Lesson One: Scales Revision

A tetrachord is the pattern of tones (T) and semitones (ST) between the first four notes of every diatonic scale (tetra means four). As there are eight notes in each scale, there are two tetrachords in every scale. A tetrachord is built of the interval pattern Tone, Tone, Semitone. There are three intervals here, but they fit in between four notes like third:

Tetrachord 1: C TONE D TONE E SEMITONE F
Tetrachord 2: G TONE A TONE B SEMITONE C

You can play hear the intervals within a tetrachord by playing them on these online pianos.

An interval of a TONE joins the two tetrachords together.
By now you should know many scales and remember how to write them and how to mark where the tones and semitones are. Do you remember the pattern of tones and semitones in a tetrachord? Fill in the blanks T for Tone and ST for Semitone
___ ___ ___ ___ ___ ___ ___

There is more to tetrachords than just how each scale by itself is organised. Tetrachords also help us to understand how each scale is related to all the others.

Every scale that we know can be made from the C major scale if we understand how tetrachords are related to each other. All major scales sound the same as they have the same arrangement of tones and semitones. If we were to play the C major scale and then play the eight notes from G to G, we would find that we need to change only one note to have the second scale beginning with the key note of G sound like the C major scale. That note would be? ____

If we begin with the second tetrachord of the C major scale (which has no sharps or flats): G-A-B-C and place another tetrachord above it we find that we have to raise the F to an F# in order to keep the interval pattern T, T, ST. The second tetrachord of the G major scale would therefore be D-E-F#-G.

When we play the scale beginning on the key note F we also have to change only one note to have the scale sound like C and G major. What is it?_____

This time however rather than beginning with the second tetrachord of C major to construct the F major scale we have done something different. Do you know what it is?
___________________________________________________________________________________________________
___________________________________________________________________________________________________

Rather than take the second tetrachord of the C major scale and put another tetrachord on top, we take the first tetrachord of C major (C-D-E-F), and place another tetrachord BELOW that. Because we are going DOWN in pitch we must LOWER the note B to Bb to make sure the pattern of T-T-ST stays in place. When we changed the note F to F# for the G major scale we use a sharp sign because we were RAISING the F not lowering the G. Note names become very important in 4th grade theory for our lessons on intervals but we will learn more about that later.

When we are building the scales with sharps in their key signatures we take the SECOND tetrachord of the previous major scale and build another tetrachord above the first.When we are building scales with flats in their key signature we take the FIRST tetrachord of the previous scale and build another tetrachord below the first. Try building the scale with the key signature of two flats. Begin with the F major scale: F-G-A-Bb-C-D-E-F

What notes form the first tetrachord of the F major scale? __ __ __ ___
The last note in the first tetrachord will be the key or tonic note of your next major scale. What note is this? ____
What notes would form a tetrachord that could fit below this tetrachord? ___ ___ ___ ___
This new scale will have one more flat than the previous one. If the F major scale had one flat for a key signature, the new scale will have two flats. What are they? ____ and _____

When building the scales with sharps in their key signatures, we move from C major in an upward direction and find that the scale with one sharp is G major. If we take the second tetrachord of G major with the notes D-E-F#-G and place another tetrachord above that what is the new scale? _________
To find the major scale with a key signature of three sharps we begin with the second tetrachord of the last scale. The first note in the second tetrachord will be the new keynote or tonic of the scale with one more sharp in the key signature. If we are beginning the new scale with the second tetrachord of D major the new keynote will be? ___

Try this activity to build all your major scales with flats. You can also try this activity at the piano and see how the scales overlap as they descend in pitch (for the flat scales) or ascend in pitch (for the sharp scales). You can put the tetrachord cards against the piano keys so that they match up.

Lesson Two: Sharps and Flats    Back 

In the last lesson we learned that when we are raising a white note we use a sharp (#) and if we are lowering a white note we use a flat (b). This is because we can have only one NOTE NAME for each note in our scale. For instance if we were writing the F major scale and we used an A# rather than a Bb (as they are the same pitch - just different names) we would end up with these notes: F, G, A, A#, C, D, E, F! We would have two A notes and no B notes so this is why we are careful about which sign we use to write the note.

However, sometimes we might want to raise or lower a note by more than a semitone. There are signs for doing this. To raise a note by two semitones we use a DOUBLE SHARP sign which looks like an 'x'. If we want to lower a note by two semitones we use two flat signs like this: 'bb'. This sign is called a DOUBLE FLAT sign. We know that there is more than one way to write the same pitch. For example, F# can also be known as Gb. Fb is more often known as E natural. Fx (F##) is another name for G. What is another name for Fbb? ______
Fill in the following alternate note names:

The scales we have been learning to write have been diatonic scales made up of tones and semitones. We may also practice other types of scales if we play an instrument and this could include chromatic scales. Chromatic scales have lots of accidentals in them and no key signature. These scales are made up of chromatic semitones. This is where the same note is written twice with a sharp or flat sign before the second note:
C, C#, D, D#, E, F, F#, G, G#, A, A#, B, C.
When we are using the descending form of the chromatic scale we must use flat signs rather than sharp signatures like this:
C, B, Bb, A, Ab, G, Gb, F, E, Eb, D, Db, C.

