Related
Unisons, fourths, fifths and octaves take neither major nor minor but a different word: perfect. This is not a naming quirk; they genuinely belong to a different physical class.
The four simplest ratios
In the harmonic series, these are the first ratios to appear:
| Interval | Ratio | Position in the series |
|---|---|---|
| perfect unison | 1 : 1 | the same tone |
| perfect octave | 2 : 1 | partials 1 and 2 |
| perfect fifth | 3 : 2 | partials 2 and 3 |
| perfect fourth | 4 : 3 | partials 3 and 4 |
The simpler the ratio, the more the two tones' partials overlap, and the emptier and more colourless the sound. Thirds, sixths and sevenths have major and minor forms precisely because their ratios (5:4, 6:5) are more complex — complexity is what gives them character. Perfect intervals have no character, and that is their defining feature.
Augmented and diminished
Perfect intervals cannot become major or minor, but they can widen or narrow:
| Change | Name | Example |
|---|---|---|
| one semitone wider | augmented | perfect fifth → augmented fifth |
| one semitone narrower | diminished | perfect fifth → diminished fifth |
One trap: a perfect fourth widened by a semitone is an augmented fourth, and that interval has the same size as a diminished fifth (6 semitones each) while being spelled and tending differently — see augmented and diminished and enharmonic.
Why the fifth governs tonality
The perfect fifth's 3:2 is the only non-octave member among the simplest ratios. Stack fifths and after twelve steps you arrive almost back where you started — that is the circle of fifths, and the whole key system (related keys, the order of key signatures, dominant function) is built on that chain.
Diagram: where the perfect intervals sit
Listen: the perfect fifth
A fifth sounds hollow because it carries almost no tension that wants resolving. That hollowness is exactly why it turns up everywhere, in tuning, stringing and harmonic scaffolding across the world.
Common misconceptions
- "Perfect means in tune." Here it means the simplest ratio (2:1, 3:2, 4:3), nothing about intonation.
- "Perfect intervals cannot be augmented or diminished." They can. A fifth widened by a semitone is augmented; narrowed, diminished.
- "The fourth sounds more consonant than the fifth because it is narrower." Narrower is not more consonant. Consonance follows ratio simplicity; fourth and fifth rank alike, just pointing opposite ways.
- "Thirds would be more consonant if they were perfect." Their ratios (5:4 and 6:5) are already more complex than the fourth and fifth, which is why they split into major and minor and carry colour.
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Listen in the library
All tracks from midicn-lib — inline badge is the license tier (C1 commercial / C2 non-commercial / C3 study only).
Sources
- {'纯音程的频率比（1': '1 / 4:3 / 3:2 / 2:1）与泛音列中的位置，属音乐声学通则'}
- 纯音程只有增减、不加大小的命名规则，为通行乐理表述
Used for fact-checking only; all prose is original.