect fifth. Therefore, the Triad is Major.
The Second Triad is D-F-A, a Minor third, and a Perfect fifth. Therefore, the Triad is Minor.
The Third Triad is E-G-B, a Minor third, and a Perfect fifth. Therefore, the Triad is also Minor.
The Fourth Triad is F-A-C, a Major third, and a Perfect fifth. Therefore, the Triad is also Major. The Fifth Triad is G-B-D, a Major third, and a Perfect fifth. Therefore, the Triad is also Major.
The Sixth Triad is A-C-E, a Minor third, and a Perfect fifth. Therefore, the Triad is also Minor.
The Seventh Triad is B-D-F, a Minor third, and a Diminished fifth. Therefore, the Triad is Diminished.
The Eighth Triad is a repetition of the First (C-E-G), making it Major.
The First Triad of a Major Scale will always be Major, the Second and Third Triads will always be Minor, etc.

Next, we will uncover the Diatonic Triads of the C Natural Minor Scale.
First, we construct the ScaleKey Signature will be used rather than placing the Accidentals by each note.
Again, we stack two (2) generic thirds on top of each note.
Finally, we analyze the resulting Triads.

The First Triad is C-Eb-G, a Minor third, and a Perfect fifth. Therefore, the Triad is Minor.
The Second Triad is D-F-Ab, a Minor third, and a Diminished fifth. Therefore, the Triad is Diminished.
The Third Triad is Eb-G-Bb, a Major third, and a Perfect fifth. Therefore, the Triad is Major.
The Fourth Triad is F-Ab-C, a Minor third, and a Perfect fifth. Therefore, the Triad is also Minor. The Fifth Triad is G-Bb-D, a Minor third, and a Perfect fifth. Therefore, the Triad is also Minor. The Sixth Triad is Ab-C-Eb, a Major third, and a Perfect fifth. Therefore, the Triad is also Major. The Seventh Triad is Bb-D-F, a Major third, and a Perfect fifth. Therefore, the Triad is also Major.
The Eighth Triad is a repetition of the First (C-Eb-G), making it Minor.

Now the discussion is about the Diatonic Triads of Harmonic Minor.

To convert Natural Minor to Harmonic Minor, the seventh tone is raised a Half Step (HS). Therefore, each Bb (the seventh tone of C Natural Minor) is raised to a B.
Since the Third, Fifth, and Seventh Chords have been altered, they need to be reanalyzed.

The Third Triad is now Eb-G-B, a Major third and an Augmented fifth. Therefore, it is an Augmented.
The Fifth Triad is now G-B-D, a Major third, and a Perfect fifth. Therefore, it is a Major.
The Seventh Triad is now B-D-F, a Minor third, and a Diminished fifth. Therefore, it is a Diminished.

Finally, are going to discuss the Diatonic Triads of Melodic Minor.

To convert Natural Minor to Melodic Minor, the sixth tone is raised a Half Step (HS). Therefore, each Ab (the sixth tone of C Natural Minor) is raised to A.
Since the Second, Fourth, and Sixth Chords have been altered, they need to be reanalyzed.

The Second Triad is now D-F-A, a Minor third, and a Perfect fifth. Therefore, it is Minor.
The Fourth Triad is now F-A-C, a Major third, and a Perfect fifth. Therefore, it is a Major.
The Sixth Triad is now A-C-Eb, a Minor third, and a Diminished fifth. Therefore, it is a Diminished.

Roman Numeral Analysis: Triads

When analyzing Music, each Diatonic Triad is identified by a Roman Numeral.
The First Diatonic Triad of a Scale uses the Roman Numeral for one.
The Second Diatonic Triad uses the Roman Numeral for two.
This pattern continues.

In addition, the modern Roman Numeral system uses different styles for each Triad type.
Upper-case Numerals represent Major Triads.
Lower-case Numerals represent Minor Triads.
Upper-case Numerals with a small plus (+) sign represent Augmented Triads.
Lower-case Numerals with a small circle represent Diminished Triads.

Let’s apply Roman Numerals to the C Major Scale.
Since the first Triad is Major, its Numeral is Upper-case.
The second Triad is Minor. Its Numeral is Lower-case.
The third Triad‘s Numeral is also Lower-case.
The fourth Triad‘s Numeral is Upper-case.
The fifth Triad‘s Numeral is also Upper-case.
The sixth Triad‘s Numeral is Lower-case.
The seventh Triad‘s Numeral is also Upper-case.
Again, the last Triad is the same as the first.