Every chromatic scale is made up entirely of semitones and there are twelve different note names in every chromatic scale. As you can see from the above example of the chromatic scale beginning on C, there are some notes that already have semitones between them.
Can you write the chromatic scale beginning on the note D (use a piano if you like)?
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

As we can see from the chromatic scales, a semitone that is made between two notes that share the same letter (example G-G#) is called a CHROMATIC SEMITONE. A semitone that is made from two different note names is called a DIATONIC SEMITONE. Write in diatonic or chromatic in the blanks to indicate whether the interval indicated is a diatonic or chromatic semitone:

Now write these notes one chromatic semitone higher. This means that the same note name must be used.

Now lower these note names by one chromatic semitone.

Now go back and answer the last two questions to change the note names by a DIATONIC semitone. This means that you will need to raise D# to E rather than for the previous question for which you should have written D x for D double sharp.

The differences between diatonic and chromatic intervals becomes important for when we learn about augmented and diminished intervals because the old intervals we already know eg 3rds, 5ths, octaves can be raised or lowered by a chromatic semitone to make them augmented or diminished.

Lesson Three: More on Scales    Back 

So far we have been concentrating on the major scales. Each major scale has a minor scale that shares the same key signature. The minor scale with sharp key signatures always begin a 4th below the previous key signature. For instance, the minor scale with no sharps or flats in the key signature is A minor. To find the minor scale with one sharp, we descend from A a perfect 4th and begin our new scale on that note. The minor scale with one sharp will be the E minor scale. E is our new key note or tonic. If we want to make the minor scale with two sharps for a key signature we begin on the note that is a perfect 4th below E.
That note will be? ________
 

Use this information to help you fill out the following table.

TABLE OF SHARPS

Lesson Four: Italian Terms    Back 

Try to learn 5 Italian Terms per week.

Lesson Five: Intervals    Back 

We already know some different kinds of intervals. We have been learning the different kinds of intervals found in the scales that we know. In the major and harmonic minor scales that we know, we should remember that unisons, 4ths, 5ths and octaves are perfect (never major or minor); 2nds, 3rds and 6ths can be major or minor; 2nds and 7ths are major.

If you compare the major and minor scale notes we find that in both major and minor scales the only intervals which vary are the 3rd and 6th which are major in a major key and minor in a minor key:
A, B, C#, D, E, F#, G#, A
A, B, C,   D, E, F,   G#, A

Notice that the 2nd from A-B is the same in both major and minor keys, as is the major 7th from A-G#. The unison (A-A), octave (A-A), 4th (A-D) and 5th (A-E) are all perfect in both major and minor keys. All of these intervals are called DIATONIC intervals which means that they conform to the key signature.

Now it is time to learn about intervals that do not conform to the key signature and so can not be found in our major or minor scales. These intervals are called CHROMATIC intervals and can be found in the chromatic scales. The new interval QUALITIES we need to learn are AUGMENTED and DIMINISHED intervals

An augmented interval is one semitone larger than a major or perfect interval. A diminished interval is one semitone smaller than a minor or perfect interval.

Do you remember how to count up your interval NUMBERS? This is important, because if you count the note names incorrectly you will be marked wrong. If you are identifying the interval C-A, you must count every DIATONIC note name including C and A. Like this:

You do not need to worry about how many tones or semitones are inside your intervals as this is not the easiest way of telling what your intervals are. Using the note name counting method, C - A is a 6th. We should know that this is also a major 6th. If the key was C minor the interval C - Ab would be a minor 6th. What however, would happen if the interval was C - A#? What kind of interval would this be? We still have a 6th from C - A but it is a different kind of 6th, an AUGMENTED 6TH.

When we are sorting out our augmented and diminished intervals the LETTER NAME of the note is very important as this tells us the correct number for the interval. For example:

You will notice that A# and Bb are actually the same note when you play them, however they belong to different intervals. So to identify your intervals at this level you need to pay special attention to the note name before you decide whether the interval is diminished, minor, major or augmented etc. We need to have different ways of writing the same sounds so that composers can stick to the key signature but still use notes that are foreign to it for special purposes.

