Interval Size and Quality

From here on the subject is relationships between notes. The first thing to measure is the distance between two of them: the interval.

Nearly everything else rests on this. A scale is a sequence of intervals; a chord is a stack of them; a chord progression is a chain of relationships between those stacks. Vagueness here propagates into everything downstream, so this lesson takes its time.

An interval name has two parts

Interval names always come in two words — “major 3rd,” “perfect 5th,” “augmented 4th”:

• the quality (major, minor, perfect, augmented, diminished)
• the number (unison, 2nd, 3rd, and so on)

And the two are determined by different things.

Part	Determined by
Number	counting the letters in the note names
Quality	counting half steps

That two-stage structure is the whole idea. Neither the number alone nor the half-step count alone identifies an interval. You need both.

Numbers are counted inclusively

There is exactly one trap in counting interval numbers: you include both endpoints.

From C to E, count C, D, E — that is a 3rd, not a 2nd. It is not “how many steps did I move.” A consequence of counting this way is that a note against itself is a unison, numbered 1 rather than 0.

The crucial point is that the number ignores accidentals entirely. C to E, C to Eb, and C to E# are all thirds, because the letters run C, D, E in every case. Accidentals change the quality; they never change the number.

This is where the previous unit’s principle pays off. Write E# as F and C to E# (a 3rd) turns into C to F (a 4th) — the number itself changes. Spelling is not cosmetic; it is what the measurement is made of.

Check

What number is the interval from D up to A?

4th5th6th7th

Check answer

Quality comes from half steps, in two families

With the number settled, the quality is next. Here an awkward fact appears: different numbers use different vocabulary.

Unisons, 4ths, 5ths, and octaves take perfect as their reference. 2nds, 3rds, 6ths, and 7ths take major as theirs.

Why two families? Build all these intervals inside a major scale and the reason surfaces. Taking C as the lower note in C major:

Upper note	Number	Half steps	Quality
C	1	0	perfect unison
D	2	2	major 2nd
E	3	4	major 3rd
F	4	5	perfect 4th
G	5	7	perfect 5th
A	6	9	major 6th
B	7	11	major 7th
C	8	12	perfect octave

The 1st, 4th, 5th, and 8th have a special property: they keep their quality when you flip the two notes, which is exactly what the next lesson examines. That symmetry is what “perfect” is naming.

Departures from the reference

Once the reference is fixed, the remaining qualities are just distances from it.

Perfect family (1, 4, 5, 8)

• at the reference → perfect
• a half step wider → augmented
• a half step narrower → diminished

Major/minor family (2, 3, 6, 7)

• at the reference → major
• a half step narrower → minor
• another half step narrower → diminished
• a half step wider → augmented

Only the second family has the three-stage major-minor-diminished chain. The perfect family has no “minor” at all. There is no such interval as a minor 5th; the correct name for that sound is a diminished 5th.

One note apart: major and minor thirds

▶Major 3rd (C–E)▶Minor 3rd (C–Eb)▶One after the other (C→E)▶One after the other (C→Eb)

Check: The lower note is C in both. The only difference is whether the upper note is E or Eb — a single half step. That half step is the entire difference between a major and a minor chord, and it carries a startling share of the emotional weight in Western music.

four half steps, bright

Check

What is the interval from C up to A♭?

augmented 5thdiminished 6thminor 6thmajor 6th

Check answer

Same half steps, different interval

This is the single most important idea in the lesson. Equal half-step counts do not make equal intervals if the numbers differ.

The classic pair spans six half steps each.

• F up to B: F, G, A, B is a 4th. One half step wider than a perfect 4th (five) → augmented 4th
• B up to F: B, C, D, E, F is a 5th. One half step narrower than a perfect 5th (seven) → diminished 5th

On a keyboard the distance is identical and the sound is indistinguishable. Theory still separates them, and the reason is that they resolve in opposite directions.

An augmented interval wants to keep expanding: the lower note moves down, the upper note moves up. A diminished interval wants to contract inward. Identical sound, opposite tendency — and the spelling is what records which one you meant.

This six-half-step interval is the tritone, literally three whole tones. It has a special standing in Western harmony as the source of tension in the dominant seventh chord, and it returns repeatedly in the units ahead.

Tension and resolution in the tritone

▶Augmented 4th F–B▶Resolving outward → E–C▶Diminished 5th B–F▶Resolving inward → C–E

Check: The first is the augmented 4th F–B on its own — notice how strongly it wants to go somewhere. The second shows it opening outward to E–C. The third is the diminished 5th B–F, and the fourth closes it inward to C–E. Same six half steps, opposite directions of travel.

tension

A working procedure

Until it becomes automatic, run every interval through the same two mechanical steps.

1. Count letters to get the number, ignoring accidentals completely
2. Count half steps and compare against the reference for that number

The reference sizes are worth having available.

Number	Reference	Half steps
1	perfect	0
2	major	2
3	major	4
4	perfect	5
5	perfect	7
6	major	9
7	major	11
8	perfect	12

Since these references are just the intervals of a major scale, knowing the major scale from its tonic makes the table unnecessary. Most people never memorize it; they count up the scale in their head instead, which is faster and harder to forget.

▶ Practice against the interval calculator Pick two notes and it reports the number, quality, half-step count, and consonance. The way to get value out of it is to commit to an answer out loud first, then check Interval Calculator → ▶ Start putting intervals in your ear Once the reasoning is in place, the ear is next. Starting with just perfect 5ths, major 3rds, and minor 3rds keeps the early going manageable Ear Training →

The next lesson looks at what happens when you turn an interval upside down. That is where the asymmetry between the perfect and major/minor families finally explains itself.