Jazz Theory 4 INTERVALS 2Other Intervals
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JT 4.1 - Altering Perfect Intervals

When an interval is enlarged ('raised') or shortened ('lowered') by a semitone it changes in quality.

• When a perfect interval is raised by a semitone it becomes augmented.

• When a perfect interval is lowered by a semitone it becomes diminished.

For example :

The symbol for augmented is : + or aug

The symbol for diminished is : o or dim

 In above example the intervals C-Gb and C-F# are the same, but are called differently according to how they are notated. (Gb and F# refer to the same note. They are called enharmonic equivalents) Likewise C-Fb and C-E are also the same, but written as C-E it is called a major 3rd, written as C-Fb is a diminished 4th. (Again Fb and E refer to the same note, and are enharmonic equivalents.)

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JT 4.2 - Altering Major Intervals

• When a major interval is raised by a semitone it becomes augmented.

• When a major interval is lowered by a semitone it becomes minor.

For example :

The symbol for minor is : m or min

Again, the name of the interval depends on how it is notated.

C ---> D# (+2) is the same as C ---> Eb (m3)

C ---> Db (m2) is the same as C ---> C# (+unison)

C ---> Ab (m6) is the same as C ---> G# (+5)

 D# and EbC# and Db G# and Ab are enharmonic equivalents

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JT 4.3 - Altering Minor Intervals

• When a minor interval is raised by a semitone it becomes major.

• When a minor interval is lowered by a semitone it becomes diminished.

For example :

C-Ebb ('E double flat') is the same as C-D (major 2nd)

C-Abb (dim6) is the same as C-G (perfect 5th)

(Don't worry too much about all these enharmonic equivalents, it is not a vital part of this course.)

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JT 4.4 - The Five Interval Qualities

We have now dealt with all five possible interval qualities.
They are :

 P = perfect M = major m = minor + = augmented o = diminished

The Interval Qualities Diagram (
IQD) below shows how these five interval qualities are related to each other:

Here you see that the major and perfect intervals both become augmented when raised (#).

But when lowered (b) perfect intervals become diminished, while major intervals first become minor. Only when these are lowered once more (a semitone) they also become diminished.

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JT 4.5 - How to Identify any Interval

To identify an interval you need to know :

1. The major scale of the bottom note of the interval

2. The Interval Qualities Diagram (IQD)

The examples below show how it works.

Example A
Identify these intervals.

The major scale of the bottom note, F, is :

 F1 G2 A3 Bb4 C5 D6 E7 f8

If the top note is in the F major scale the interval is either perfect or major.

Case 1 (F-Bb) : Bb is the 4th note of the F major scale. F-Bb is therefore a perfect 4th (P4).

Case 2 (F-B) : B is not in the F major scale. B is a semitone above the nearest note (and letter name)Bb.
F-Bb is a P4. Therefore F-B is a 'raised P4' which, according to the IQD, is an augmented 4th (+4).

Case 3 (F-Eb) : Eb is not in the F major scale. Eb is a semitone below the nearest note (and lettername) E.
F-E is a major 7th (M7). F-Eb is therefore a lowered major 7th, which (according to the IQD) is a minor 7th (m7).

Example B
Identify the upper note for each of these intervals.

The major scale of the lower note, D is :

 D1 E2 F#3 G4 A5 B6 C#7 d8

Case 1 : count 3 notes up on the D major scale --> F# = M3

Case 2 : count 4 notes up the D major scale, G, raise this note G# = +4

Case 3 : count 6 notes up the D major scale, B, lower this note Bb = m6

Case 4 : count 3 notes up the D major scale, F# = M3, lower this F = m3, lower this again : Fb = o3

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JT 4.6 - Inverting Intervals

When an interval is turned upside down it is called inverted.
For example :

Audio 1

The original interval can be inverted by either :

• raising the lower note an octave (a), or by

• lowering the upper note an octave (b).

(a) and (b) are inversions of the original interval.

Inversion Rule 1
The original interval number + the number of the inverted interval always add up to 9.

