Primary Triads

Just as there are three primary colours, every scale has three primary triads.  The primary triads are built upon the FIRST, FOURTH and FIFTH notes of any scale.

The technical name of the FIRST NOTE of the scale is the ______________________.  So, the triad built upon this note is called the ________________ TRIAD.

The FOURTH NOTE of the scale is also called the ______________________. So, the triad built upon this note is called the ________________ TRIAD.

The FIFTH NOTE of the scale is also called the ______________________. So, the triad built upon this note is called the ________________ TRIAD.

Primary triads have two important features.

Firstly, they contain all notes of the scale to which they belong.  Find all the notes of the scales above in the three primary triads.  Which scale degrees occur twice? ________________________.

Secondly, notice the distance between the tonic triad and the other two.  If you place the subdominant triad below and the dominant triad above, the distance is ______________.

This means that the three primary triads are next to each other on the circle of fifths.  Therefore, the subdominant triad and the dominant triad also represent the two most closely related keys to the tonic.

You will find the worksheet for this topic here:
https://docs.google.com/file/d/0B9JdpU-tw7FuRHlOekFycFhBcFU/edit?usp=sharing

We also did some Music Theory craft!  The following worksheet has two pages.  The first contains two strips.  Cut each strip out and glue them together using the spare tabs at the end of each strip.  Provided you glue them together with both parts upright, there is only one way to do this.  This is the circle of fifths.  The second page has an irregular shape in the middle, which you need to cut out (I laminated mine).  When this is placed over the loop created from the first page, it shows you every possible key signature with the primary triads of both the major and minor scales.  If you wish to you can cut out the slots on either side of the centre cutout, to thread the loop through (but you would need to glue the last part of the lop together after you do this).

You will find this worksheet here:
https://docs.google.com/file/d/0B9JdpU-tw7FudXRLeVRHWVF2aUk/edit?usp=sharing

Harmony: Using Primary Triads

In class, we used the melody, "Michael, Row the boat ashore" as a first example, using primary triads to create a four part vocal arrangement.  You will find it on our worksheet for this topic.

Write the primary triads in C major, labeling them I, IV and V.

Write the melody out, with all stems pointing upwards.  This will be your Soprano part.  Then, follow the steps below to provide a simple harmonization in four part vocal style using the primary triads.

1. Familiarise yourself with the RULES TO FOLLOW [see below].
2. Identify which triad[s] can be used to harmonize each note.
3. Write the root of each chord in the bass, stem pointing down.  This will be the Bass part.  Check for consecutives [see rule 4].  If you get this right now it is much easier to complete the internal parts.
4. Are there any places where it would be appropriate to write a FIRST inversion chord for a little variation?  If you make any changes, check for consecutives again.  [Second inversions should only be used in very specific ways you don’t know about yet].
5. Insert the Alto [stems pointing down on the treble clef] and Tenor [stems pointing up on the bass clef].  You will find this easiest if the two inner parts are as BORING AS POSSIBLE, that is, making frequent use of repeated notes and small steps.  Rewrite the Bass as necessary as you go, checking for consecutives with the Soprano if you make any changes.
6. Check all possible pairs or parts to make sure that you have not written consecutive fifths, unisons or octaves.  Pay special attention to the pairs that use different clefs, as these are hardest to spot (Soprano-Tenor, Soprano-Bass, Alto-Tenor, Alto-Bass).

RULES TO FOLLOW:

1. Each part should adhere to the notes of its own range.
2. Every chord must contain its root and its third.  The fifth of the triad is optional.
3. You may double the root or the fifth, but you may not double the third.
4. You must avoid consecutive perfect fifths, unisons and octaves at all times.  That is, no two parts should move in such a way that they are a fifth, octave or unison apart for two consecutive chords.  However, two parts MAY repeat the intervals of a fifth, unison or octave (that is, they may repeat the same notes).
5. There should be no more than an octave between the Soprano and the Alto or between the Alto and the Tenor.  However you may have any distance between the Tenor and the Bass.
6. Parts cannot CROSS.  That is, every chord should have the Soprano on the top, Alto underneath, Tenor underneath that, and Bass at the bottom.
7. Parts cannot OVERLAP.  That is, two parts MAY sing the same note, and they may repeat it, but they should approach it and leave it in opposite directions (alternatively, one may repeat it again while the other approaches and / or leaves it from its own direction).

You will find the worksheet for this session here:
https://docs.google.com/file/d/0B9JdpU-tw7FuRDlra05mU3BGNDQ/edit?usp=sharing

The Circle of Fifths

The circle of fifths is an arrangement of the 12 notes of western music in perfect fifths.  It helps us to understand the relationship of the various keys.