Look at this table of options for the intervals in each scale. Note that all intervals can be diminished or augmented. Here are the possibilities:

Intervals and Chords

Intervals play a role in triads and harmony. Thus far, triads have been identified according to the 3rd as either major or minor. Eg, the tonic triad beginning on C will be a major triad in C major (due to the E natural) and a minor triad in C minor (due to the Eb in C minor). In major keys these are the major triads: I, IV, V- the primary triads. In a minor key the major triads are chord V and VI due to the raised leading note which forms the 3rd in chord V.

However what kind of triad is chord on the leading note? This is B, D, F- all naturals in both keys. The 3rd is minor but the 5th is not a perfect 5th, it is a diminished 5th. When a triad has a diminished 5th, it takes its quality as a traid from the 5th, is called a DIMINISHED TRIAD and will always have a minor third. When a triad has an augmented 5th it is an AUGMENTED TRIAD and will always have a major third.

Write the quality of the triad next to the triad notes:

So far we have been talking about triads that have the root from which they are built on the bottom and the 3rd and 5th above. When a triad is in this formation or 'inversion' it is called root position.

The root of the triad is the note the triad is built on. However, it is not always found in this formation. Sometimes it will have the 3rd (E, in this example) on the bottom, then the 5th (G) and the C above that. This formation is called first inversion. When the 5th (G) is on the bottom the root is in the middle and the 3rd is on top it is called second inversion. Look at the table above and write in the C major triad in 1st and 2nd inversion.

One way the position or inversion of a triad is identified is by the numbers put in place of notes which make up the bass part in old harpsichord music. This was called using a 'Figured' (figures/numbers) Bass. Composers used to put numbers to tell the note above the bass note rather than put the notes themselves in. If the key was C major and lowest note was a C (and so the chord was in root position) in the bass clef part, the numbers

would appear under the bass staff to indicate that the performer should play a 3rd (E) and then 5th (G) above it.

If the chord was to be a first inversion the numbers (figures) would be:

If the chord was to be a second inversion the numbers

would appear under the bass staff to indicate that a fourth above the lowest bass note should be played along with the sixth note from the lowest note.

Find some manuscript and write out the the C major triad C, E and G in root position. Even if you are using the treble clef, the space or interval between the bottom note C and those above it should be a 3rd and a 5th as indicated in the above example Here the interval between the notes of the triad/chord are counted from the lowest note (in pitch) rather than from the tonic or the root as the root is being moved around.

Look at the triads here.. They are different inversions/positions of the C major tonic triad. We indicate it is the tonic triad of the key (C major) by placing a Roman numeral I under it. To indicate the inversion, place a small letter b next to the I (Ib) for first inversion or a c ( Ic ) for second inversion. For this grade you need only to be able to tell apart root position and 1st inversion triads. If there is no b next to the Roman numeral it is assumed that it is in root position. This is like when we leave out the zero and decimal point in numbers when we are using whole numbers because we know the zero is there even though it is not written. For example 5.0 is usually written as 5. In music if no inversion is indicated we assume it is in root position just as we assume the zero is there even though it has not been written down.

Understanding the figured bass approach to harmony notation allows you to understand why the different triad positions look different on the manuscript when they are written as notes. If you can see the spaces between the notes you will be able to tell which inversion the triad is in very quickly.

For this next exercise you must write under each triad that it is chord I of the key and what inversion it is in. If it is in root position just write the I. If it is in first inversion write Ib. All these chords are the tonic triad, but the key is different for each line/staff. You will need to know the key but if you count up from the lowest note you can tell which inversion it is in without worrying about what key it is in as the numbers are the same in every key.

The last exercise used only the tonic triad of many keys. Now see if you can identify whether the triads shown are the tonic, subdominant or dominant of the key and what inversion they are in. For this exercise, place a Roman numeral to indicate the triad. This will be I for tonic, IV for subdominant (meaning the triad is built on the 4th degree of that scale) or V for the dominant triad. You will still need to indicate the inversion. If the triad is root position the Roman numeral is all you need. If it is in 1st inversion place a small b after it.

In writing cadences in four-part harmony you will notice that in using four note chords (rather than three note triads) one note of the triad must be repeated. Additionally, one note of the triad can be left out. This will usually be the 5th. To work out which inversion of the chord you are looking at or writing, use the lowest note (in the bass part) as your guide. If it is the root then the chord is in root position even if the 5th is missing and the root doubled (making up the extra note). If the 3rd of the chord is in the lowest bass part then the chord is in 1st inversion. Because four-part harmony requires that some triad notes be left out and one be doubled, the figured bass approach does not always help you identify the inversion. However, it is simply a matter of looking at the lowest bass note.

Lesson Six: Simple and Compound Times    Back 

The terms simple and compound refer to the way that notes are grouped within each MAIN BEAT of a bar. As we know, a time signature is made up of two numbers. These numbers tell us different things. The bottom number tells us what kind of beats and the top number tells us how many in each bar. If we think of the semibreve as a whole note, the minim as a half note, the crotchet as a quarter note and the quaver is an eighth note then we can see how this relates to a time signature.

