Music · Lesson 4

Quality, number, inversion, compound intervals, consonance and enharmonic intervals

JAMBWAECNECO

What the syllabus asks

JAMB: JAMB Music Section A 6 (diatonic and chromatic intervals and their inversions: perfect unison, 4th, 5th, octave; major/minor 2nd, 3rd, 6th, 7th; diminished 5th, augmented 4th; consonant and dissonant intervals). WAEC/NECO Theory 1(A)(f) Intervals.

WAEC: JAMB Music Section A 6 (diatonic and chromatic intervals and their inversions: perfect unison, 4th, 5th, octave; major/minor 2nd, 3rd, 6th, 7th; diminished 5th, augmented 4th; consonant and dissonant intervals). WAEC/NECO Theory 1(A)(f) Intervals.

NECO: JAMB Music Section A 6 (diatonic and chromatic intervals and their inversions: perfect unison, 4th, 5th, octave; major/minor 2nd, 3rd, 6th, 7th; diminished 5th, augmented 4th; consonant and dissonant intervals). WAEC/NECO Theory 1(A)(f) Intervals.

What you will learn

Find the number and quality of any interval.
Write an interval above or below a given note.
Invert intervals and name the inversions.
Name compound intervals.
Classify intervals as consonant or dissonant.
Explain enharmonic intervals and the tritone.
Relate intervals to melody and to African vocal styles.

Key points

Count letters for the number.
Lower note as major tonic decides quality.
Perfect family: 1, 4, 5, 8; major/minor family: 2, 3, 6, 7.
Semitones: m3 = 3, M3 = 4, P4 = 5, tritone = 6, P5 = 7.
Augmented: one larger than major/perfect; diminished: one smaller than minor/perfect.
Raising the lower note shrinks the interval.
Inversions add to 9 and swap quality.
Compound: subtract 7.
Consonances: P1, P5, P8, 3rds, 6ths.
Dissonances: 2nds, 7ths, augmented and diminished.
Tritone F–B in C major resolves to E–C.
Spelling, not only sound, decides the name.

Start here: What an interval is

An interval is the distance in pitch between two notes. If the notes are sounded one after the other, it is a melodic interval; if together, a harmonic interval. Intervals are the building blocks of melody, of chords and of harmony, and almost every theory question (scales, triads, cadences, transposition) depends on naming them correctly.

Every interval has two parts to its name: a number and a quality. “Major 3rd”, “perfect 5th”, “diminished 7th”.

Step 1: the number

Count the letter names from the lower note to the upper note, including both. C up to E: C, D, E = three letters, a 3rd. C up to A: C D E F G A = a 6th. Two notes on the same line or space are a unison (1st); eight letters is an octave (8th).

The number depends only on letters, never on sharps and flats. C to E♭, C to E and C to E♯ are all 3rds, of different qualities. On the staff there is a quick check: a 3rd, 5th or 7th goes from line to line or space to space; a 2nd, 4th, 6th or octave goes from line to space or space to line.

Step 2: the quality

Quality depends on the exact number of semitones. The words used are perfect, major, minor, augmented and diminished. Sections 4.2–4.4 show how to decide.

Worked example: Interval numbers. Give the number of: (a) D up to B; (b) F♯ up to E; (c) G down to A (lower note A).
Solution. (a) D E F G A B = 6th. (b) F G A B C D E = 7th (the sharp does not change the number). (c) From A up to G: A B C D E F G = 7th.

Worked example: Line or space?. Without counting letters, say whether the interval from a note on the second line to a note on the fourth line could be a 4th.
Solution. Line to line is always an odd number (3rd, 5th, 7th). Line 2 to line 4 skips one line, so it is a 3rd, never a 4th. This quick check catches many counting slips.

Both harmonic and melodic intervals are named in exactly the same way. In aural tests you may be asked to recognise intervals by ear; link each one to a familiar song opening. For example, the first two notes of “Here comes the bride” form a perfect 4th, and the opening of the hymn “Amazing grace” rises a perfect 4th too. Find Nigerian songs you know for each interval and make your own list.

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Practice questions

1. C up to G is a

perfect 5th
major 5th
perfect 4th
major 6th

Show answer

A: perfect 5th
Five letters, 7 semitones.

2. E up to C is a

major 6th
minor 7th
perfect 5th
minor 6th

Show answer

D: minor 6th
8 semitones.

3. F up to B is a

diminished 5th
major 4th
augmented 4th
perfect 4th

Show answer

C: augmented 4th
6 semitones over four letters.

4. B up to F is a

minor 5th
diminished 5th
perfect 5th
augmented 4th

Show answer

B: diminished 5th
6 semitones over five letters.

5. D up to C♯ is a

major 7th
minor 7th
augmented 6th
diminished 8th

Show answer

A: major 7th
11 semitones.

Key words

Interval: Distance in pitch between two notes.
Melodic interval: Notes sounded one after another.
Harmonic interval: Notes sounded together.
Perfect: Quality of unison, 4th, 5th, octave in the major scale.
Major: Quality of 2nd, 3rd, 6th, 7th in the major scale.
Minor: A major interval made a semitone smaller.
Augmented: A perfect or major interval made a semitone larger.
Diminished: A perfect or minor interval made a semitone smaller.
Tritone: Interval of three whole tones.
Inversion: Interval with its notes swapped by an octave.
Compound interval: Interval larger than an octave.
Consonance: Stable-sounding interval.

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