Next, let’s apply Roman Numerals to the C Natural Minor Scale.
Since the first Triad is Minor, its Numeral is Lower-case.
The second Triad is Diminished. Its Numeral is Lower-case with a small circle.
The third Triad‘s Numeral is Upper-case.
The fourth Triad‘s Numeral is Lower-case.
The fifth Triad‘s Numeral is also Lower-case.
The sixth Triad‘s Numeral is Upper-case.
The seventh Triad‘s Numeral is also Upper-case.
Again, the last Triad is the same as the first.

Next, let’s apply Roman Numerals to the Harmonic C Minor Scale.
The third Triad is now Augmented. Its Numeral is Upper-case with a small plus (+) sign.
The fifth Triad is now Major. Its Numeral is Upper-case.
The seventh Triad is now Diminished. Its Numeral is Lower-case with a small circle.

Next, let’s apply Roman Numerals to the Melodic C Minor Scale.
The second Triad is now Minor. Its Numeral is Lower-case with no circle.
The fourth Triad is now Major. Its Numeral is Upper-case.
The sixth Triad is now Diminished. Its Numeral is Lower-case with a small circle.

The Roman Numeral system can also indicate Inversions.

First Inversion is represented by a small 6 after the Numeral. This is due to the Root being a generic sixth above the bass note.

Second Inversion is represented with both a small 6 and 4 after the Numeral. This is due to the Root and third, being a generic sixth and fourth above the bass note.

Some theorists use both a and a 3 to represent the First Inversion.
While we will use the 6 alone, one should be aware of the other representation.

Diatonic Seventh Chords

In addition to Diatonic Triads, every Major and Minor Scale has seven (7) Diatonic Seventh Chords.

Let’s examine the Diatonic Seventh Chords of the C Major Scale.
First, we construct the Scale.
Next, we stack three (3) generic thirds on top of each note.
Finally, we analyze the resulting Seventh Chords.

The First Chord is C-E-G-B, a Major Triad and a Major Seventh. Therefore, it is a Major Seventh Chord.
The Second Chord is D-F-A-C, a Minor Triad, and a Minor Seventh. Therefore, it is a Minor Seventh Chord.
The Third Chord is E-G-B-D, a Minor Triad, and a Minor Seventh. Therefore, it is also a Minor Seventh Chord.
The Fourth Chord is F-A-C-E, a Major Triad and a Major Seventh. Therefore, it is a Major Seventh Chord.
The Fifth Chord is G-B-D-F, a Major Triad and a Minor Seventh. Therefore, it is a Dominant Seventh Chord.
The Sixth Chord is A-C-E-G, a Minor Triad, and a Minor Seventh. Therefore, it is a Minor Seventh Chord.
The Seventh Chord is B-D-F-A, a Diminished Triad, and a Minor Seventh. Therefore, it is a Half-Diminished Seventh Chord.
The Eighth Chord is the repetition of the First (C-E-G-B), making it a Major Seventh Chord.
The first seventh chord of a Major Seventh Scale will always be a Major Seventh, the second and third seventh chords will always be Minor Sevenths, etc.

We will uncover now the Diatonic Seventh Chords of the C Natural Minor Scale.
First, we construct the Scale.
Again, we stack three (3) generic thirds on top of each note.
And finally, we analyze the resulting Seventh Chords.

The First Chord is C-Eb-G-Bb, a Minor Triad, and a Minor Seventh. Therefore, it is a Minor Seventh Chord.
The Second Chord is D-F-Ab-C, a Diminished Triad, and a Minor Seventh. Therefore, it is a Half-Diminished Seventh Chord.
The Third Chord is Eb-G-Bb-D, a Major Triad, and a Major Seventh. Therefore, it is also a Major Seventh Chord.
The Fourth Chord is F-Ab-C-Eb, a Minor Triad, and a Minor Seventh. Therefore, it is a Minor Seventh Chord.
The Fifth Chord is G-Bb-D-F, a Minor Triad, and a Minor Seventh. Therefore, it is also a Minor Seventh Chord.
The Sixth Chord is Ab-C-Eb-G, a Major Triad, and a Major Seventh. Therefore, it is a Major Seventh Chord.
The Seventh Chord is Bb-D-F-Ab, a Major Triad, and a Minor Seventh. Therefore, it is a Dominant Seventh Chord.
The Eighth Chord is the repetition of the First (C-Eb-G-Bb), making it a Minor Seventh Chord.
The first seventh chord of a Natural Minor Seventh Scale will always be a Minor Seventh, the second Half-Diminished Seventh Chord, the third seventh chords always a Major Sevenths, etc.