Activity: Draw up a chart which shows the relationships between note values: semibreve, minim, crotchet, quavers, semiquavers, demi-semiquavers.

We usually see time signatures with a 2 or 4 on the bottom. We do not see time signatures with a 3 on the bottom because in the choices available, whole note being 1, half note being 2 or quarter note being 4 there are only multiples of 2 available. Multiples of three are not possible with the bottom number of the time signature.

We can have multiples of 2 or 3 for the top number of the key signature because it is theoretically possible to have any number of beats per bar. The bottom number tells us what kind of beats there are so there are limits to the different kinds of beats- whole note, half note or quarter note.

For example, the time signature 3 over 8 (3/8) means that there are three quaver beats in each bar. The time signature 3/2 means that there are three minim beats in each bar. The time signature 6/4 means that there are six crotchet beats in every bar. The time signature 12/8 means that there are 12 quaver beats per bar.

Fill out this table:
 

There is a further division in time signatures between simple and compound time. These terms refer to how notes are grouped inside each beat within the bar. For time signatures that have a 2 (minim) or 4 (crotchet) on the bottom notes will be grouped accordingly. ie In every bar of 3/2 smaller notes must fit into each minim:

3 minim, crotchet + 2 quavers , 4 quavers | 2 crotchets, minim, minim |etc
2

This is fairly straight forward and is called SIMPLE TIME.
*(+) indicates that these notes are part of the same beat.

Where there is an 8 on the bottom, that means that the notes are groups of quavers. If there is a multiple of 3 for the top number that means that we are grouping our notes in fractions like 1 and a half beats, or multiples of this like 3 beats, 6 beats, 9 or 12 beats. This is COMPOUND TIME.

3quaver, quaver, quaver| crotchet, quaver, 2 semi-quavers | etc
8

The DIFFERENCE between compound and simple time is whether the beat can be broken down into 2 separate parts (simple) or 3 separate parts (compound). For example, in 4/4 there are four crotchet beats to each bar. These can be further simplified to two minim beats when we are joining tails or tying notes. In 6/8 each main beat lasts for one and a half beats (3 quaver beats) so that notes must be grouped according to divisions of one and a half beats.

How many main beats in these time signatures?

3____________
4

6____________
8

3____________
8

6____________
4

12___________
8

Can they be divided into smaller groups of 2 or 3 beats? 1._____ 2.______ 3.______ 4.______ 5.________

Which are simple? ____________________________________________________
Which are compound? __________________________________________________

Lesson Seven: Folk Song Memorisation    Back 

For the  theory exam you will be asked to write out the whole of one of the following songs:

Learn one song at a time by playing it on your instrument and singing along with the midi's. The music for these songs can be found in "Fifty Folk Songs".

Print out the above gif files and fill in the phrasing and lyrics as they appear in Fifty Folk Songs published by Brandon. This book is stocked by Allans Music.

Answer the following questions for each song:

1. What is the title? ________________

2. What is the key? ________________

3. What is the time signature? ________________

4. Is it in simple/compound/duple/triple time? _______________

5. How many bars is it?________________

6. Does it begin with an anacrusis? _________________

7. How many cadence points would you put in if you were adding harmony? _______________

8. What kind of notes are mostly used in the piece? _____________________

9. In what bars do any slurs occur? ________________

10. Circle any sequencing.

11. What form is each song in?___________________________

12. Harmonise the cadence points using cadences from this grade. This activity can be completed after lessons on new cadences have been completed later on in the course.

Lesson Eight: Inverted Intervals    Back 

Intervals can be inverted or turned upside down so that both their number and their quality become opposites. To find the opposite we must divide up the major scale between the 4th and 5th degrees:

1------------2----------3---------4--------|---------5----------6----------7-----------8
perfect-major-major/minor-perfect  |   perfect-major/minor-major-perfect

We could fold the major scale in half and we would get the same interval QUALITIES on both sides of the paper! Using this model, the opposite of a 5th is a 4th, the opposite of a 3rd is a 6th, the opposite of a 2nd is a 7th and the opposite of the unison (1st)is an octave (8th).This works for qualities too. When we add in the augmented and diminished qualities the scale looks like this: P=perfect; D=diminished; A=augmented; Ma=Major; Mi=Minor

Interval Inverter

Try this Interval Inverter by folding a piece of paper in half and drawing the scale above, onto it with the division between the 4th and 5th degrees along the center fold.
All you have to do is draw a line or arc from one side to the opposite position on the other side. Begin by drawing a curve over the center fold from the A under the 4 to the D under the 5 and work out from there. To find your inversion, all you have to do is follow the line across.

