Science Fair Project Encyclopedia
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.
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.
|# semitones||Interval class||# cents in equal temperament||Most common diatonic name||Comparable just interval||# cents in just interval||Just interval vs. equal-tempered interval|
|1||1||100||minor second||16:15||112||12 cents larger|
- Dahlhaus, Carl, trans. Gjerdingen, Robert O. (1990). Studies in the Origin of Harmonic Tonality. Princeton University Press. ISBN 0691091358.
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