Currently, our discussion will be about the Diatonic Seventh Chords of Harmonic Minor, namely about the Diatonic Seventh Chord of the Harmonic C Minor Scale.

To convert a Natural Minor to a Harmonic Minor, the Seventh Tone is raised a Half Step (HS). Therefore, each Bb (the seventh tone of C Minor) is raised to a B.
Each Chord which contained a Bb needs to be reanalyzed.

The First Chord is now C-Eb-G-B, a Minor Triad, and a Major Seventh. Therefore, it is a Minor-Major Seventh Chord.
The Third Chord is now Eb-G-B-D, an Augmented Triad, and a Major Seventh. Therefore, it is an Augmented-Major Seventh Chord.
The Fifth Chord is now G-B-D-F, a Major Triad, and a Minor Seventh. Therefore, it is also a Dominant Seventh Chord.
The Seventh Chord is now B-D-F-Ab, a Diminished Triad, and a Diminished Seventh. Therefore, it is a Diminished (or a Fully-Diminished) Seventh Chord.
The Eighth Chord is the repetition of the First (C-Eb-G-Bb), making it a Minor-Major Seventh Chord.

Finally, we will have a discussion be about the Diatonic Seventh Chords of Melodic Minor, pointed to the Diatonic Seventh Chord of the Melodic C Minor Scale.

To convert a Harmonic Minor to a Melodic Minor, the Sixth Tone is raised a Half Step (HS). Therefore, each Ab (the seventh tone of C Minor) is raised to an A.
Each Chord which contained an Ab needs to be reanalyzed.

The Second Chord is now D-F-A-C, a Minor Triad, and a Minor Seventh. Therefore, it is a Minor Seventh Chord.
The Fourth Chord is now F-A-C-Eb, a Major Triad, and a Minor Seventh. Therefore, it is a Dominant Seventh Chord.
The Sixth Chord is now A-C-Eb-G, a Diminished Triad, and a Minor Seventh. Therefore, it is a Half-Diminished Seventh Chord.
The Seventh Chord is now B-D-F-A, a Diminished Triad, and a Minor Seventh. Therefore, it is also a Half-Diminished Seventh Chord.

Roman Numeral Analysis: Seventh Chords

In addition to Triads, the Roman Numeral Analysis System also identifies Diatonic Seventh Chords.

Let’s discover these analysis symbols of the Major and Harmonic Minor Scales.
three-step process is used.
First, we write the analysis symbols for the corresponding Diatonic Triads.
Next, we add a small seven (7).
And finally, we add a slash through the circle of each Half-Diminished Seventh Chord.

Some theorists use a variation of this system. They prefer to add an upper-case ‘M‘ to each Seventh Chord which uses a Major Seventh.
Although we will not use their system, one should be aware of its existence.

Next, let’s look at Inverted Seventh Chords.
The previously-discussed 7 identifies a root position Seventh Chord.
6 and 5 identify a First Inversion Seventh Chord.
4 and 3 identify a Second Inversion Seventh Chord.
Alone 2 identifies a Third Inversion Seventh Chord.

Let’s arrange the symbols in a different way. Notice anything unusual?
The Inversion numbers are in numeric order from 7 to 2.
One can use this pattern to remember the Inversion numbers for Seventh Chords.

Composing with Minor Scales ø

Unlike the Major Scale, three different Minor Scales exist.
Composers will often merge two (2) of these ScalesNatural Minor and Harmonic Minor, for a more pleasing sound.
Recall the Diatonic Triads of both Scales.
Notice that many of the Triads are the same.
Three (3) pairs of Triads (III-III+, v-V, and VII-vii°) are different due to Harmonic Minor‘s raised seventh degree.