If you look at the last row in the table above you can see that if you begin with a minor 3rd and follow the line across you will end up with a major 6th. You can do this yourself with your own interval inverter.

1. Invert the following intervals by number and quality:

2. Find the following intervals above F# and Bb:

3.Find the following intervals above B and Db:

Now, with the help of your Interval Inverter, find the inverted forms of the above intervals in exercises 2 and 3.

Lesson Nine: New Cadences    Back 

A cadence is a musical punctuation mark. Some cadences make the music sound like it must keep going and others sound like the music is finished. Plagal and perfect cadences make the music sound finished, like a full stop. Imperfect and interrupted cadences make the music sound like it must keep going, like a musical comma or question mark that something must follow. In our last grade we learned how to write perfect (V-I) imperfect (I-V) and (IV-I) plagal cadences.

Now we are going to learn some new types of cadence:
 

As we know, there are some rules that we must stick to when we write our cadences. There are also some steps to follow make writing cadences according to the rules a bit easier:

Special rules for special cadences: The imperfect cadence IV - V is also called a MIXED cadence because it is formed from chords which can be found in both the plagal cadence and perfect/imperfect cadences. The three upper parts, soprano, alto and tenor must move in CONTRARY MOTION to the bass part. There are no common notes between chords IV and V.

The imperfect cadence VI - V has no common note between the chords and the 3rd must be doubled in chord VI. In chord VI it is always good to double the 3rd because this will be the TONIC note of the key. In the interrupted cadence V - VI, there are no common notes and you must put in a DESCENDING 3rd from the root of chord V to the 5th of chord VI. If you put this in after you have put the bass part in it will make it much easier to avoid making mistakes with the other parts of the cadence. You must check your cadences for these mistakes:

Questions:
1.Which cadences bring the music to a close? (name and Roman numerals)
_______________________________________________________________________
2.Which cadences are the musical commas/question marks? (name and numerals)
_______________________________________________________________________
3.Which cadences do NOT have common notes between the chords?
_______________________________________________________________________
4.Which cadence is also known as a MIXED cadence?
__________________________________________________
5.In which chord is it best to double the 3rd?
______________ Why? ___________________________________________________
6.In which two cadences do you find this chord?__________________________
7.In which cadence is it best to have the three upper parts moving in contrary motion to the base (and similar motion with each other)?
____________________________________
8.Why is chord V always a major triad in both major and minor keys?
_______________________________________________________________________
9.Which triads are major in major keys?__________________________________
10.Which triads are minor in major keys?__________________________________
11.Which triads are major in minor keys?__________________________________
12.Which triads are minor in minor keys?__________________________________
13.Name the primary triads_________________________
14.Name the secondary triads________________________
15.Which cadence has a descending interval of a 3rd in one of the parts between the first and second chords?_________________________________
 

Lesson Ten: Harmonic Analysis    Back 

UNESSENTIAL NOTES (including passing, auxiliary and changing notes).
These words are used to describe notes that are not from the triad which forms the basic harmony of that bar. Sometimes we can get confused when we are trying to analyse the harmonic structure of music because these notes are used as well as chordal notes. These notes will form a discord with the harmony notes but that is fine as they 'resolve' to the chordal note.

In the following hints, the word chord and triad are used interchangeably. This is because, when analysing music written in four part harmony, you will be analysing chords which could have 4 or more notes in them but they will always be based on the TRIADS of the key.

One way of improving your understanding of harmony is to practice analysing pieces of music by writing underneath each bar, the ROMAN NUMERAL for the triad that that part of the bar is based on. There will usually be two main chords per bar and you should be able to find some cadences that you are studying.

It is important to choose a relatively short and simple piece of music. You could use one of your piano pieces or if you play another instrument, the piano accompaniment for one of your instrumental/vocal pieces. It is better to avoid 20th century and Baroque music for this purpose. A simple study or piece from the Romantic or Classical period will be easier to analyse.

If the piece begins with an anacrusis it will most likely be from a chord V on the unfinished bar to chord I in the first full bar. If it is difficult to figure out the chord structure, look at the first few notes of the melody and see if they are from one of the primary triads. The bass part should give you a good idea of which chord is being used to harmonise. Always use a pencil and rubber when doing harmonic analysis and if the piece is more than few bars do only 4-8 at a time.

Most pieces will use the primary triads: I, IV and V as harmony. You might be able to find some secondary triads, II, III, VI or VII, particularly in some of the cadences which you have just learned. The perfect and plagal cadence should be found moving from a weak beat for chord IV or V to the strong beat for chord I. The interrupted and imperfect cadences should be found moving from a strong beat for chord II, IV or VI to a weak beat for chord V.

When you are analysing the chord structure of a piece of music you should indicate the position/inversion of the chord. This can be found by looking at the bass note. The bass note may not always be the root of the chord.

