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

More on Modulations

During our last session on modulations, we successfully identified the accidental[s] required to modulate from a variety of keys into new ones.  However, it was still a little difficult to be given a piece of music and actually identify real modulations.  Here’s some more tips:

Sharps as accidentals
One of things we notice about major key signatures is that the last sharp is the seventh note of the scale.  While that’s not true of minor key signatures, we do know that the seventh note of the minor scale is raised, so it is often written as a sharp too.  That means that if we have a modulation to the dominant or the relative minor (both very common), in both cases the seventh note of the new key is likely to be marked with a sharp.  So, why not check this out as a first port of call - if you find a sharp as an accidental, begin by assuming its the NEW seventh note, go one step up to find the assumed new tonic and see if key signature of the new key fits with the all the accidentals present in the piece at that point (that is, the sum total of the key signature plus any accidentals).

Flats as accidentals
We could try this one with flats too.  The last flat in a key signature is the fourth note of the major key, so if there’s a flat maybe it’s the fourth note of a new major key signature.  However this would only work for a major scale - it would actually be the sixth note of a minor scale with the corresponding key signature, but that’s just another possibility you may want to check out.

Naturals as accidentals
The problem with naturals is that they have two functions.  They may cancel a sharp (that is they lower it a semitone) or cancel a flat (raise it).  This means that it might do either - how can you tell?  You have to ask yourself, “What is this accidental doing at this point in this music?”  If it’s raising a note from the key signature, then treat it as though its a sharp, if it’s lowering a note from the key signature, then treat it as though its a flat.  If its canceling an accidental, then its returning the music to the key signature from wherever it’s been.  Remember, it may represent a modulation from a minor key to its relative major (which would need to loose the raised seventh).

Flats AND sharps as accidentals in the same place
There are no key signatures which contain both sharps and flats.  This means that there is only one solution to this particular problem, that is, you have a flat key signature and a raised seventh, which means a modulation to a minor key.

Multiple key changes in succession
It is quite common for a piece of music to pass through a number of key changes in succession without returning to the home key of the piece.  If this happens, you will gain more accidentals, possibly loose others, and it may take some time before the music settles back to its original key.  When you see something like this taking place, each new key will be related to the key immediately before it, not necessarily the home key of the piece.  Beware that modulations can take place every bar, or even every beat.  To solve these, you need to take a very thin “slice” of the music and sample the accidentals within that slice, then see how long those accidentals last before they change again.

These should see you through for most simple examples you are likely to meet in an exam. But be aware of other possibilities too, especially for “real world” music ...

Melodic minor scales
These can provide a trap for the unwary!  A melodic minor scale changes its notes depending upon its direction - raised sixth AND seventh notes on the way up and returned to the key signature (often called, “lowered”, although not really) on the way down.  Melodic minor scales are so called because we use them to write melody.  The reason for this is that they’re much easier to sing and play and they sounds nicer than harmonic minor scales which are used for harmony.  The problem for us, trying to identify modulations, is that they introduce another accidental to try and account for.  Just be aware that they may be used in a melody, of where the music is melodic, such as keyboard works by J S Bach - two raised notes in a row in an ascending sequence of notes may indicate that they are the sixth and seventh notes of the melodic minor scale, which would give away the new key.

Ornaments
It is quite common for an ornament to include an accidental which has no bearing of the key whatsoever.  For example, a main note of the melody may drop a semitone, to the note below it raised by a sharp or natural, and then returning to the same note again.  Don’t dismiss it out of hand, but don’t assume that it must be a modulation either.  In such cases, you should ask whether you can find that same accidental elsewhere in the music, or whether it has a harmonising chord underneath it.

Chromatic scales
Chromatic scales are quite common in music and have absolutely no effect upon the key of the piece at all, because they don’t have the patterns (of TONES AND SEMITONES) necessary to help the ear focus in upon a particular key note or tonic.  If you are searching for modulations they certainly look fearful, but in terms of finding a new key they are absolutely meaningless.  Just notice what’s happening where they begin and where they end.

