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