The Perfect Interval
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Question
Why are certain intervals, called 'perfect' and what is it about
them that entitles them to have such a special name?
Answer 1
The Perfect intervals are the fourth, fifth and octave. Their
frequencies are in the most simple of ratios, 4:3, 3:2, and
2:1 respectively. Unison (1:1) is also considered a perfect
interval. They are perfect because they have no major or minor
variant, neither are they diminished or augmented. To create
harmony as we Westerners understand it, they need to be mixed
with an imperfect interval (eg the major 3rd). A stereotype
of Chinese-style harmony uses fourth or fifth intervals in
parallel motion. Because they are so simple, they sound hollow.
In essence, Perfect intervals are based on the octave or the
fifth (the fourth is only an 'upside down' fifth). Anything
else is gloriously imperfect.
Answer 2
Answer 1 is good but it is a little circular in that it suggests
that perfect intervals are perfect because they are perfect.
It does hint at a more robust explanation when he states that "In
essence, Perfect intervals are based on the octave or the fifth
(the fourth is only an 'upside down' fifth)." One will
find that this "upsidedownness" does not apply to
other intervals. For example, an upside down third is not a
sixth. It is a semitone out. What you will find is that an
upside down minor third is a major sixth and an upside down
major third is a major sixth. This will also work for seconds
and sevenths. In case there is any misunderstanding, to augment
a fourth or fifth you only have to add a semitone, whereas
for the non perfect intervals it is only the major interval
that can be augmented. Similarly to diminish the fourth or
fifth you lower it by a semitone, but you can only diminish
the minor non perfect intervals.
Answer 3
Certain intervals in the major scale, when inverted remain an
interval also occurring in the same major scale. Obviously
an inverted 8ve remains an 8ve but when an ordinary 5th is
inverted it becomes an ordinary 4th and vice versa (e.g. in
C Major, C to G is a Perfect 5th and G to C is a Perfect 4th,
C being the fourth note in G Major). their "perfection" lies
in their remaining in the major scale of the lower note, whichever
way up they are. This is not the case however with the other
intervals. For example in C Major, C to E is a Major 3rd but
the inversion, E to C is a Minor 6th because the sixth note
of E Major would be C#. Basically, on inversions of any two
note interval, Majors and minors interchange and Augmenteds
and diminisheds also switch. For example C to F# is an Augmented
4th while F# to C is a diminished 5th. How this makes the mud
a little clearer.
Answer 4
In the early period of part-writing (10th-12th centuries) the
perfect fourth was regarded, with the perfect fifth and octave,
as a concord of the greatest 'perfection'. By the 14th century
it had fallen from grace and was relegated to the category
of discords. Almost simultaneously with this great change,
the third was promoted from a position of bare tolerance to
one of imperfect consonance. Such may be the changes of aesthetic
fashion: the ear is, finally, the judge of what sounds satisfactory.
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