Now, have a look at this example, the Allemande from Bach's fourth English Suite, and see if you can identify the various modulations which take place during the course of the piece.  Of course, you should begin by identifying the home key ...




https://docs.google.com/open?id=0B9JdpU-tw7FuVjVWMDduTU5NdEU

Identifying Modulations

IDENTIFYING MODULATIONS

A modulation occurs when a piece of music moves away from its home key or tonic, to another key which is usually related in some way to the home key.  The most common modulations are:

• To the dominant [you may remember that the "dominant" note is the fifth note of a scale - the "dominant key", then, is the key which begins on that note]
• Major to relative minor
• Minor to relative major

Modulations can be shown by:

• Changing the key signature, or
• The use of accidentals to add or delete sharps or flats from the key signature.

Which is the most common method? [The use of accidentals - these are used whenever the modulation is brief, either passing quickly on to another key or back to the original.  Pretty much ANY piece of music does this.  A new key signature is used for a larger section in a piece of music which will then remain in that new key for an extended period.]

The worksheet [see the link at the bottom] will take you through the following modulations ...

MODULATING TO THE DOMINANT [in major keys]
Name the original key.  Work out the dominant key and key signature.  Identify the accidental needed to make that change.

MODULATING TO THE RELATIVE MINOR
Now the relative minor: remember, ANY minor key has an accidental on the [seventh] note of the scale.  So, the new accidental will be on that note.

MODULATING TO THE RELATIVE MAJOR
What change would you expect, then, if we move in the opposite direction - from minor to relative major?  [We would see the raised seventh of the original minor key become a natural - it would "disappear".  This can make it hard to spot - how do you identify something that isn't there!?]

MODULATING TO THE DOMINANT [in minor keys]
BEWARE!  Modulating to the Dominant key in the minor will require more accidentals than you expect.  Firstly you will change the keysignature - that will add an accidental.  Secondly you will loose one raised seventh and gain another - potentially two more accidentals, making a TOTAL of THREE!  This would explain why its much less common to do this.

OTHER MODULATIONS will require different (and possibly more) accidentals:

• Modulating to the Subdominant [in major keys]
• Modulating to the Subdominant [in minor keys]
• Modulating to the PARALLEL major or minor [the other mode beginning on the same tonic, e.g. C major to C minor and vice versa]
• Modulating to the Supertonic minor [this is actually quite a common modulation]

https://docs.google.com/open?id=0B9JdpU-tw7FuVkJZczFySGZ6Rkk

Key Signatures - Minor Keys

KEY SIGNATURES - MINOR SCALES

“What do you get when you drop a piano down a mine shaft?”

Answer: A FLAT MINOR

RELATIVE SCALES are a minor third apart - Major scale above, minor scale below.  Here are the steps:

• Work out the major key signature.
• Work a third down through the major scale from the tonic [to the sixth note or submediant], and this will give you the keynote [or tonic] of the relative minor scale.
• Remember that the seventh note [second last] of the minor scale is raised a semitone.
• If you know the minor keynote, you will need to do the opposite to find the relative major - go a minor third higher - and then work out the key signature.

https://docs.google.com/open?id=0B9JdpU-tw7FuRnM2S0lYS2hKM1E

Key Signatures - Major Keys

KEY SIGNATURES: MAJOR KEYS - “The only sentence you will ever need to learn”

Key signatures will ALWAYS be identical on both staves.  Yes, it is possible for them to be different - its called "polytonality" [literally "many key signatures"] or "bitonality [literally "two key signatures"] - we’ll look at that later.  You will need to be able to read them and write them in either clef, remembering that the letter names have different positions on each.

Learn this sentence:

Father

Charles

Goes

Down

And

Ends

Battle

Read downwards it is the order of sharps, so the key signature that has one sharp WILL ALWAYS BE an f sharp.  Four sharps would be f, c, g & d.  Identifying the key note [the tonic or first note of the scale] of the MAJOR SCALE is easy from a key signature.  Remember this: the LAST SHARP in the key signature is ALWAYS the SEVENTH NOTE of the scale [the one before the key note or tonic].  So, for example, the key signature of f sharp: f sharp would be the seventh note, going one step up gives you a G = G major.  The four sharp signature given above, the last sharp is d ["Father Charles Goes Down]", going one step up to E = E major.  This is true of ALL key signatures containing sharps.

For flat key signatures, go back to the sentence and read it BACKWARDS:

Battle

Ends

And

Down

Goes

Charles'

Father

This is the order of flats.  So the key signature with two flats will be b flat and e flat.  Five flats would be b, e, a, d, g.  Identifying the key note is also easy for flats, just different.  The SECOND LAST FLAT IS the key note. So, for two flats, the second last flat is b flat = B flat major.  For the five flat key signature above, the second last one is D flat = D flat major.  This is true of ALL key signatures containing flats [almost - see below].