 In the example above : F - c = P5 c - f = P4 ---> 5 + 4 = 9

Inversion Rule 2

• Perfect intervals remain perfect

• Major intervals become minor (and vice versa)

• Augmented intervals become diminished (and vice versa)

One can draw a diagram very similar to the
IQD :

Therefore the inversion of a major 2nd (C-D) becomes a minor 7th (D -c) (M --> m, 2 + 7 = 9).

A minor 3rd (D-F) becomes a major 6th (F - d) , a perfect 4th (D - G) becomes a perfect 5th (G - d).

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JT 4.7 - Symmetry

The +4 and its inversion the o5 are a special case.
Although their names are different, they are exactly the same size, 6 semitones each (or 3 whole tones each).

These two intervals are called symmetric intervals.

Audio 2

The interval of 3 whole tones is an important interval in Jazz. It is called a tritone.

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JT 4.8 - Ear Training

Learn to recognise intervals by relating them to the beginning of a song.

Identify the minor, diminished and augmented intervals using the beginnings of these popular tunes.

Audio Demo
Minor, diminished and augmented intervals.

 m2 (minor 2nd) - The Entertainer(Also +1 : augmented unison) m3 (minor 3rd) - Greensleeves (Also +2 : augmented 2nd) o5 (diminished 5th) - Maria (from 'Westside Story') (Also +4 : augmented 4th) m6 (minor 6th) - Black Orpheus (Also +5 : augmented 5th) m7 (minor 7th) - There's a Place for Us (from 'Westside Story') (Also +6 : augmented 6th) The augmented 6th and minor 7th sound the same. The difference lies in the different music notation : C - A# is an augmented 6th, while C - Bb is a minor 7th.

First listen to the Demo, then try to identify the intervals on the Ear tests.

Here is an overview of all the intervals within the Octave :

 Interval In C Size Song P1 - Perfect Unison C - C 0 - +1 - augmented unisonm2 - minor 2nd C - C#C - Db 1 semitone M2 - Major 2nd C - D 2 semitones +2 - augmented 2ndm3 - minor 3rd C - D#C - Eb 3 semitones M3 - Major 3rd C - E 4 semitones P4 - Perfect 4th C - F 5 semitones +4 - augmented 4tho5 - diminished 5th C - F#C - Gb 6 semitones P5 - Perfect 5th C - G 7 semitones +5 - augmented 5thm6 - minor 6th C - G#C - Ab 8 semitones M6 - Major 6th C - A 9 semitones +6 - augmented 6thm7 - minor 7th C - A#C - Bb 10 semitones M7 - Major 7th C - B 11 semitones P8 - Perfect Octave C - c 12 semitones

(* = The 1st and 3rd note of 'Over the Rainbow' form a major 7th interval.)

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JT 4.9 - Quiz

A.
Identify these intervals.

B.
Identify the upper note for each of these intervals.

C.
Starting with C, keep on building perfect 5ths on top of each successive note until you reach another C, like this :
 P5 above C ---> G, P5 above G ---> D, P5 above D ---> ? , etc.

(If you duplicate any other note before you reach C again, you've made a mistake somewhere.)

D.
Congratulations ! Your Bush bass performance of 'Swing Time' was received with a standing ovation by the audience.
This has inspired you to consider this instrument more seriously and do some scale practice !

You know already the fingering positions for C, D, F, G, A, and c.

Find the fingering positions for the notes E and B, so that you can start playing the C major scale.

E.
Invert all intervals of Question A. What are their names ?

F.
Mark the tritone for each note on the Keyboard Diagrams.
The tritone interval is 6 semitones. It is exactly in the middle of a full octave. Example for the note E :

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JT 4.10 - Ear tests 8 & 9

Here is the Audio Demo to refresh your memory of minor, diminished and augmented intervals.

In Ear tests 8 and 9 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

 Ear test 8 - 12 intervals : minor and diminished 5th qualities only

 Ear test 9 - 12 intervals : perfect, major, minor and dim.5th

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JT 4.11 - Lesson Material

File Name Contents
jt04fac.gif Jazz Theory 4 - Facts sheet
jtx101.gif Keyboard Diagrams

Manuscript paper