Looking at the notes of a scale on a keyboard, we see the letter names occur in alphabetical order.

This might lead us to conclude that the most closely related scales are those which begin on notes that are next to each other.  However, when you consider the scales of C major and B major, for example, you will see that they have very few notes in common.  What letter names do C major and B major have in common?

The scales which have the most notes in common with C major would be the scales with key signatures that are most similar to the key signature of C major - in this case the key signatures with the least number of sharps or flats, because C major has no sharps or flats.  The two scales that have these key signatures are?

What intervals separate these new key notes from C, remembering that you can find them both above AND below C?

Of course, the other scale which is closely related to C major is its RELATIVE minor (the scale that SHARES its key signature), in this case it is?

When music MODULATES (changes key), it can move anywhere on the circuit, but to do so, it is going to go past it’s immediate neighbours first, then past their neighbour’s neighbours, and so on.  That is, it will most likely travel around the circle of fifths in one direction or another.

Now, test this out on some music you are playing.  Trace it’s journey around the circuit.

Have a look at my previous post on identifying modulations and see how the circle of fifths relates to what is written here.

Here's our worksheet for this topic:

https://docs.google.com/file/d/0B9JdpU-tw7FuaGZoRGF4YmtnREk/edit?usp=sharing

Triad Quality

There are FOUR different quality of triads.  The most familiar ones are MAJOR and MINOR.  The less common ones are DIMINISHED and AUGMENTED.

Triads are made up of different combinations of major and/or minor thirds. If a triad is made up of a pair of thirds, here are only four possible combinations of these, and these are the four types of triads.

A MAJOR TRIAD is a major third between the lower two notes, and a minor third between the top two.

A MINOR TRIAD is the reverse - a minor third between the lower two notes and a major third between the top two.

A DIMINISHED TRIAD is made up of two minor thirds.

AN AUGMENTED TRIAD is made up of two major thirds.

Try writing all four triads in root position, beginning on the same root note.  This will help you understand the differences (and similarities) between the qualities of triad.  Playing them on a keyboard will help you hear the differences.

TRIADS OF THE MAJOR SCALE
In the last post, we wrote out the major scale and based a triad on each note of that scale.  The following activity can be found on the worksheet: Write one octave ascending of the major scale with TWO SHARPS in the key signature.  Then, add two more notes to each note of the scale to create a series of triads.  Label each triad using roman numerals (I, II, etc) and state the QUALITY of each triad.

It doesn't matter which major scale you do this with, the series of triads will always be the same quality:
I - Major, II - minor, III - minor, IV - Major, V - Major, VI - minor, VII - diminished, VIII [=I] - Major

TRIADS OF THE MINOR SCALE
You can do the same with the minor scale.  The worksheet activity is: Write one octave ascending of the minor scale which commences on the same key note as the example above.  Create a series of triads as before, label each triad using roman numerals (I, II, etc) and state the QUALITY of each triad.  Remember the raised seventh! (HINT: you will need to write it more than once, won’t you!?)

It doesn't matter which minor scale you do this with, the series of triads will always be the same quality:
I - minor, II - diminished, III - Augmented, IV - minor, V - Major, VI - Major, VII - diminished, VIII [=I] - minor

Here is the worksheet for this topic:

https://docs.google.com/file/d/0B9JdpU-tw7FuLWh3ZXEyZXJXeEE/edit?usp=sharing

Triads

TRIADS

A TRIAD is a three note chord, each note written a third away from the next note.  Triads are easy to write.  When written in root position the notes will appear either all on lines or all on spaces.

When we refer to the individual notes of a triad, it is usual to refer to them as “the root”, “the third” and “the fifth” because these are the intervals between the notes.

When we write a triad like this, it is described as being in:

• CLOSE (or closed) POSITION - because the notes are written as close as they can be, and
• ROOT POSITION - because the ROOT of the triad (the note we base it upon) is on the bottom.

Triads can be written in OPEN POSITION, by using the same letter names, but writing them further apart.

Triads can be written in AN INVERSION by putting one of the other two notes on the bottom:

• ROOT POSITION always has the root at the bottom, 
• FIRST INVERSION always has the third at the bottom, and
• SECOND INVERSION always has the fifth at the bottom.

What are the intervals between the notes of these inversions in closed position?

