Minor third

Minor Third

Inverse	major sixth
Name
Other names	-
Abbreviation	m3
Size
Semitones	3
Interval class	3
Just interval	6:5 or 19:16[1]
Cents
Equal temperament	300
24 equal temperament	300
Just intonation	316 or 298

Minor third  Play (help·info) equal tempered or  just (help·info) (6:5).

19th harmonic (19:16), E¹⁹♭  Play (help·info).

In classical music from Western culture, a third is a musical interval encompassing three staff positions (see Interval (music)#Number for more details), and the minor third is one of two commonly occurring thirds. The minor quality specification identifies it as being the smallest of the two: the minor third spans three semitones, the major third four. For example, the interval from A to C is a minor third, as the note C lies three semitones above A, and there are three staff positions from A to C. Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five). However, the minor third is a skip melodically.

The minor third may be derived from the harmonic series as the interval between the fifth and sixth harmonics, or from the 19th harmonic.

The minor third is commonly used to express sadness in music, and research has shown that this mirrors its use in speech, as a tone similar to a minor third is produced during sad speech.^[2]

The minor scale is so named because of the presence of this interval between its tonic and mediant (1st and 3rd) scale degrees. Minor chords too, take their name from the presence of this interval built on the chord's root (provided that the interval of a perfect fifth from the root is also present or implied).

A minor third in just intonation corresponds to a pitch ratio of 6:5 ( play (help·info)) or 315.64 cents. In an equal tempered tuning, a minor third is equal to three semitones, a ratio of 2^1/4:1 (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 ( play (help·info))), 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 will be a ratio of 19:16, this produces an interval of 297.51 cents^{[citation needed]}. The 12-TET minor third (300 cents) more closely approximates the 19-limit (Limit (music)) minor third 16:19  Play (help·info) (297.51 cents, the nineteenth harmonic) with only 2.49 cents error.^[3]

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.

The minor third is classed as an imperfect consonance and is considered one of the most consonant intervals after the unison, octave, perfect fifth, and perfect fourth.

Instruments in A are a minor 3rd lower than the written pitch in the concert pitch, i.e. how they are heard. Therefore, to get the written pitch, transpose the concert pitch up a minor 3rd.

Pythagorean minor third

Semiditone (32:27) on C  Play (help·info).

Semiditone as two octaves minus three justly tuned fifths.

In music theory, a semiditone (or Pythagorean minor third^[4]) is the interval 32:27. It is 294.13 cents. It is the minor third in Pythagorean tuning.

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.

See also

• musical tuning
• List of meantone intervals
• Pythagorean interval

References

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0824747143. 19th harmonic, overtone minor tone.
2. ^ Curtis ME, Bharucha JJ (June 2010). "The minor third communicates sadness in speech, mirroring its use in music". Emotion 10 (3): 335–48. doi:10.1037/a0017928. PMID 20515223. 
3. ^ Alexander J. Ellis (translating Hermann Helmholtz): On the Sensations of Tone as a Physiological Basis for the Theory of Music, page 455. Dover Publications, Inc., New York, 1954. "16:19...The 19th harmonic, ex. 297.513 [cents]". Later reprintings: ISBN 1150366028 or ISBN 1143494512.
4. ^ John Fonville. "Ben Johnston's Extended Just Intonation- A Guide for Interpreters", p.124, Perspectives of New Music, Vol. 29, No. 2 (Summer, 1991), pp. 106-137.