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This article is from the Piano General Topics FAQ, by Isako Hoshino rmmpfaq@yahoo.com with numerous contributions by others.

8.2] Interval nomenclatures? (Piano)

Here's a crash course on interval nomenclatures.

  perfect unison:    2 notes on same pitch
  minor second:      1/2 step
  major second:      1 step
  minor third:       1-1/2 steps
  major third:       2 steps
  perfect fourth:    2-1/2 steps
  augmented fourth:  3 steps   (see enharmonic intervals)
  diminished fifth:  3 steps   (see enharmonic intervals)
  perfect fifth:     3-1/2 steps
  minor sixth:       4 steps
  major sixth:       4-1/2 steps
  minor seventh:     5 steps
  major seventh:     5-1/2 steps
  perfect octave:    6 steps

perfect consonances: unisons (or primes), fourths, fifths,
and octave are only perfect, diminished or augmented.

imperfect consonances: thirds and sixths intervals

dissonances: seconds and sevenths intervals. only major,
minor, diminished or augmented

Major intervals: 1/2 step larger than minor intervals. only
major, minor, diminished or augmented

Augmented intervals: 1/2 step larger than perfect or major
intervals.

Diminished intervals: 1/2 step lower than perfect or minor
intervals.

Enharmonic intervals: intervals that use the same pitches but
are spelled differently (and thus function differently).

Tritone: augmented fourths and diminished fifths are
enharmonic, and both are commonly referred to as the
tritone. (for example, C to F# and C to Gb are not the
same interval, but they are enharmonically the same)

Other intervals:
compound intervals...larger than an octave
inverted intervals...major becomes minor, etc., but note
that perfect inverts to perfect,
imperfect to imperfect, and dissonant
to dissonant

Sources of this information:

Benjamin, Horvit, and Nelson, "Techniques and Materials of
Tonal Music" (Houghton Mifflin, 1975):

 

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