III is preferred to III+. This is because III+, being an Augmented Chord, has a peculiar sound.
V is preferred to v since V contains a leading tone (and therefore is stronger). This does not mean that v cannot be used.
VII and vii° are both used equally. As you will later learn, each has a different function.
The Merged Minor Scale contains nine different Diatonic Triads.

Voicing Chords

Composers will often arrange the notes of a Chord in numerous ways in order to vary its sound.
This process is called Voicing.

We will voice an F Major Triad in root position to demonstrate this.
Notice that we can arrange the notes in any order as long as F, A, and C are used and F is the lowest note.

Next, we will voice an F Major Triad in First Inversion.
By definition, a Chord is in First Inversion when the Third is the lowest note. Thus, we need to make sure that each of our voicings uses A for the bottom note.

Finally, we will voice an F Major Triad in Second Inversion.
The process is the same; however, we must be certain that the Fifth (C) is used as the lowest note.

Analysis: O Canada

Analyzing the notes and Chords of a song is a major part of Music Theory.
In this analysis, we will be looking at the first four (4) measures of O Canada! the national anthem of Canada.

The first step in the analysis is to determine the Key. Since the Key Signature contains three (3flats, we have two (2) possibilities: Eb Major or C Minor.
The first Chord contains an Eb, Bb, Eb, and G – an Eb Major Triad. Since this is the I of the Roman Numeral in Eb Major, we are most likely in that Key.
The second Chord contains a D, Bb, F, and Bb – a Bb Major Triad. We the Roman Numeral, this is a V in Eb Major. Since the third is the lowest note, the Triad is in the First Inversion.
Since the third Chord is the same as the previous one, we do not have to repeat the analysis symbol.

The first Chord of the second measure contains a C, G, C, and Eb – a C Minor Triad. Thus, it is vi.
The second Chord contains a Bb, Bb, D, and F – another Bb Major Triad. This time, it is in root position.

The first Chord of the third measure contains an Eb, Bb, Eb, and G – an Eb Major Triad. Thus, it is another I Chord.
The second Chord contains a G, G, Eb, and Bb – an Eb Major Triad in the First Inversion.
The fourth Chord contains an Ab, C, Eb, and C – another Ab Major Triad. We can notice that it is in the root position now.

The final measure contains a Bb, Bb, D, and F – a Bb Major Triad. Thus, we end with a V Chord.

Nonharmonic Tones

Nonharmonic Tones (or Non-Chord Tones) are notes that do not belong in a certain Chord.
In this example, the F is Nonharmonic Tone because it does not fit into the Chord (which contains C, E, and G).
Before we discuss the different types of Nonharmonic Tones, we need to define two (2) terms:
Step is equal to an Interval of a generic second.
Skip is equal to an Interval of a generic third or more.

Passing Tone (PT) is approached by Step a then continues by Step in the same direction.
If a PT occurs with the second Chord (instead of in the middle of the two Chords), it is called an Accented Passing Tone (>PT).

Neighboring Tone (NT) is approached by Step and then returns by Step to the original note.
If it occurs with the second Chord, it is called an Accented Neighboring Tone (>NT).

An Anticipation (Ant.) is approached by step and then remains the same. It is basically a note of the second Chord played early.
Anticipations are not Accented.

An Escape Tone (ET) is approached by Step and then Skips in the opposite direction.
Escape Tones are not Accented – they occur in between the Chords.

An Appoggiatura (App.) is approached by Skip and then Steps in the opposite direction.
Appoggiaturas are not Accented – they occur with the second Chord.

Suspension (Sus.) keeps a note the same and then steps downward.
Retardation (Ret.) keeps a note the same and then steps upward.
Both the Retardation and Suspension are Accented.

Finally, Changing Tones (CT) use two Nonharmonic Tones in succession.
The first Nonharmonic Tone is approached by Step and then skips in the opposite direction to the second Nonharmonic Tone.
The second Nonharmonic Tone then resolves by Step.
They are sometimes called Double Neighboring Tones or a Neighbor Group.
While the named Nonharmonic Tones discussed in this lesson are the most common, composers may choose to use others.

Phrases and Cadences

Phrase is a series of notes that sound complete even when played apart from the main song.
We will use this musical example to demonstrate Phrases.