If the chord has the root in the bass it is in ROOT POSITION and we just write the Roman numeral for the triad upon which that chord is based.
If the chord has the 3rd of the triad in the bass we notate (indicate) that by placing a small letter 'b' next to the Roman numeral for that triad. eg Vb.
If the chord has the 5th of the triad upon which it is based in the bass, we write a little 'c' next to the Roman numeral like this: Ic. You should practice doing this when you analyse your piece of music.

Questions:
 

1. What is the title and composer of your piece of music?
_______________________________________________________________________
2. How may bars long is it?_______________________
3.Are there any accidentals? List them:________________________________
4. What key is it in?______________________
5. What are the notes of the primary triads in that key?
_______________________________________________________________________
6. What are the notes of the secondary triads in that key?
_______________________________________________________________________
7. Does the piece begin with an anacrusis?_____________________________
8. Does the piece modulate (change key)? ______________________________
9. What cadence ends the piece? __________________________________
10. Is there a cadence half way though, if so what?_____________________
11. What is the chord progression in the first 4 bars?__________________
12. What is the chord progression in the last 4 bars?__________________
 

Help Identifying Cadences:
During your harmonic analysis you may notice many chords in succession that can form cadences. However, this does not mean that they are all cadences. How do you tell the the difference between a cadence and two chords in succession? What did you learn as a definition of a cadence in your previous lessons on cadences?
____________________________________________________________________________________________________
____________________________________________________________________________________________________

You should recall that a cadence is like musical punctuation in that certain chords are used at particular points to form specific effects. A perfect or plagal cadence tells us when the music is finished. An interrupted or imperfect cadence tells us when there is something following.

For instance, it would not make sense to have a perfect cadence at the end of an introduction as the introduction is put there to build up some expectation of the wonderful music yet to come. The cadence will be found in the last bar of the introduction and it will be an imperfect or interrupted cadence to indicate that the theme is about to begin. If a perfect or plagal cadence were put in the last bar of the introduction it would sound like the music was finished rather early and the audience might go home before they have even heard you play! No doubt when the introduction is finished and the first theme begins, it will begin with a tonic chord. If you have been busily writing in your chord progression it might look something like this:
 

V - IV-|I - VI - V-||:I - II -V|.......

If the first two bars are the introduction and the third is the first bar of the theme, then it may look as if there is a perfect cadence between bars 2 and 3 (V-I). This is where your knowledge of how cadences are used is needed. The cadence in this chord progression is VI-V in bar 2.
What kind of cadence is this and what effect does it have on the listener?
____________________________________________________________________________________________________
____________________________________________________________________________________________________

This is something you need to be careful of when you are identifying cadences. You need to be aware of what the composer is intending with that section of the music. You should also remember that half-close cadences will occur from a strong to a weak beat -especially as you consider that there is something more to follow that will begin on a strong beat. Full closes occur from a weak to a strong beat, usually over a bar line from the second last to the last bar.

Motion of Parts

In harmony we often talk of the 'motion' of the parts. Music is always moving but here we are referring to the direction the parts are moving IN RELATION to each other. There are three basic ways that we can detect parts moving in: oblique, similar and contrary.

Click the links above to listen to the different types of motion between the parts.

Look at the piece of music that you have analysed. Can you see where these types of motion are used? Try to find one example of each kind of motion. Look in other music if you have to.

Go to the next lesson and download the gifs and midi's of the three carols. The last bars have only two parts given so that they can be completed as a harmonisation lesson. For now just see if you can identify (either orally or from the score) where parts move in similar, contrary or oblique motion.

Lesson Eleven:Four Part Harmony    Back 

Rules for 4 Part Harmony

Exercise:

Name all the cadences and the Roman Numerals for them that you should know for this grade:
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When should 1st inversion chords be used?
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Which note should never be omitted?
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Which note should always rise by one semitone?
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Which note should never be doubled?
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Which notes are best to double?
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When is it a good idea to double the 3rd?
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Which notes should not be used in the lead up to a cadence?
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Which parts should move in either oblique or contrary motion?
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Which chords harmonise an anacrusis? ___________________________________

Exercise:

Write out an example of each cadence for this grade.

It is a good idea to familiarise yourself with different styles of harmonic structure. This will help you understand what you are aiming for when you write your own four part harmonies.

Examples of four part harmony writing can be found in hymn music. You can look at the following carols as a guide to learning your four part harmony writing:

To practice your four part harmisation that you will need for your exam, fill in the missing two parts in the final bars of each of the above scores above. In each case the first bars are given in four-part harmony. In the final bars, only two parts are given and you must fill in the missing two. Make sure your stems are pointing in the right direction for that part ie

Different styles of hamonisation are as follows:

Monophonic: 'mono' means one as in one voice. Phonic means voice. Some of your studies may be unaccompanied and so would be called monophonic in harmonic structure.

