Minor second
Encyclopedia : M : MI : MIN : Minor second
| Inversion (music)>Inverse | major seventh | |
|---|---|---|
| Name | ||
| Other names | semitone | |
| Abbreviation | m2 | |
| Size | ||
| semitone>Semitones | 1 | |
| Interval class | 1 | |
| Just intonation>Just interval | 16:15 | |
| Cents | ||
| Equal temperament | 100 | |
| Just intonation | 112 | |
A minor second in just intonation most often corresponds to a pitch ratio of 16/15 or 1:1.066666667 or 1:1+(1/15) (approximately 111.7312853 cents), called the just diatonic semitone; there are various other ratios which may function as a minor second, in particular the septimal diatonic semitone of 15/14.
In Pythagorean tuning the minor second is the ratio 256/243 or 1:1.053497942 or 1:1+(13/243) (approximately 90.22499567 cents), called the Pythagorean limma. It is sometimes called the Pythagorean minor semitone, but it corresponds to the diatonic and not the chromatic semitone.
In the standard 12-tone equal temperament tuning, a minor second is equal to one semitone, and is a ratio of 21/12 (approximately 1:1.059463094), or 100 cents, 11.731 cents narrower than the 16:15 ratio.
Traditionally the minor second is considered the most dissonant interval, followed by the major second.
According to Carl Dahlhaus (1990), "as late as 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 perceived 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 clausulae 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.
The minor second is synonymous with the term "diatonic semitone"; the other type of semitone, the "chromatic semitone", is technically the interval called the "augmented prime".
See also
| Diatonic intervals | [http://encycl.opentopia.com/ edit ] |
| Perfect : unison (0) | fourth (5) | fifth (7) | octave (12) | |
| Major : second (2) | third (4) | sixth (9)| seventh (11) | |
| Minor : second (1) | third (3)| sixth (8)| seventh (10) | |
| Augmented/Diminished : tritone (6) | |
| semitones of equal temperament are given in brackets | |
Source
- Dahlhaus, Carl, trans. Gjerdingen, Robert O. (1990). Studies in the Origin of Harmonic Tonality. Princeton University Press. ISBN 0691091358.
External links
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