Play the first two (2) measures, notice how they sound incomplete.
Now, play the first four (4) measures, they sound more complete.
These measures could be considered a Phrase.
Play the fifth through eight measures.
Due to their completeness, they also form a phrase.

Before we move to the next section, let’s harmonize these two phrases with various Chords.

Cadence is a Two-Chord progression that occurs at the end of a Phrase.
If a Phrase ends with any Chord going to V, a Half Cadence (HC) occurs.
Replay the first four measures and notice the sound of the Half Cadence.

Most people will hear a Half Cadence as sounding incomplete. Hence, composers usually follow them with a Phrase ending in an Authentic Cadence (AC).
An Authentic Cadence occurs whenever a Phrase ends with V or vii° going to I (or i if Minor).
Play this example and notice the sound of both Cadences.

Authentic Cadences are often classified as either Perfect or Imperfect.
To be considered a Perfect Authentic Cadence (PAC), the Cadence must meet three (3) requirements.
First, V must be used rather than vii°
Second, both Chords must be in root position
And finally, the highest note of the I (or iChord must be the Tonic of the Scale.

An Imperfect Authentic Cadence (IAC) fails to meet these requirements.
These Authentic Cadences are all Imperfect due to various reasons.
In the first example, a vii° is used instead of V.
In the second example, one of the Chords is not in root position.
In the third example, the highest note of the I Chord is not the Tonic of the Scale.

In addition to Authentic and Half Cadences, two (2) other kinds exist.
If a Phrase ends with IV (or iv) going to I (or i), a Plagal Cadence (PC) occurs.
Play this example and notice the sound of the Plagal Cadence.

If a Phrase ends with V going to a Chord other than I (or i), a Deceptive Cadence (DC) occurs.
Deceptive Cadence is often used in place of an Authentic Cadence.
Recall the musical example used at the beginning of this lesson. Let’s replace the Authentic Cadence at the end of the second Phrase with a Deceptive Cadence.
Play the modified example. Notice how the Cadence “deceives” you (since you are expecting to hear a I).

Cercle Progressions

Root Motion is the movement from one Chord’s root to another Chord’s root.
To demonstrate Root Motion, we will use a I and a vi Chords in C Major.
The Root of the Chord (a C Major Triad) is C.
The Root of the iv Chord (an A Minor Triad) is A.
Therefore, the Root Motion between I and iv (C to A) is down a third.
Due to Interval Inversion, the Root Motion could also be classified as up a sixth.

Let’s try another example: a IV Chord going to V.
The Root of the first Chord (an F Major Triad) is F.
The Root of second Chord (a G Major Triad) is G.
Therefore, the Root Motion of these two (2) Chords is up a second or down a seventh.

Let’s try another example once more: a I Chord in First Inversion going to a root position V.
The Root of the first Chord (a C Major Triad) is C. Since the Chord is Inverted, the root is not the lowest note.
The Root of the second Chord is G.
The Root Motion of these two (2) Chords is down a fourth or up a fifth.

Circle Progression (CP) occurs when Root Motion is equal to up a fourth or down a fifth
Both I -> IV and ii -> V are Cercle Progressions.
iii
 -> vi and IV -> vii° are also Cercle Progressions.

Let’s work out all possible Cercle Progressions for a Major Scale, starting at I.
I progress to IV.
IV progress to vii°.
vii° progress to iii.
iii progress to vi.
vi progress to ii.
ii progress to V.
V progress to I.
The Major Scale Circle Progressions are: I -> IV -> vii° -> iii -> vi -> ii -> V -> I.

Next, we will work out all possible Cercle Progressions for a Minor Scale.
i progress to iv.
iv progress to VII (not vii°).
VII progress to III.
III progress to VI.
VI progress to ii°.
ii° progress to V (not v).
V progress to i.
The Major Scale Circle Progressions are: i -> iv -> VII -> III -> VI -> ii° -> V -> i.

Common Chord Progressions

Although hundreds of different Chord Progressions are possible, most tend to follow a Pattern.
In Major Key, the goal of any Chord Progression is the I Chord.
The rest of the Pattern is based around the strongest ways to get to this Chord.
An authentic cadence (V -> I) or (vii° -> I) is the strongest way to approach a I Chord.

