The
musical interval of a half
step, semitone, or minor second is the
relationship between the leading tone and the first note (the root
or tonic) in a
major scale. It is the
inversion of the
major seventh. It is often
abbreviated as m2.
A minor second in
just intonation most often
corresponds to a pitch ratio of 16/15 or 1:1.0666, or various
other ratios, while in an
equal tempered tuning it is a
ratio of 1:21/12 (approximately 1.059), or 100 cents,
11.731
cents
flat of 16:15.
Traditionally the minor second is considered the
most
dissonant interval after the
tritone.
According to
Carl Dahlhaus (1990), "as late at
the 13th century the half step was experienced as a problematic
interval not easily understood, as the irrational remainder
between the perfect fourth and the
ditone [4/3 / (9/8)2 =
256/243!]." In a melodic half step, no "tendency was preceived of
the lower tone toward the upper, or of the upper toward the lower.
The second tone was not taken to be the 'goal' of the first.
Instead, the half step was avoided in
clausulas because it lacked
clarity as an interval." Beginning in the 13th century cadences
begin to require motion in one voice by half step and the other a
whole step in contrary motion.
See also