Jazz Theory 3 INTERVALS 1 Intervals of the Major scale Introduction Classification of Intervals Perfect Intervals Major Intervals Compound Intervals Ear Training Quiz - Quiz Answers Ear tests 6 & 7 - Answers Lesson Material - General files Jazz Theory lessons online

JT 3.1 - Introduction

Music can be described as an inter-action of sounds.
One sound can of course have its beauty and interest, but it requires a second sound to produce an interval, the first word of a musical 'story'.

In the previous two Lessons we dealt with the smallest building blocks in Western music, semitone and tones.

Sometimes it is appropriate to express the distance between two notes as so many semitones (or tones), e.g. C to E are 4 semitones.

However in music each interval has its own unique sound, quality and mood.

For example (Audio 1) :

• the interval C - E consists of 4 semitones. It creates a happy and positive mood.

• Now reduce this interval by only one semitone into C - Eb, and the mood has instantly changed to mellow and somewhat sad.

Intervals are therefore usually called by their own unique name.
In above example the interval C - E is called a major 3rd, not '4 semitones'.
The interval C - Eb is called a minor 3rd, rather than '3 semitones'.

Compare this with the difference between describing a masonry structure as '5600 bricks', instead of calling it a 'stone wall' or a 'chimney' .
The first description is useful to the bricklayer who has to build the structure, but the second description is obviously more meaningful as it conveys to us a clear image of the structure.

JT 3.2 - Classification of Intervals

Intervals are named and classified using the major scale as basis.

Each name consists of a number and a quality.

The number is the number of major scale letter names included within the interval.

Audio 2

For example the interval :

• C-D is called a '2nd' for it includes two letter names, C and D.
  
  
• C-F is called a '4th', for it includes the four letter names C, D, E and F.
  
  
• E-G# is called a '3rd', for it includes the (E-) major scale letter names E, F(#) and G(#).

JT 3.3 - Perfect Intervals

Intervals are divided into five different qualities.
These qualities are :

In this Lesson we will deal with the perfect and major intervals only.

The most important intervals in music are the perfect intervals.
There are four perfect intervals :

Audio 3

The perfect intervals were first defined by the Greek scientist Pythagoras more than 2500 years ago, using his single stringed instrument the 'Monochord'.

Pythagoras discovered the simple mathematical relationship that exists between the tonic (first note) and the 4th, 5th and octave of (what we now call) the major scale. He tensioned his Monochord to produce the note 'C' on its full length string, he then produced : the note 'F' by shortening the string length to three quarters of its full length. Reducing the string (and wave-) length further, to two thirds of the full length produced the note 'G'. When he finally put his finger exactly in the middle of the string he produced another 'c', an octave higher than the pitch produced by the full string length. Pythagoras recognised these simple mathematical and acoustical relationships as most important, and classified the intervals they defined as perfect.

These relationships occur between the tonic, 4th, 5th and octave of the major scale in any key.

Audio 4

You can check this out on any string instrument, like a guitar, violin, bass.

On a guitar E string for example (vibrating string length 650 mm).

• Reduce the vibrating string length (with your finger) to 3/4 of its full length (487.5 mm), and it will produce an 'A' (a perfect 4th up from E).
  
  
• Now reduce the vibrating string length to 2/3 of its full length (433.3 mm). This will produce the perfect 5th : B.
  
  
• When you put your finger in the middle of the string (325 mm) it will produce another E, a perfect octave higher than the full string tone.

JT 3.4 - Major Intervals

The remaining intervals between the tonic and the other notes of the major scale are all classified as major. They are the :

Audio 5

Here are all intervals of the major scale, measured from the tonic note upwards.

Audio 2

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JT 3.5 - Compound Intervals

Intervals larger than an octave are compound intervals.

A compound interval has the same quality as the corresponding interval an octave smaller.

For example :

• the 9th is a major 9th = an octave larger than a major 2nd.

• the 10th is a major 10th = an octave larger than a major 3rd.

• the 11th is a perfect 11th = an octave larger than a perfect 4th.

• the 12th is a perfect 12th = an octave larger than a perfect 5th. and so on

Audio 6

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JT 3.6 - Ear Training

It is a good idea to learn to recognise intervals by ear.

An easy way to learn this is by associating an interval with the beginning of a song you know.

Start with the Perfect intervals.
Practise singing them by starting on different notes. And when you hear an interval try to match the correct song with it.

Here are some song suggestions.

On the Audio Demos (1 & 2) each interval is played three times.

1. one note after the other, lower note first
2. repeat of above
3. both notes played together
4. then follows the beginning of the melody which starts with that interval

Audio Demo 1

When you think you can recognise the perfect intervals try Ear test 6 (or do it later in the Ear test Section).

After this move on to recognising major intervals.
First listen to the Audio.

Audio Demo 2

Then try Ear test 7. This one contains both perfect and major intervals.

Here is an overview of all intervals we have dealt with so far.

JT 3.7 - Quiz

To find the answers to Quiz sections A., B. and C., imagine the major scale of the bottom note, then count your way up that scale to the top note.

A.
Identify these intervals. The first note is the lower one. All intervals are within the range of an octave.

1 = F - A	2 = F - E	3 = F - G	4 = F - Bb	5 = F - D
6 = D - C#	7 = D - A	8 = D - F#	9 = D - B	10 = D - G
11 = G - D	12 = G - A	13 = G - E	14 = G - F#	15 = G - B

C.
Form the interval indicated by placing the correct note above the one shown.

D. You have an old tea chest with one string. The string is 120 cm long and is tuned to a low C. You want to play a bass line (using chord root tones only) for 'I Got Rhythm' in the key of F. Calculate the finger positions on the string to play the required bass notes, which are : C - D - F - G - A Hints : 1. Make your calculations using Pythagoras' formulas 2. Use the perfect intervals of the C major scale and D major scale. 3. For the tones to lie within one octave : all fingering positions must be within the 120 cm - 60 cm range.

E.
Mark the perfect intervals (P4, P5 and P8) for the tonic note of all 12 major scales on the Keyboard Diagrams.
Like this for the E major scale :

1. P4 and P5 (measured from the tonic note) are the 4th and 5th note of each major scale.
2. Count the number of semitone from the scale tonic (1st note) upwards.
   perfect 4th = 5 semitones
   perfect 5th = 7 semitones

F.
Write the perfect intervals (P4, P5 and P8) for the tonic note of all 12 major scales on the Scale Letters Diagrams.
Like this :

JT 3.8 - Ear test 6 & 7

Ear test 6
Here is Audio Demo 1 to refresh your memory of perfect intervals.

In Ear tests 5 and 6 each interval is played three times :

1. first one note after the other, lower note first
2. repeat of above
3. both notes played together

JT 3.9 - Lesson Material