Intervals and Scales (SACE Stage 2 Music)

What this dot point is asking

You need to be able to look at two notes and name the interval, build an interval above or below a given note, and write or hear any major or minor scale. This is the foundation for chords, transcription and analysis, so it has to be automatic.

Counting interval number

The interval number counts letter names from the lower note to the upper note, including both ends. From C up to G is C, D, E, F, G, which is five letter names, so it is a fifth. From E up to E (same letter, next octave) is an octave. Always count the letters first and ignore sharps and flats at this stage, because accidentals affect quality, not number.

Interval quality

Once you have the number, the quality tells you the exact size in semitones.

Unisons, fourths, fifths and octaves use perfect (P). Seconds, thirds, sixths and sevenths use major (M) and minor (m). The reference is always the major scale of the lower note: if the upper note belongs to that major scale, the interval is major (for 2,3,6,7) or perfect (for 1,4,5,8).

From there:

• A major interval made one semitone smaller becomes minor.
• A minor or perfect interval made one semitone smaller becomes diminished (d).
• A major or perfect interval made one semitone larger becomes augmented (A).

For example, C to E is a major third (four semitones). C to E flat shrinks it by a semitone to a minor third (three semitones). C to G is a perfect fifth (seven semitones); C to G flat is a diminished fifth (six semitones), the famous tritone.

Compound and inverted intervals

Intervals larger than an octave are compound: a ninth is a compound second, an eleventh a compound fourth. To analyse one, subtract seven from the number to find the simple equivalent.

Inversion flips the two notes so the lower becomes the upper. The numbers always add to nine (a third inverts to a sixth, a second to a seventh) and the quality reverses: major becomes minor, augmented becomes diminished, while perfect stays perfect. This is a quick way to check your work.

Building the major scale

The major scale uses the pattern T T S T T T S (T = tone, S = semitone). Starting on C this gives C D E F G A B C with no accidentals. Starting on G you need an F sharp to keep the tone between the sixth and seventh and the semitone between the seventh and eighth, which is why G major has one sharp.

The three minor scales

All minor scales start with the pattern T S T T, giving the characteristic minor third above the tonic. They differ above the fifth degree:

• Natural minor: T S T T S T T. In A minor this is A B C D E F G A, no accidentals. The seventh is a tone below the tonic.
• Harmonic minor: raise the seventh by a semitone, creating a leading note a semitone below the tonic. In A minor this is A B C D E F G sharp A. This produces an augmented second between the sixth and seventh.
• Melodic minor: raise both the sixth and seventh ascending (A B C D E F sharp G sharp A), then revert to the natural minor descending (A G F E D C B A).

Why this matters

Every chord is a stack of intervals, every key signature comes from a scale, and every melody you transcribe is a chain of intervals. If you can name and hear intervals instantly and write any scale from memory, the aural test, the harmony questions and the analysis questions all become far easier. Practise by singing intervals against a drone, writing scales in every key, and checking your spelling with inversion.