A minor third, in
just intonation, corresponds to a pitch ratio of 6:5 or 315.64
cents. In an
equal tempered tuning, a minor third is equal to three
semitones, a ratio of 21/4:1 (about 1.189), or 300 cents, 15.64 cents narrower than the 6:5 ratio. In other
meantone tunings it is wider, and in
19 equal temperament it is very nearly the 6:5 ratio of just intonation; in more complex
schismatic temperaments, such as
53 equal temperament, the "minor third" is often significantly flat (being close to
Pythagorean tuning ()), although the "
augmented second" produced by such scales is often within ten cents of a pure 6:5 ratio. If a minor third is tuned in accordance with the fundamental of the
overtone series, the result is a ratio of 19:16 or 297.51 cents (the nineteenth harmonic). The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error. M. Ergo mistakenly claimed that the nineteenth harmonic was the highest ever written, for the bass-trumpet in
Richard Wagner's
Der Ring des Nibelungen (1848–74), when
Robert Schumann's Op. 86
Konzertstück for 4 Horns and Orchestra (1849) features the
twentieth harmonic (four octaves and a major third above the fundamental) in the first horn part three times. Other pitch ratios are given related names, the
septimal minor third with ratio 7:6 and the tridecimal minor third with ratio 13:11 in particular.
Pythagorean minor third In
music theory, a
semiditone (or
Pythagorean minor third) is the
interval 32:27 (approximately 294.13
cents). It is the minor third in
Pythagorean tuning. It arises in
Ptolemy's intense diatonic scale between the 2nd and 4th degrees (in the C
major scale, between D and F). It can be thought of as two
octaves minus three
justly tuned fifths. It is narrower than a justly tuned minor third by a
syntonic comma. Its inversion is a
Pythagorean major sixth. ==See also==