Next, we use Circle Progressions.
The strongest way to approach V is a Circle Progression from ii.
The strongest way to approach vii° is a Circle Progression from IV.

The strongest way to approach IV is a Circle Progression from I; however, since I is already on the chart, we will not repeat it.
Circle Progression from vi leads us to ii.
Circle Progression from iii leads us to vi.
The strongest way to approach iii is a Circle Progression from vii°; which is already on the chart. Finally, since I is the main Chord of the Scale, it can go to any other Chord.

Now that the chart is complete, there are a few terms that one should learn.
Recall that the term “Dominant” means the Fifth Scale Degree. Since the V Chord is built on the Dominant, it is a Dominant Chord.
Since vii° functions like (by going to I), it can also be labeled as a Dominant Chord. Hence, V and vii° are Dominant Chords.
Since ii and IV come before V and vii°, they are usually labeled as Predominant Chords.

Let’s work out a Chord Progression using the chart. We will start at I.
Next, we can choose any Chord. Let’s go to vi.
Now, we can choose either ii or IV.
Let’s go with IV.
Now, we can choose either V or vii°. Let’s go with V.
Finally, V takes us back to I.
Our finished Chord Progression is: I -> vi -> IV -> V -> I.

The Chord Progression chart for Minor Scales is very similar to the Major Scale chart. There is only one main difference.
The strongest way to approach III is not vii°. Instead, it is a Circle Progression from VII.
Circle Progression from iv to VII completes the chart.

It should be noted that the charts do not have to be followed strictly. If a progression is not presented, a composer is not banned from using it.

Triads in First Inversion

In the previous lesson, we learned how to construct, identify, and analyze First Inversion Triads. One question still remains: when exactly do we use them?
One use of First Inversion is to smooth out the Bass Line.
Look at the example. Notice how the Bass Line changes direction during the second V Chord.
By placing this Chord in First Inversion, the Bass Line becomes smoother.
We can also use the First Inversion when repeating a Chord.
In this example, the first two Chords are duplicates. A composer may feel that this passage needs more movement.
Instead of altering the top voices, the Chord is placed in First Inversion.

The Diminished Triad presents the final use for First Inversion.
Early composers did not like using Augmented or Diminished Intervals.
Notice that a root position Diminished Triad contains a Diminished Fifth.
The Second Inversion of the same Triad contains an Augmented Fourth.
Only the First Inversion contains no Augmented nor Diminished Intervals.
Because of this, composers prefer First Inversion Diminished Triad.
While root position Diminished Triads are used occasionally, Second Inversion is rarely encountered.

It should be noted that the examples presented in this lesson are not strict rules. Sometimes, First Inversion is used simply because a composer likes its sound.

Triads in Second Inversion

While composers use root position and First Inversion Triads freely, Second Inversion usually occurs in three (3) situations.

Like First InversionSecond Inversion may be used to smooth out a Bass Line.
Look at this example – notice the movement of the Bass Line.
By using a Second Inversion V Chord, the Bass Line moves by Step and becomes smooth.
Second Inversion Triad used in this fashion is called a Passing Six-Four Chord.

Second Inversion may also be used to straighten a Bass Line.
Look at this example – notice how the Bass Line jumps up to the F and then returns back to C.
By using a Second Inversion IV Chord, the movement in the Bass Line is eliminated.
Second Inversion Triad used in this fashion is called a Pedal Six-Four Chord.

The Cadential Six-Four Chord is the final and most noticeable use.
In this form, the Second Inversion Triad precedes a V Chord in a Cadence.
Often, the Cadence will sound stronger due to the Cadential Six-Four’s presence.

Examine the Cadential Six-Four Chord and its resolution to V.
Some theorists prefer to identify the Cadential Six-Four Chord as a V with two Nonharmonic Tones.
They often explicitly show the Nonharmonic resolution in their analysis.
Although we will use I, one should be aware of this alternate system.

On the Chord Progression Chart, the Cadential Six-Four occurs in between Predominants and Dominants.

Analysis: Auld Lang Sine

In this analysis, we will look at the first few measures of Auld Lang Syne, a traditional Scottish ballad.

First, we must determine the Key. Since the Key Signature contains one flat, two possibilities exist: F Major or D Minor.
The first Chord contains F-A-C, an F Major Triad. Since this is I in F Major, we are most likely in that Key.
The next measure contains all F’sA’s, and C’s. Thus, all four Chords are I. Since we would be repeating an analysis symbol, there is no need to write it again.