Between the:	Root Position	First Inversion	Second Inversion
top notes	3rd	4th	3rd
bottom notes	3rd	3rd	4th

ANALYSING TRIADS

When you are asked to analyse triads in music, the notes are rarely written in closed position.  To analyse any triad in a piece of music, your first task will be to rearrange the notes given - either on paper or in your head - to a closed position so that the triad and its inversions are easy to recognise.  Often there will be four parts.  This will mean that at least one note will be doubled (played or sung by two instruments or voices), and sometimes one note may be missing.

To analyse a piece of music, follow these steps:

• Work out the key of the piece, using the key signature, and last notes.
• Write ONE OCTAVE ASCENDING of this scale.
• ADD a THIRD and a FIFTH above each note to create its triad.
• Then label each triad using ROMAN NUMERALS (I, II, III, IV, etc)
• Work through the piece, one chord at a time, indicating the root note of each triad (using the roman numerals, above) and its position (using “a” for root position, “b” for first inversion, and “c” for second inversion).

NOTE: Many pieces include complications, such as seventh chords and passing notes, which we'll deal with in another session.

You wil find the worksheet for this topic here: https://docs.google.com/file/d/0B9JdpU-tw7FuY0hEMzRBMTE4N2c/edit?usp=sharing

Intervals - Inversions

Inverting an interval means to turn it upside down - the bottom note becomes the top note and vice versa.

Does it matter which note we choose to move?

No.  You can invert interval two different ways: moving the bottom note to the top, or moving the top note to the bottom.  The result is the same either way, just written in different octaves.  In an exam, unless it says otherwise, do whatever is easiest.

There is a simple formula for working out the inversion of ANY interval.

NUMBER:  Remember the number 9.

9 - [Interval number] = [Inversion number]

So, a sixth inverted becomes a third - obviously, the reverse is also true (a third becomes a sixth).

QUALITY:  This is a bit more complicated, but not a lot ...

• PERFECT remains PERFECT
• MAJOR becomes MINOR [and vice versa]
• AUGMENTED becomes DIMINISHED [and vice versa]

Invert these intervals:

Interval	Inversion
Minor 3rd
Diminished 5th
Major 7th
Perfect octave
Major 6th
Augmented 2nd
Augmented unison

The only interval this DOESN’T work for is the Augmented Octave.  WHY NOT?

If you follow the proceedure given here, an Augmented Octave would becomes a Diminished Unison.  But think about it - to diminish an interval is to make it a semitone smaller.  Yet a perfect unison is the interval between any note and itself.  So, you cannot diminish a unison, only augment it (make it larger).

Notice, this works for intervals up to an octave.

Here's the link to our worksheet.

https://docs.google.com/file/d/0B9JdpU-tw7FuRm9lb2g1ZTNySDA/edit?usp=sharing

Naming intervals by number and quality

INTERVALS BY NUMBER

The trick to giving intervals their numeric value is to count the first note as ONE (it is also called a “unison”), NOT ZERO.

QUALITY: PERFECT, MAJOR and MINOR

Always think about intervals from the major scale beginning on the lower note.  If the top note fits into the major scale beginning on the bottom note, it will be a PERFECT or MAJOR interval.  The PERFECT intervals are Unison, 4th, 5th and Octave, all others are MAJOR (that is, 2nds, 3rds, 6ths & 7ths).

A MINOR interval is one semitone shorter than a major interval.

QUALITY: AUGMENTED and DIMINISHED

Beyond these three (Perfect, Major and Minor) there are two other qualities of interval.  AUGMENTED can be applied to any interval: it is one semitone larger than a Major or Perfect interval.  DIMINISHED can also apply to any interval, and is one semitone smaller than a Perfect or Minor interval.

TWO HELPFUL HINTS

Firstly, remember that it is possible to find EVERY type of interval within a major scale ... if the lowest note on the interval is not the first note of the scale.  Name these intervals, all found in C major:

Secondly, naming intervals where the lower note is an accidental can be a problem, because of having to think about complicated key signatures.  But there’s an easy way around this.

Look at the first pair of intervals in the next example [refer to the worksheet].  The first two intervals are the same - they are both a major third, but in the case of the second interval I’ve removed the sharps so it’s easier to work out.  You can do this to any interval, so long as you do the same to BOTH notes at the same time - remember that adding a flat has the same effect as removing a sharp and vice versa.  Have a look at the following three pairs.  Notice the change in the notes from the first example to the other, and name the intervals according to quality and number.

Also, notice that you should NEVER change the note names, only the accidental.

Here's our worksheet for this topic:

https://docs.google.com/open?id=0B9JdpU-tw7FuOWE3Q01kZ3ZJYWc