{{Infobox | title = Minor third | headerstyle = background-color:palegoldenrod; color:inherit; | label1 = [[Inversion (music)#Intervals|Inverse]] | data1 = [[Major sixth]] | header2 = Name | label3 = Other names | data3 = Sesquitone | label4 = Abbreviation | data4 = m3 | header5 = Tuning | label6 = [[12 equal temperament]] | data6 = 3 [[semitone]]s (300 [[Cent (music)|cents]]) | label7 = [[Pythagorean tuning]] | data7 = 32:27 (294 cents)<ref>Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p. xxiv. {{ISBN|0-8247-4714-3}}. 19th harmonic, overtone minor tone.</ref> | label8 = [[5-limit tuning]] | data8 = 6:5 (316 cents) | label9 = [[7-limit tuning]] | data9 = [[Septimal minor third|7:6]] (267 cents) | label10 = [[13-limit tuning]] | data10 = 13:11 (289 cents) | label11 = [[19-limit tuning]] | data11 = 19:16 (298 cents) }}
[[File:19th harmonic on C.png|thumb|19th harmonic (19:16), E<sup>19</sup>{{music|flat}}[[File:19th harmonic on C.mid]]|175x175px]] In [[music theory]], a '''minor third''' is a [[interval (music)|musical interval]] that encompasses three [[half step]]s, or [[semitone]]s. [[Staff notation]] represents the minor third as encompassing three [[staff position]]s (see: [[interval (music)#Number|interval number]]). The minor third is one of two commonly occurring thirds. It is called ''minor'' because it is the smaller of the two: the [[major third]] spans an additional semitone. For example, the interval from A to C is a minor third, as the note C lies three semitones above A. :<score sound> { \override Score.TimeSignature #'stencil = ##f \relative c'' { \time 4/4 \set Score.tempoHideNote = ##t \tempo 1 = 20 <a c>1 } } </score> [[Diminished third|Diminished]] and [[augmented third]]s span the same number of staff positions, but consist of a different number of semitones (two and five). The minor third is a [[skip (music)|skip]] melodically.
The minor third is classed as an [[consonance and dissonance|imperfect consonance]] and is considered one of the most consonant intervals after the [[unison]], [[octave]], [[perfect fifth]], and [[perfect fourth]]. It may be derived from the [[Harmonic series (music)|harmonic series]] as the interval between the fifth and sixth harmonics, or from the 19th [[harmonic series (music)|harmonic]].
The minor third is commonly used to express sadness in music, and research shows that this mirrors its use in speech, as a tone similar to a minor third is produced during sad speech.<ref>{{cite journal|author1=Curtis, M. E.|author2=Bharucha, J. J.|title=The minor third communicates sadness in speech, mirroring its use in music|journal=[[Emotion (journal)|Emotion]]|volume=10|issue=3|pages=335–348|date=June 2010|pmid=20515223 |doi=10.1037/a0017928}}</ref> It is also a [[quartal and quintal harmony|quartal]] (based on an ascendance of one or more [[perfect fourth]]s) [[wikt:tertian|tertian]] interval, as opposed to the [[major third|major third's]] quintality. The minor third is also obtainable in reference to a [[fundamental (music)|fundamental note]] from the [[undertone series]], while the major third is obtainable as such from the [[overtone series]]. (See [[Otonality and Utonality]].)
The [[minor scale]] is so named because of the presence of this interval between its [[tonic (music)|tonic]] and [[mediant]] (1st and 3rd) [[scale degrees]]. [[Minor chord]]s too take their name from the presence of this interval built on the chord's [[root (chord)|root]] (provided that the interval of a [[perfect fifth]] from the root is also present or implied).
The [[sopranino saxophone]] and [[E-flat clarinet|E♭ clarinet]] sound in the [[concert pitch]] (C) a minor third higher than the written pitch; therefore, to get the sounding pitch one must [[transposition (music)|transpose]] the written pitch up a minor third. Instruments in A – most commonly the [[A clarinet]], sound a minor third lower than the written pitch.
== In other tunings == {{Listen | header = | type = music | filename = Minor third on C.mid | title = Equal tempered | filename2 = Just minor third on C.mid | title2 = Just | filename4 = }} [[File:Comparison of minor thirds.png|upright=1.3|thumb|Comparison, in cents, of intervals at or near a minor third]]A minor third, in [[just intonation]], corresponds to a pitch ratio of 6:5 or 315.64 [[cent (music)|cents]]. In an [[equal tempered]] tuning, a minor third is equal to three [[semitone]]s, a ratio of 2<sup>1/4</sup>:1 (about 1.189), or 300 cents, 15.64 cents narrower than the 6:5 ratio. In other [[meantone temperament|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 temperament]]s, such as [[53 equal temperament]], the "minor third" is often significantly flat (being close to [[Pythagorean tuning]] ({{Audio|Pythagorean minor third on C.mid|play}})), 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).<ref>Dowsett, Peter (2015). ''Audio Production Tips: Getting the Sound Right at the Source'', p. 3.6.3. CRC. {{ISBN|9781317614203}}. "The minor third, however, does not appear in the harmonic series until the nineteenth harmonic. Your ear almost expects to hear the major third ([on A:] C{{music|#}}), and when that is replaced with a more distantly related note, this makes the listener feel more 'unpleasant', 'tense', or 'sad'."</ref>
The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error.<ref>[[Alexander John Ellis|Alexander J. Ellis]] (translating [[Hermann von Helmholtz|Hermann Helmholtz]]): ''On the Sensations of Tone as a Physiological Basis for the Theory of Music'', p. 455. Dover Publications, New York, 1954. "16:19...The 19th harmonic, ex. 297.513 [cents]". Later reprintings: {{ISBN|1-150-36602-8}} or {{ISBN|1-143-49451-2}}.</ref> 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<!--E natural in alt.-->.<ref>[[Ebenezer Prout|Prout, Ebenezer]] (December 1, 1908). "[https://books.google.com/books?id=N_E2AQAAMAAJ&q=%22nineteenth+harmonic%22&pg=PA268 In the Forecourts of Instrumentation"], ''The Monthly Musical Record''. p. 268.</ref>
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<!--[[Pythagorean minor third]] and [[semiditone]] redirect directly here.--> === In [[music theory]], a ''semiditone'' (or ''Pythagorean minor third'')<ref>[[John Fonville]]. "[[Ben Johnston (composer)|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.</ref> is the [[Interval (music)|interval]] 32:27 (approximately 294.13 [[Cent (music)|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).<ref>[[Oscar Paul|Paul, Oscar]] (1885). ''[https://books.google.com/books?id=4WEJAQAAMAAJ&q=musical+interval+%22pythagorean+major+third%22 A manual of harmony for use in music-schools and seminaries and for self-instruction]'', p. 165. [[Theodore Baker]], trans. G. Schirmer.</ref> {{audio|Pythagorean minor third in scale.mid|Play}}
It can be thought of as two [[octave]]s minus three [[Just intonation|justly tuned]] [[Perfect fifth|fifths]]. It is narrower than a justly tuned minor third by a [[syntonic comma]]. Its inversion is a [[Pythagorean major sixth]].
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==See also== * [[Musical tuning]] * [[List of meantone intervals]] * [[Pythagorean interval]]
==References== {{reflist}}
{{Intervals}}
{{DEFAULTSORT:Minor Third}} [[Category:Minor intervals]] [[Category:Thirds (music)]]
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