The first Chord of the next measure contains C-C-E-G, a C Major Triad. Thus, it is a V Chord.
The second Chord contains C-C-D-F. This doesn’t fit nicely into a Triad – let’s skip it for now.
The third Chord is a duplicate of the first.
The fourth Chord contains a C-Bb-E-A. This Chord also doesn’t fit into a Triad. Let’s skip it as well.

The next measure contains F-A-C. Again, all four (4) Chords are I Chords.
The final measure contains Bb-Bb-F-D, a Bb Major Triad. Thus, it is a IV Chord.

Let’s go back and analyze the Chords that we skipped.
If we consider Nonharmonic Tones, the first skipped Chord can be analyzed as a continuation of the V with two Neighboring Tones.

The second skipped Chord is trickier.
When voicing Seventh Chords, composers sometimes leave out the Fifth.
Notice that the bottom three (3) notes are the rootthird, and seventh of a C Dominant Seventh Chord. Only the G (the fifth) is missing.
Hence, we can analyze it as V7 with a Nonharmonic A.
Since the A is approached by Step and then Skips, it is an Escape Tone.
This analysis is reinforced by the fact that V Chords commonly resolve to I.
Play these measures of Auld Lang Syne.

NEAPOLITAN CHORDS

Building Neapolitan Chords

Neapolitan Chord is simply a Major Triad that is built on a special note.
This note is the lowered second degree (the Supertonic) of a Major or a Minor Scale.

Let’s build the Neapolitan of C Minor.
First, we have to figure out the Second Degree.
In C Minor, this is D.
Next, we will lower it to Db.
Now we have to build a Major Triad. This results in Db-F-Ab.
Db Major Chord is the Neapolitan of C Minor.

Next, let’s build the Neapolitan of E Minor.
Again, we need to figure out the Second Scale Degree. In E Minor, this is F#.
And then, we lower it to F natural.
Now we build a Major Triad. This results in F-A-C.
Thus an F Major Chord is the Neapolitan of E Minor.

Next, let’s build the Neapolitan of Ab Major.
In this Key, the Second Scale Degree is Bb.
This lowered a Half Step (HS) gives us Bbb.
Now we build a Major Triad. And this results in Bbb-Db-Fb.
Thus a Bbb Major Chord is the Neapolitan of Ab Minor.

For our final example, let’s build the Neapolitan of A Major.
The Second Scale Degree of this Key is B.
And then, we lower it to Bb.
Now we build a Major Triad. This results in Bb-D-F.
Thus an Ab Major Chord is the Neapolitan of A Major.

Using Neapolitan Chords

In the previous lesson, we learned how to construct Neapolitan Chords. In this current lesson, we will learn how to use them.

Although root position and Second Inversion Neapolitans exist, First Inversion is normally used.
In this Inversion, the Neapolitan is called a Neapolitan Sixth.

Notice that the Neapolitan Sixth‘s Bass Note is the same as a First Inversion ii° (or ii) or a root position iv (or IV).
For this reason, it often substitutes for these Chords. Hence, it primarily functions as a Predominant.

Consider this example.
We can replace the ii6 Chord with a Neapolitan Sixth.

Next, consider this example.
This time, we will replace the iv Chord with a Neapolitan Sixth.

Use this chart to reference the Neapolitan Sixth Chord‘s usage.

Analysis: Moonlight Sonata

In this analysis, we will be examining measures 49-51 of Beethoven’s Moonlight Sonata (Opus 27, Number 2 Movement 1)
Since we are starting in the middle of the piece, I will reveal the Key Signature: it is in C# Minor.

The first half of measure 49 contains G#-B#-D-#F#, a G# Dominant Seventh Chord. Since the B# is the lowest note, the Chord is in First Inversion.
The second half of measure 49 contains C#-E-G#, a C# Minor Triad.
The first half of measure 50 contains D-F#-A, a D Major Triad in First Inversion. This is the Neapolitan Sixth Chord in C# Minor.
The second half of measure 50 contains G#-B#-F#, a G# Dominant Seventh Chord with a missing Fifth.
The first part of measure 51contains C#-E-G#, another C Minor Triad.

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