Perfect intervals

Perfect, not major or minor

Ear training explains it like this: an interval is named by the number of steps it spans. Because the steps of a major scale are of different sizes, the count needs a qualifier, namely “perfect” for unison, fourth, fifth and octave, and “major” or “minor” for second, third, sixth and seventh. Diminished and augmented come in when a note is altered chromatically. In the glossary they have separate entries as the perfect fourth and the perfect fifth.

The simplest ratios

For each interval the page Intervals gives the frequency ratio. The perfect intervals have the plainest numbers: the unison is 1:1 and the most complete of all consonances, the fourth 4:3, the fifth 3:2. The page calls the fifth the purest and strongest consonance after the octave. That it sounds strong, open and almost “empty” is, according to the page, because there is no third in it that would give it a major or minor colouring.

The fret distances are given on the page Intervals with the respective fingering: the fourth lies five frets, the fifth seven frets above the starting note. The octave is twelve semitones away, on the guitar twelve frets.

From listening to playing

The perfect intervals are easy to find on an instrument. On the guitar, according to the page Intervals, each string at the 5th fret sounds the same as the next higher open string, except for the G string; this is the traditional way of tuning. The fifth has an easy-to-play harmonic at the 7th fret: the 3rd partial lies an octave plus a perfect fifth above the fundamental.

Perfect and equal-tempered

“Perfect” also means the exact numerical ratio. The page Intervals points out that the ratios given are the pure values, whereas guitar frets and the piano are tuned in equal temperament and deviate slightly. As an example it gives 329.63 Hz × 16/15 = 351.6 Hz against 349.23 Hz for the equal-tempered F. The equal-tempered fifth is therefore not quite 3:2. Why a tuned piano never sounds entirely pure is explained in the article Equal, meantone, just — why your piano is slightly out of tune.