Interval

Tone and semitone measure the short steps, from one note to its neighbour. But a melody also leaps: from C4 straight to G4, for example. To say how far any note is from any other, music uses the interval.

An interval is not measured in centimetres, nor in semitones. It is measured in note names.

Counting by names

To find the interval between two notes, count the names from one to the other, including both ends. From C to E: C, D, E. Three names, and the interval is a third.

Hear the notes

From C to G: C, D, E, F, G. Five names, a fifth.

Hear the notes

Intervals are named with ordinal numbers. Starting from C:

From	To	Names counted	Interval
C	C (the same)	1	unison
C	D	2	second
C	E	3	third
C	F	4	fourth
C	G	5	fifth
C	A	6	sixth
C	B	7	seventh
C	C above	8	octave

The most common mistake is to count the steps instead of the names. From C to D there is one step but two names, and the interval is a second. Think of the fingers of your hand: from thumb to middle finger is three fingers, even though only two gaps lie between them.

When counting, always go from the lower note to the higher. Lacerda insists on this: an interval is classified by the number of notes from the lower to the higher, counting both (Lacerda 1966, ch. XXVIII).

The unison

When both notes have the same name and the same pitch, only one name is counted, and the result is the unison. Med also calls it the prime and treats it as the first of the intervals (Med 1996, ch. X). Lacerda reads it another way: equal sounds form no interval at all, they form a unison (Lacerda 1966, ch. XXVIII). In practice the two say the same thing, and here the unison joins the list so that counting starts at 1.

Melodic and harmonic

The two notes of an interval can sound one after the other or at the same time. One after the other, the interval is melodic, because that is how a melody moves.

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At the same time, the interval is harmonic, because that is how chords are formed.

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Both examples are the same fifth. The way it sounds changes; the distance does not.

Ascending and descending

A melodic interval also has a direction. If the second note is higher, it is ascending; if lower, descending.

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In the first measure the melody rises from E to C; in the second it falls from C to E. Both times the count is the same, from the lower note to the higher: E, F, G, A, B, C. It is an ascending sixth and then a descending sixth. A harmonic interval has no direction, since both notes sound together.

Conjunct and disjunct

When a melody moves from one note to its neighbour, by seconds, the motion is conjunct. It is the easiest way to sing.

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When it leaps, by thirds or larger intervals, the motion is disjunct.

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Almost every melody mixes the two. Blatter notes that disjunct motion is more typical of instrumental music, and gives the everyday names for both: stepwise motion and motion by leaps (Blatter 2007, part 2, art. 1).

On the staff, an interval has a shape

Counting works without any names too, straight on the staff: every line and every space is one name. And that gives a shortcut. Look at the notes in each measure:

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The second goes from a line to the space just above. The third goes from a line to the next line. The fourth ends in a space again, and the fifth on a line. The pattern repeats: in intervals with an odd number (third, fifth, seventh), both notes sit on lines or both in spaces; in those with an even number (second, fourth, sixth, octave), one sits on a line and the other in a space.

With that shape, a musician recognises an interval before even reading the names of the notes. This is the path Blatter takes: he presents each interval by the figure it makes on the staff, without a clef, because counting an interval does not require knowing which notes they are (Blatter 2007, part 2, art. 1).

An accidental does not change the number

Because the count is made by names, an accidental does not change an interval's number. Med is explicit: the numerical classification takes neither accidentals nor clefs into account (Med 1996, ch. X).

Hear the passage

All three measures hold thirds: C and E, C and E flat, C sharp and E. In each, three names, and both notes on lines. But listen: they do not sound the same. Count on the keyboard. From C to E is four semitones; from C to E flat, three; from C sharp to E, three as well.

So the number tells only part of the story. Two thirds can be different sizes, and telling them apart is what interval quality is for: major third, minor third, perfect fifth, and so on. That is the next subject.

Simple and compound

Up to the octave, an interval is simple. Beyond the octave, it is compound.

Hear the passage

From C to the D in the octave above is nine names: C, D, E, F, G, A, B, C, D. It is a ninth, or, put another way, an octave plus a second.

There is a sum for going from one to the other. To find the compound interval, add 7 to the simple one for each octave: a second plus an octave is 2 + 7 = 9, a ninth; a third becomes a tenth, a fifth becomes a twelfth. To get back to the simple interval, take 7 away. Why 7 and not 8? Because the note in the middle, the upper C in the example, is at once the end of the octave and the start of the second, and cannot be counted twice (Med 1996, ch. XII).

Here the books differ on the name. Med numbers compound intervals as far as needed: ninth, tenth, eleventh, twelfth. Lacerda prefers to call a compound interval by the name of the simple one, as in "compound fifth", and makes an exception only for the ninth and the tenth, which have names of their own in common use (Lacerda 1966, ch. XXVIII). Blatter accepts both: a ninth, or an octave plus a second. All three describe the same distance.

What comes next

C–E and C–E flat are both thirds, and they sound different. Telling one from the other, by counting the tones and semitones in each interval, is interval quality: major, minor, perfect, augmented and diminished. And stacking thirds leads to chords.