Homophonic: 'homo' also means one but here it means one MELODY.

Polyphonic: 'poly' means more than one and here it means more than one MELODY

The reason that it is important to distinguish between one or more MELODIES and one or more PARTS is so that we can see how a piece of music has been harmonised. If it has a melody in the top part and chords in the bass part then it is homophonic as there is melody only in one part.

However, if there are two melodies one in the treble and one in the bass then this is in polyphonic structure. A lot of Bach's music is polyphonic. His Two Part Inventions are good examples of counterpoint (or polyphonics).

'Counterpoint' and 'contrapuntal' are other words for polyphonic and mean literally 'point against point', as each separate part can be an independent melody on its own. Counterpoint is difficult music to write to because each melody must harmonise with each other part.

Lesson Twelve: Form    Back 

Form of a Different Kind.

Thus far we have considered form as the pattern of melodies within a piece of music. We have learned binary and ternary form (AB) and (ABA). Now we will begin our studies of form as the overall work of music within which each 'movement' forms a part. We have dance music today- usually fast paced music with a strong emphasis on fast rhythms written as a single piece of music but which is usually blended into the previous and following songs by technical means. People love to dance for entertainment and for expressions of their culture. Think of the Aboriginal coroboree or the waltz or the hula dancers of Hawaii. Some of these dance forms are many thousands of years old and still survive today. The Renaissance and Baroque period saw the development of sets of dances written to be performed one after the other. The 'Suites' of dances had a common theme although the individual dances varied from each other for interest.

The Dance Suite

There are many different dance types which can be included in a dance suite but the typical outlay of a dance suite would begin with an Allemande followed by a Courante, then a slow Sarabande for change and a lively Gigue (Jig) would conclude the suite. Optional extras could include the Minuet (or Menuet in French), the Gavotte, the Passepied or the Bouree. You may have learned some of these dances for your exams or played them in an ensemble.

For the grade 4 exam you will need to be able to identify the main dances from an example of a few bars. As each dance type has characteristics typical of each, this can be done by close analysis of the following points:

Three types of dances are in simple triple time, the Courant, Minuet and Sarabande which are found one after the other in a suite (if the minuet is included). The Allemande (which comes first) is in simple quadruple and the Gigue (which comes last) is in compound duple. The Gavotte which is second last to the Gigue is in simple duple or quadruple time.

Characteristics

TIME SIGNATURE Give examples of time signatures for each dance:

ANACRUSIS

There are four dances which begin before the main beat with an anacrusis: the Allemand, the Courante and the Gigue. The Gavotte has a longer anacrusis. This is a good clue to figuring out which type of dance you are looking at or listening to. Circle the two dances out of the following which do NOT begin with an anacrusis:

Allemande, Courante, Minuet, Sarabande, Gavotte, Gigue.

TEMPO

The slower dance movements are the Minuet which is of a moderate tempo and the Saraband which is slow or stately. The two fast dances are the Courante and the Gigue and the Gavotte and Allemande are moderately fast. Write the dance tempo next to the name:

HARMONIC STRUCTURE

As these dances were popular in the Baroque period they feature a lot of movement in the melody line and are frequently polyphonic (contrapuntal). This can be where one part is stationary but another is moving (as with oblique motion). The dances which have little or no polyphonics are the Gavotte, Minuet, the Allemande and the Sarabande. However, the Allemande, the Courante and the Gavotte do have continuous movement but that may be only in the melody line which will give them a running feeling but the bass part will play a lesser role in the achievement of this effect. A dance may be more or less polyphonic rather than but look to see which part the melody line is. If there is a lot of 'imitation' -where parts of the melody are repeated in the other parts then this is a good clue to indicate polyphonic structure. If there are a lot of chords or parts moving in similar motion then the dance is more homophonic than polyphonic.

Listen to some dance suites and see if you can hear the different characteristics in the different dances. You will notice a difference in the French Suite Courante's compared to the Italian Suite Courante with the Italian Courante featuring continuous movement while the Italian Courante having varied rhythms which sometimes change time-signatures at cadence points. This will be easier to identify if you have the written music so it is worth getting hold of some dance suites to learn to identify the different dances and to compare dance suites from the French and Italian Styles.

Early Music Page See if you can find dance suites by Baroque composers. Try to pick which kind of dance you are listening to. You might like to try writing a simple Minuet of a few bars (12 or 16) or a Gavotte according to the characteristics outlined above. You can write a dance for one instrument only to keep things simple.

