Interval quality

The topic on intervals left a question open. C–E, C–E flat and C sharp–E are all thirds: three names, both notes on lines. But they do not sound the same.

Hear the passage

An interval's number counts names; it does not measure the exact distance. For that, an interval takes a second name, its quality. Lacerda makes the point with sixths: C–A, C–A flat and C–A sharp are all sixths, but the difference in pitch changes with the accidental, and each needs a qualifier to tell it from the others (Lacerda 1966, ch. XXIX).

Measuring in tones and semitones

Quality's ruler is the semitone. From C to E there are four semitones, two tones. From C to E flat there are three, a tone and a half.

Hear the notes

Hear the notes

The major third is the one of two tones; the minor third, the one of a tone and a semitone (Med 1996, ch. X). Every interval is measured this way, by counting the tones and semitones between its two notes.

Two families

Intervals are not all qualified with the same words. There are two families (Med 1996, ch. X):

• seconds, thirds, sixths and sevenths can be major or minor;
• unisons, fourths, fifths and octaves are perfect.

A major scale shows both families at once. From the first note of the C major scale to each of the others, the intervals are: major second, major third, perfect fourth, perfect fifth, major sixth, major seventh and perfect octave (Lacerda 1966, ch. XXIX).

Hear the passage

Lacerda notes an important rule: a perfect interval never becomes minor. If it shrinks, it goes straight to diminished.

The size of each

With the semitone as ruler, each simple interval has its size:

Interval	Tones and semitones	Semitones
minor second	a semitone	1
major second	a tone	2
minor third	a tone and a semitone	3
major third	two tones	4
perfect fourth	two tones and a semitone	5
perfect fifth	three tones and a semitone	7
minor sixth	three tones and two semitones	8
major sixth	four tones and a semitone	9
minor seventh	four tones and two semitones	10
major seventh	five tones and a semitone	11
perfect octave	five tones and two semitones	12

Med writes the sizes exactly like this, in tones and semitones; and he points out that a minor sixth is a perfect fifth plus a semitone, while a major seventh is a perfect octave less a semitone (Med 1996, ch. X).

On the white keys

With no accidentals, only natural notes, each kind of interval comes in seven pairs, and Blatter checks them one by one on the keyboard (Blatter 2007, part 2, art. 1):

• seconds: all major, except E–F and B–C, which are minor;
• thirds: C–E, F–A and G–B are major; the other four, minor;
• fourths: all perfect, except F–B;
• fifths: all perfect, except B–F;
• sixths: C–A, D–B, F–D and G–E are major; the other three, minor;
• sevenths: C–B and F–E are major; the other five, minor.

The reason lies in the two natural semitones, E–F and B–C. Of two intervals with the same number, the one that crosses more of those semitones is the smaller. Med notes this with sixths and sevenths: the major ones contain one natural semitone; the minor ones, two (Med 1996, ch. X).

Hear the passage

Minor second, major second, minor third, major third.

Augmented and diminished

An interval can go beyond the sizes in the table. A semitone more than perfect or major, it is augmented; a semitone less than perfect or minor, it is diminished (Med 1996, ch. XI). The two families then follow different ladders:

Family	From smaller to larger
major and minor	diminished, minor, major, augmented
perfect	diminished, perfect, augmented

And there is one more rung at each end. A semitone past augmented, or short of diminished, and the books start to disagree about the name. Lacerda speaks of "more-than-augmented" and "more-than-diminished" (Lacerda 1966, ch. XXIX); Med of "superaumentado" and "superdiminuto", also called "excedente" and "deficiente", and he carries the series on, in theory, to five times augmented (Med 1996, ch. XI); Blatter uses only doubly augmented and doubly diminished.

The unison is a case apart. There is an augmented unison, such as C–C sharp, but no diminished unison (Med 1996, ch. XI).

What accidentals do

With the natural size of each interval in mind, accidentals follow a simple rule, which the three books give in the same way (Lacerda 1966, ch. XXIX):

• the interval grows when the upper note rises or the lower note falls;
• the interval shrinks when the upper note falls or the lower note rises;
• the interval stays the same when both notes take the same accidental.

Hear the passage

D–F is a minor third. With D flat below, the lower note fell: the interval grows and becomes a major third. With F sharp above, it grows once more: an augmented third. This is Blatter's procedure, in steps: first the number, then the quality without accidentals, then the effect of each accidental, one at a time (Blatter 2007, part 2, art. 1).

Hear the passage

Here, by contrast, both notes rise together, or fall together, and the minor third stays a minor third.

The tritone

Among the natural fourths, F–B is the only augmented one; among the fifths, B–F is the only diminished one. Both measure three tones, and the augmented fourth has a name of its own: tritone. Med relates that from the fifteenth to the nineteenth century it was considered a dangerous interval, nicknamed diabolus in musica (Med 1996, ch. XI).

Hear the passage

Listen to both. They sound the same size, three tones, and yet one is a fourth and the other a fifth, because the names differ: F, G, A, B is four; B, C, D, E, F is five. Blatter insists on this for every interval: never swap a note's spelling for an equivalent one when naming an interval (Blatter 2007, part 2, art. 1). C–D sharp and C–E flat use the same keys, but the first is an augmented second and the second a minor third.

What comes next

Qualifying a written interval is reading. The next step is writing: given a note and a quality, find the other note, which is building intervals. And two intervals that add up to an octave, such as the major third and the minor sixth, are the subject of inversion.