Intervals: Check the Letter Distance and Quality

Intervals: check the letter distance and quality

An interval name answers two different questions. How many letter positions separate the written notes? How many semitones separate their pitches? The first gives the interval number; the second helps determine its quality. Checking only the semitones can miss the written distinction between an augmented fourth and a diminished fifth.

This lesson concerns ascending simple intervals from unison through octave in common-practice Western notation. Pitch names use C4 for middle C. The examples are original two-note studies: each note is a minim, or half note, so each 4/4 bar contains 2 + 2 = 4 crotchet beats. The two pitches sound in sequence. The same interval size and quality can also be written with simultaneous notes.

1. Count letters inclusively

Start with the lower note as one. C to E is C–D–E: three letter names, so the interval is a third. G4 to D5 is G–A–B–C–D: a fifth. Do not count only the steps between names; that would make each result one too small. Accidentals do not change this letter count. C to F sharp is still a fourth because F is the fourth letter position above C.

Second, third, sixth and seventh belong to the major/minor family. Unison, fourth, fifth and octave belong to the perfect family. Raising the size in semitones by one beyond major or perfect produces augmented quality, provided the written interval number stays fixed. Lowering minor or perfect by one produces diminished quality. A perfect fifth reduced by a semitone is therefore diminished, not minor.

2. Worked case: an accidental changes a third

For D4 to F sharp 4, count D–E–F: a third. Count the four semitone moves D to D sharp, to E, to F, to F sharp. The result is a major third. For D4 to F4, the letter count is unchanged but only three semitone moves remain. That interval is a minor third. Both scores have the same two-beat values; interval quality is a pitch relationship, not a duration.

The first score has no key-signature sharps, so F sharp is written as a local accidental. It applies to that written pitch within the bar under the ordinary convention used here. The second score is a separate example with its own empty signature. It does not inherit the first example’s accidental. Always distinguish a continuing bar from a separate example.

3. Worked case: a perfect-family interval

G4 to D5 covers G–A–B–C–D, five letter positions. Its semitone distance is seven: G to A is two, A to B adds two, B to C adds one, and C to D adds two. Therefore it is a perfect fifth. The octave boundary does not restart the interval count; C5 follows B4 normally.

If the upper note were D flat 5, the interval would still be a fifth but would contain six semitones, making it diminished. If it were D sharp 5, it would contain eight semitones, making it augmented. Those are construction checks. Changing the upper letter to E flat instead would produce a sixth and require a different name, even if some pitch distances happened to match.

4. Worked comparison: the same semitone total, different names

C4 to F sharp 4 spans four letters and six semitones. A perfect fourth has five semitones, so this fourth is augmented. C4 to G flat 4 spans five letters and also six semitones. A perfect fifth has seven, so this fifth is diminished. In twelve-tone equal temperament, F sharp and G flat can sound at the same pitch, but their written spellings give different interval numbers.

“Six semitones” is a useful answer to a distance question, but it is incomplete when the task asks for the full written interval name. The spelling contains information about the musical notation and possible context. This is why a keyboard-only count should be paired with a staff or letter-name check.

5. Construct an interval in the reverse order

To write a minor sixth above E4, first count E–F–G–A–B–C. The destination must use the letter C in the next octave. Then check E4 to C5: eight semitones. That is already the required minor sixth, so no accidental is needed. Choosing B sharp because it may sound like C in equal temperament would break the required six-letter span.

When a key signature is present, apply it before checking quality. In a G-major signature, a written F without a local sign is F sharp. A natural sign can cancel that default for the affected note in the bar. The staff position alone does not supply the whole pitch. Record the final sounding spelling in your ledger before counting semitones.

6. Three fresh tasks, with solutions

1. Name B3 to D4. Answer: B–C–D is a third. B to C is one semitone and C to D is two, totalling three. The interval is a minor third, even though the octave number changes.

2. Construct a perfect fourth above A4. Answer: count A–B–C–D, so use D5. A4 to D5 has five semitones and needs no accidental. D sharp 5 would make an augmented fourth.

3. Name F4 to B4 and F4 to C flat 5. Answer: F–G–A–B gives an augmented fourth at six semitones. F–G–A–B–C gives a diminished fifth, also six semitones. The ordinary flat sign alters C without changing its letter position.

