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{{Short description|Musical interval encompassing three half steps}}
{{Infobox Interval|
{{Infobox
main_interval_name = Minor third|
| title = Minor third
⚫
inverse = [[major sixth]]|
| headerstyle = background-color:palegoldenrod; color:inherit;
complement = [[major sixth]]|
| label1 = [[Inversion (music)#Intervals|Inverse]]
other_names = - |
⚫
| data1 = [[Major sixth]]
abbreviation = m3 |
| header2 = Name
semitones = 3 |
| label3 = Other names
interval_class = 3 |
| data3 = Sesquitone
⚫
just_interval = 6:5, 19:16,<ref>Haluska, Jan (2003). ''The Mathematical Theory of Tone Systems'', p.xxiv. ISBN 0-8247-4714-3. 19th harmonic, overtone minor tone.</ref> 32:27|
| label4 = Abbreviation
cents_equal_temperament = 300|
| data4 = m3
cents_24T_equal_temperament = 300|
| header5 = Tuning
cents_just_intonation = 316, 298, 294
| 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)
}}
}}
[[Image:Minor third on C.png|thumb|right|Minor third {{Audio|Minor third on C.mid|Play}} equal tempered or {{audio|Just minor third on C.mid|just}} (6:5).]]
⚫
[[Image:19th harmonic on C.png|thumb|right|19th harmonic (19:16), E<sup>19</sup>{{music|flat}} {{Audio|19th harmonic on C.mid|Play}}.]]
[[File:Comparison of minor thirds.png|right|thumb|Comparison, in cents, of intervals at or near a minor third]]


⚫
[[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 the [[music theory]] of [[Western culture]], 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, and (coincidentally) there are three staff positions from A to C. [[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. A good 5-limit approximation is '''32/27''', though 6/5 is also commonly used for its simplicity.
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]].
Notable examples of ascending minor thirds include the opening two notes of "[[Greensleeves]]" and of "[[Light My Fire]]".


⚫
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]]'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 third 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 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 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 |author=Curtis ME, Bharucha JJ |title=The minor third communicates sadness in speech, mirroring its use in music |journal=Emotion |volume=10 |issue=3 |pages=335–48 |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|perfect fourths]]) [[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 [[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.
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).


== In other tunings ==
⚫
A minor third, in [[just intonation]], corresponds to a pitch ratio of 6:5 ({{Audio|Just minor third on C.mid|play}}) 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, this produces an interval of 297.51 cents.<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 harmmonic. 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 [[harmonic|19-limit]] ([[Limit (music)]]) minor third 16:19 {{audio|19th harmonic on C.mid|Play}} (297.51 cents, the '''nineteenth harmonic''') with only 2.49 cents error.<ref>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 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 WWV 86 ''[[Der Ring des Nibelungen]]'' (1848 to 1874), when [[Robert Schumann]]'s Op. 86 ''Konzertstück'' for 4 Horns and Orchestra (1849) features the [[twentieth harmonic]] (octave of the fifth harmonic, or major third) in the first horn part three times<!--E natural in alt.-->.<ref>Prout, Ebenezer (December 1, 1908). "[https://books.google.com/books?id=N_E2AQAAMAAJ&pg=PA268&dq=%22nineteenth+harmonic%22+music&hl=en&sa=X&ved=0ahUKEwji7teRx_PJAhVU8WMKHXHpCFQQ6AEINjAD#v=onepage&q=%22nineteenth%20harmonic%22&f=false In the Forecourts of Instrumentation", ''The Monthly Musical Record]''. p.268.</ref>
{{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.
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.--> ===
⚫
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]].
⚫
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]].
⚫
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.


{{Clear}}
⚫
==Pythagorean minor third<!--[[Pythagorean minor third]] and [[semiditone]] redirect directly here.-->==
[[Image:Semiditone on C.png|thumb|right|[[Semiditone]] (32:27) on C {{Audio|Pythagorean minor third on C.mid|Play}}.]]
[[Image:Semiditone.png|thumb|Semiditone as two octaves minus three justly tuned fifths.]]

⚫
In [[music theory]], a '''semiditone''' (or '''Pythagorean minor third'''<ref>[[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.</ref>) is the [[Interval (music)|interval]] 32:27 (approximately 294.13 [[Cent (music)|cents]]). It is the minor third in [[Pythagorean tuning]]. The 32:27 Pythagorean minor third arises in the C [[major scale]] between D and F.<ref>Paul, Oscar (1885). ''[http://books.google.com/books?id=4WEJAQAAMAAJ&dq=musical+interval+%22pythagorean+major+third%22&source=gbs_navlinks_s 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]].


==See also==
==See also==
* [[musical tuning]]
* [[Musical tuning]]
* [[List of meantone intervals]]
* [[List of meantone intervals]]
* [[Pythagorean interval]]
* [[Pythagorean interval]]
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[[Category:Minor intervals]]
[[Category:Minor intervals]]
[[Category:Thirds (music)]]
[[Category:Thirds (music)]]

[[ru:Терция (интервал)#Разновидности терции]]

Latest revision as of 18:15, 8 August 2026

Minor third
InverseMajor sixth
Name
Other namesSesquitone
Abbreviationm3
Tuning
12 equal temperament3 semitones (300 cents)
Pythagorean tuning32:27 (294 cents)[1]
5-limit tuning6:5 (316 cents)
7-limit tuning7:6 (267 cents)
13-limit tuning13:11 (289 cents)
19-limit tuning19:16 (298 cents)
19th harmonic (19:16), E19♭

In music theory, a minor third is a musical interval that encompasses three half steps, or semitones. Staff notation represents the minor third as encompassing three staff positions (see: 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.

Musical scores are temporarily disabled.

Diminished and augmented thirds span the same number of staff positions, but consist of a different number of semitones (two and five). The minor third is a skip melodically.

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. It 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 shows that this mirrors its use in speech, as a tone similar to a minor third is produced during sad speech.[2] It is also a quartal (based on an ascendance of one or more perfect fourths) tertian interval, as opposed to the major third's quintality. The minor third is also obtainable in reference to a 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 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).

The sopranino saxophone and E♭ clarinet sound in the concert pitch (C) a minor third higher than the written pitch; therefore, to get the sounding pitch one must 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

[edit | edit source]
Equal tempered
Just
Problems playing these files? See media help.
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 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 (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).[3]

The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error.[4] 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.[5]

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

[edit | edit source]

In music theory, a semiditone (or Pythagorean minor third)[6] 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).[7] Playⓘ

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

[edit | edit source]

References

[edit | edit source]
  1. ↑ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p. xxiv. ISBN 0-8247-4714-3. 19th harmonic, overtone minor tone.
  2. ↑ Curtis, M. E.; Bharucha, J. J. (June 2010). "The minor third communicates sadness in speech, mirroring its use in music". Emotion. 10 (3): 335–348. doi:10.1037/a0017928. PMID 20515223.
  3. ↑ 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♯), and when that is replaced with a more distantly related note, this makes the listener feel more 'unpleasant', 'tense', or 'sad'."
  4. ↑ Alexander J. Ellis (translating 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.
  5. ↑ Prout, Ebenezer (December 1, 1908). "In the Forecourts of Instrumentation", The Monthly Musical Record. p. 268.
  6. ↑ 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.
  7. ↑ Paul, Oscar (1885). A manual of harmony for use in music-schools and seminaries and for self-instruction, p. 165. Theodore Baker, trans. G. Schirmer.
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