For your exam you will need to learn how to tell one dance movement from another. Use the Baroque Dance Suite Quiz in the table below to test your memory of this lesson. The following table may be helpful while you are learning:

In these dances and other Baroque music you will find little signs called 'ornaments' which give the melody a pretty sound. You may know some already. Here is the list of ornaments you will need to know the names of for this grade:

This is a challenging activity but it also gives you a framework for anlysing the music you look at and hear. You can begin with music you are playing on your instrument if you have the piano accompaniments also. Some may be polyphonic (generally those ones that are hardest to keep in time with your accompanist) and others may be more homophonic where the accompaniment has mostly chords. To listen to some dance suite movements go the midi world Early Music Page and scroll down to listen to the following movements:

You might like to write your own dance suite. You don't need to write all the suite movements you are learning about, three will do. They should be in the same key with a slower movement (Sarabande or Minuet) in the middle.

Lesson Thirteen: Spot The Modulation    Back 

Feel like some detective work? Put on your Inspector Gadget hat (or, Sherlock Holmes hat if you prefer) and come modulation hunting with me!

For this grade you will need to study a short tune and decide which key it modulates to. These are the possibilities:

Spotting the modulation is not always an easy thing to do. You must look for the clues and build a case of facts that will lead you to the right conclusion just like a detective. The first thing to do is, of course, to determine which key the tune begins with. If you get this part right it will help you find out which key the tune has modulated to because the new key will have special relationships to the first key. The first thing to do is to look at the key signature.

This will give you two possible options, one major and one minor. They will be related - of course you already knew that! If the key signature is one flat (Bb) you know that the first key is either F major or D minor. To tell the difference look at the first bar and see what triad can be formed from the notes in the first bar. This is because a tune does not always begin on the tonic note if there is an anacrusis but it should begin with the tonic triad in the first complete bar.

Melodies are written with a basic underlying harmonic structure so there should be evidence of the tonic triad in the first complete bar (after the anacrusis). A further clue is the presence of any accidentals in the first four bars of the tune. If the key is minor there may be a raised leading note which can be seen as it must have a natural sign or a sharp sign in front of it. Once you have established the first or original key you will better be able to identify the key into which the tune modulates. To do this you can follow these instructions:

For example, if the original key is D major. Note down the possibilities are A major (dominant key) and  the relative minor is B minor. Knowing the possibilities makes it easier to find the clues that are there, making the job easier and faster. This is a bit like making a hypothesis and then testing it.

LESSON FOURTEEN: MELODY WRITING    Back 

Find some song music (anything from a church hymnal to sheet music for a rock song) and look at how the words are divided up into syllables. Put a line in pencil between each syllable. This marks where the strong beats begin.

For 4th grade theory  you will be asked to choose either to

What makes a series of notes a melody?

If you sit at the piano or play around on your favourite instrument you might be able to put together some notes. But what is it about them that makes them sound like a piece of music? We have learned a lot about harmony and what effects is made by different combinations of triads. Cadences are used for particular effect in the middle and at the end of a piece.

How does this relate to music writing for one voice only?

Following the rules of harmonic progression can help you with your melody writing to a great degree.

A melody should begin and end on the tonic. The exception will be when an anacrusis occurs. This is because the first (imaginary) triad will be the dominant (V) going to the tonic triad for the first important beat. Blow Away the Morning Dew (one of the set folk songs), begins with an anacrusis. The important beat is the first beat of the second bar. The word Friday will be harmonised best with the tonic triad. The anacrusis  is best harmonised with the dominant triad because that makes the chord progression into an imperfect cadence which gives the feeling that there is something coming next: the rest of the song. However, although a melody can start on a note other than the tonic when an anacrusis is involved, the melody should always end on the tonic. You can often tell what key a piece is in by looking at the last note of the melody line as it should be the tonic.  

Transposition

The easiest way to transpose a melody is to begin by writing the scale degree numbers underneath each note. You can do this for your own melodies and also for the folk songs set for memorisation. Use these numbers as a guide to writing out the melody in a new key.

Lesson 15: The String Instruments

There are four stringed instruments typically used in orchestral music:

We have already learned some terms used with string playing. Fill in the meanings from the previous lessons:

Transposing clefs

Transpose Blow Away the Morning Dew from the treble clef to the bass clef. Remember to move the key signature so that it is in the right place to denote F# in the bass clef (ie on the line below where it appears in the treble clef). Do two or four bars at a time and check your work as you go.

The alto clef used by the viola was the original letter for C. It looks like the number 3 with a thick and then thin line before it and two dots after the '3'. One dot is either side of the third line on the staff which denotes that this line will be middle C. When you are finished, put in the phrase markings and the lyrics. Put in some bow markings on the strong or weak beats.

Transpose Polly Oliver from the treble clef to the alto clef. Remember to move the notes so that they correspond to the right position in the new clef. The accidentals for D major key will also be moved to their new positions. When you are finished, put in the phrase markings and the lyrics. Put in some bow markings on the strong or weak beats.

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