Learning these, you can work out every major key that exists, with two exceptions, which you must remember:

[a] C major has no sharps or flats, so you can't apply either rule to it.

[b] F major has only one flat, so it doesn’t have a second last flat.  However notice that its last [only] flat is the fourth note of the scale, and in all the other flat key signatures the LAST flat will be the fourth note of the scale too.  You could work them all out that way - if you do, remember "SHARP SEVENTH note, FLAT FOURTH note".

You can also apply those rules in reverse to work out a key signature from any given tonic note.  What would the key signatures of the scales commencing on these notes be:

D major

B major

B flat major

A major

A flat major

E flat major

Finally, I've said "MAJOR" scales here.  MINOR keys are different, in that you've got to do all this, but there's another step involved - we'll worry about that another time.

Here's our worksheet:

https://docs.google.com/open?id=0B9JdpU-tw7FuWFBrVVFQa0dkeXM

Scale Degree Numbers, Technical Terms and the Pentatonic Scale

NOTES:

* The following table should be read from bottom to top, just like a scale.

* Scale degree number “8” is called “1”, because they are the same note, an octave apart.

Number	Technical name	Major solfa	Minor [harmonic] solfa
1	tonic	doh	la
7	leading note	ti	se
6	submediant	la	fa
5	dominant	soh	me
4	subdominant	fa	ray
3	mediant	me	doh
2	supertonic	ray	ti
1	tonic	doh	la

WE also looked at THE [anhemitonic] PENTATONIC SCALE

Pentatonic = “5 note scale”

Anhemitonic = “without semitones”

1. Write the following notes of the C major scale on the staff:

tonic, supertonic, mediant, dominant, submediant, tonic.

2. Write the appropriate solfa names [major] under each of the notes.

3. Play and / or sing it through.

Have a look at: http://www.youtube.com/watch?v=ne6tB2KiZuk

(World Science Festival 2009: Bobby McFerrin Demonstrates the Power of the Pentatonic Scale)

Here's our worksheet:

https://docs.google.com/open?id=0B9JdpU-tw7FuQlg1TEx4bnRxU1U

Writing Scales

There are a number of scales you can be asked to write.  The major scale is the first that you are likely to meet, followed closely by the harmonic minor scale.

How many letters does the musical alphabet have in it?  SEVEN

At first, you will have to write scales over one octave.  The basic structure of a scale is very easy to set out.  They all use every letter names once only, with the exception of the first note, which is given one extra appearance (once at the beginning and once at the end).  This note is called the “tonic” or “key note”.

WRITING SCALES OVER TWO OCTAVES.  A one octave has eight notes in it.  So, how many notes does a two octave scale have?  FIFTEEN

WHY?  A one octave scale contains every note of the musical alphabet played ONCE, with one exception: the key note, which gets ONE extra playing - at the top as well as the bottom.  A two octave scale contains every note of the musical alphabet TWICE, with one exception: the key note which gets ONE extra playing, not two extra playings.

https://docs.google.com/open?id=0B9JdpU-tw7FuQW5NdEEyTEdDcFk

Syllables, accent and rhythm in verse

We speak with a natural rhythm, accenting certain syllables over others.  Poetry takes advantage of these natural stresses to create a regular pulse when it is read. 

1. Find the words which contain more than one syllable in the verses below and write them down next to the verse, indicating the division between syllables with a hyphen (“-”):

• Look for prefixes and suffixes, which easily separate from the rest of the word.
• Where there are consecutive consonants, it is usual to split the word between the consonants, especially double letters.  However, consonant blends (“-ph-”, “-ch-”) should remain intact.
• Splitting a syllable immediately after a vowel implies that the vowel is a long one, and you need to decide whether that is appropriate given its usual pronunciation.

My Love is like a red, red rose

That's newly sprung in June; 

My Love is like the melody

That's sweetly play'd in tune.

(Robert Burns)

Birds of a feather flock together,

And so will pigs and swine;

Rats and mice will have their choice,

And so will I have mine.