Frequently asked questions

Why do I count both end letters?

Interval numbers count occupied letter positions inclusively. C, D and E occupy three positions, so C to E is a third.

Does an accidental change the interval number?

Not when the letter names stay the same. It changes the semitone distance and can therefore change quality while preserving the number.

Is there a minor fifth in this system?

No. Fifths belong to the perfect family. A perfect fifth reduced by one semitone is diminished, provided the letter span remains a fifth.

Can two intervals sound alike but have different names?

Yes. In twelve-tone equal temperament, C to F sharp and C to G flat have the same semitone distance but different written letter spans.

Must I apply the key signature first?

Yes. Read the complete written pitch, including the signature and local accidentals, before calculating the semitone distance.

Do octave numbers matter?

Yes. C4 to D4 is a second, whereas C4 to D5 exceeds an octave and falls outside this lesson's simple-interval scope.

How should I construct an interval?

Choose the correct destination letter and octave from the required number, then add or remove an accidental until its semitone distance matches the required quality.

Reference notes

Terminology follows common-practice Western notation. These sources support the definitions; the scores, questions and solutions above are independently composed.

• Open Music Theory, named chapter author(s), VIVA academic open textbook: Size; Perfect, Major, and Minor Qualities; Augmented and Diminished Qualities

From two-note intervals to a constructed triad

First complete the interval examples above: the letter span and the semitone distance must both be correct. Next use the complete chord reductions and pitch tables in “Cadences: read the chords before naming the ending”. Its C-, G- and F-major examples supply actual simultaneous chord notes. This short construction task connects those two lessons; it does not require a new recording.

Worked construction: build D major, then change its quality

Work in common-practice Western notation and twelve-tone equal temperament. Here a triad has three different pitch classes that can be arranged as two stacked thirds. Begin with D4 as the root. Count D–E–F to choose the third’s letter and D–E–F–G–A to choose the fifth’s letter. The unaltered framework is D4–F4–A4.

A major triad needs a major third and a perfect fifth above its root. D4 to F4 is only three semitones, so raise F4 to F sharp 4. D4 to A4 already has seven semitones. The completed chord is D4 + F sharp 4 + A4, sounding together. The plus signs mean simultaneous notes, not a melody. If each note is a minim in 2/4, all three share one two-beat duration; their durations do not add to six beats. In a staff with no key signature, write the F-sharp accidental. In the retained G-major cadence score, that same altered pitch is supplied by the signature.

The fifth keeps the letter A in every row. Substituting B flat for A sharp would give the wrong written letter span for this augmented fifth, even though the pitches coincide in equal temperament. A chord’s quality is also different from its function: D major is V in the retained G-major example, but I in D major. The notes establish the chord; the named key establishes its scale-degree role.

Construct, explain and check

For tasks 1–4, give a root-position triad in close spacing, with the root in the stated octave. State both root-to-note semitone distances and preserve correct letter spellings. These are pitch-construction tasks, so no tempo or new rhythmic pattern is required.

1. Construct A minor above A3.
2. Construct E-flat major above E flat 4.
3. Construct B diminished above B3.
4. Construct C augmented above C4.
5. A chord sounds E4, G4 and C5. A learner calls it E minor because E is lowest. Repair the analysis.

Explained answers

1. A3–C4–E4: 3 and 7 semitones above A3. C gives the minor third; E supplies the perfect fifth.
2. E flat 4–G4–B flat 4: 4 and 7. The fifth must use B; A sharp is not the required spelling.
3. B3–D4–F4: 3 and 6. Both adjacent thirds contain three semitones, so the fifth is diminished.
4. C4–E4–G sharp 4: 4 and 8. The upper interval E4–G sharp 4 is also a major third.
5. Rearrange the pitch classes as C–E–G. It is C major in first inversion: C is the root and E is the bass. E minor would need E–G–B. The bass alone does not name the chord.

Review: Check the two letter spans before the semitones; read key signatures and accidentals; distinguish root from bass; then explain the quality. A correct-sounding but wrongly spelled fifth needs correction. Revisit the retained chord reductions to connect the compact construction with more widely spaced voicings.

Terminology reference: Chelsey Hamm, “Triads,” Open Music Theory. All constructions, tasks and answers here are original. Current Kenyan syllabus placement and examination terminology require subject-teacher review.