(from Mother Goose)

Dear friends, we surely all agree

There's almost nothing worse to see

Than some repulsive little bum

Who's always chewing chewing gum.

(Roald Dahl)

Old Deuteronomy's lived a long time 

He's a cat who has lived many lives in succession 

He was famous in proverb and famous in rhyme 

A long while before Queen Victoria's accession.

(T S Eliot)

2. Find the accented syllables in these words.  Read each of these words aloud or quietly to yourself.  Notice how one syllable will stand out from the others.  Mark that syllable by underlining it.  If you’re not sure where the accent should go, experiment by stressing each syllable in turn, until you find the one that makes the most sense.

3. Choose one of the stanzas above, and place a vertical line BEFORE the accented syllables.

You will probably have more than one accent per line.  The first accent is not always on the first syllable.  If an accent falls within a multi-syllabic word, it will always be on strong syllable.  If a word is long enough, it may get a number of accents (“Supercalifragilisticexpialidocious”).

[HINT: How many marks are assigned to this question? 7 marks would indicate that the examiner will expect seven accents to be marked.  If you’ve got more or less, you’re probably wrong.]

WRITING RHYTHMS TO VERSE

This part of the exam is called, “Creative”, which means that there is more than one right answer - within limits!  Those vertical lines you marked in your verse represent bar lines in music, and if you’ve done this correctly, you’ve grouped the syllables into roughly equal groups.  This may suggest one or more appropriate time signatures to you.

Choose a time signature for your verse.

Now, write a rhythm, using ONE note per syllable.  Make sure you adhere to your bar lines.  It should reflect a natural way of saying these words, although as you get more confident doing this you could incorporate some more unusual rhythms to add an element of surprise.

Finally, you need to present the words and rhythm together.  The words will be split into syllables wherever necessary, using hyphens.  When you write the rhythm out, make sure you give yourself lots of space between notes so you can place each syllable directly underneath the note that belongs to it.

https://docs.google.com/open?id=0B9JdpU-tw7FuRmxXbzRDMDNZYTA

Time Signatures and Note Groupings

Time Signatures

Time signatures are classified using two words:

Simple or Compound
and
Duple, Triple or Quadruple

Simple / Compound refers to the beats which make up the bar - if the beat is a note without a dot it is "simple", if it is dotted it is "compound" (that is, it is NOT SIMPLE, it is complicated).  In actual fact, "compound" time refers to a time signature in which the beat is not divided equally into halves, it is divided in to thirds.

Duple / Triple / Quadruple refers to the number of beats (this is the easy bit): 3 beats is "duple", three beats is "triple", and four beats is "quadruple".

Note Groupings

The purpose of grouping notes and rests is to simplify the reading of music for the player.

Some fundamentals:

• You can fill a whole bar with a single note or rest.
• In most cases, any note that includes the first beat is OK (*see the end of the activity sheet).
• You can group beats 1 & 2 together, and beats 3 & 4 together (where they exist),
• BUT YOU CANNOT group beats 2 & 3 together.
• You can group the first and second parts of a beat together,
• BUT YOU CANNOT group the second and third parts of a beat together.

EXCEPTIONS - For when applying the usual rules makes it look more complicated (remember, the aim is simplicity for the reader).

If you’re not sure, ... GROUP TO SINGLE BEATS.

In an exam, you might be asked to:

• Complete a bar with rests (do this for the first bar in each line below)
• Complete a bar with quavers correctly grouped (do this for the second bar in each line below
• Complete a bar with semiquavers correctly grouped
• Complete a bar with notes and rests (do this for the last bar in each line below)
• Identify correct and incorrect groupings
• Identify time signatures from groupings
• Correct groupings

Here is the worksheet we completed in class:

https://docs.google.com/open?id=0B9JdpU-tw7FuTWhwR0pocGUxQVE

Note Values - 10th August 2012

Note values

Here's our first worksheet - with SOME of the answers.

https://docs.google.com/open?id=0B9JdpU-tw7FuQjhRTWpfMU01MFU

Welcome!

Welcome to my new music theory page.  This is where I'll post all the work we've done in Friday night music theory classes.  This way everyone will have somewhere to go to [a] catch up on classes you've missed, and [b] review the topics we've covered in class.

The first few posts will be retrospective - that is, I'll put up the lessons we covered in our first few weeks of classes.

Comments and questions are welcome.

Enjoy!