Editing Major third

{{about|the musical interval|the guitar tuning|major thirds tuning}}
{{see also|Ditone}}
{{More references|date=June 2020}}
{{Infobox Interval
| main_interval_name = Major third
| inverse = [[Minor sixth]]
| complement = [[Minor sixth]]
| other_names = ditone
| abbreviation = M3, {{sup|maj}}3, {{sup|M}}3, {{nobr|maj 3}}
| semitones = 4
| interval_class = 4
| just_interval = [[5-limit tuning|5:4]], [[Pythagorean tuning|81:64]], [[Septimal major third|9:7]]
| cents_equal_temperament = 400
| cents_24T_equal_temperament =
| cents_just_intonation = 386, 408, 435
}}
[[Image:Major third on C.png|thumb|right|Just major third.]]
[[Image:Ditone on C.png|thumb|right|Pythagorean major third, i.e. a [[ditone]]]]
[[File:Comparison of major thirds.png|right|thumb|Comparison, in cents, of intervals at or near a major third]]
[[File:Harmonic series klang.png|thumb|[[Harmonic series (music)|Harmonic series]], partials&nbsp;1–5, numbered
{{audio|Harmonic series klang.mid|Play}}.]]

In [[music theory]], a '''third''' is a [[Interval (music)|musical interval]] encompassing three [[staff position]]s (see [[Interval (music)#Number|Interval number]] for more details), and the '''major third''' ({{Audio|Major third on C.mid|Play}}) is a third spanning four [[Semitone|half steps]] or two [[Whole step|whole steps.]]<ref>{{cite book |author-link=Allen Forte |last=Forte |first=Allen |year=1979 |title=Tonal Harmony in Concept and Practice |page=8 |publisher=Holt, Rinehart, and Winston |edition=3rd |isbn=0-03-020756-8 |quote=A large 3rd, or ''major&nbsp;3rd'' (M3) encompassing four half steps. }}</ref> Along with the [[minor third]], the major third is one of two commonly occurring thirds. It is described as ''major'' because it is the larger interval of the two: The major third spans four semitones, whereas the [[minor third]] only spans three. For example, the interval from C to E is a major third, as the note&nbsp;E lies four semitones above C, and there are three staff positions from C to E.

{{Quote|The intervals from the [[tonic (music)|tonic]] (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh [[scale degree]]s of a major scale are called "major".<ref>{{cite book |last1=Benward |first1=Bruce |last2=Saker |first2=Marilyn |year=2003 |title=Music: In theory and practice |volume=I |page=52 |publisher=McGraw-Hill |edition=7th |isbn=978-0-07-294262-0 }}</ref>}}

[[Diminished third|Diminished]] and [[augmented third]]s are shown on the [[musical staff]] the same number of lines and spaces apart, but contain a different number of semitones in pitch (two and five).

== Harmonic and non-harmonic thirds ==
The major third may be derived from the [[harmonic series (music)|harmonic series]] as the interval between the fourth and fifth harmonics. 
The [[major scale]] is so named because of the presence of this interval between its [[tonic (music)|tonic]] and [[mediant]] (1st and 3rd) [[scale degrees]]. 
The [[major chord]] also takes its 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).

A major third is slightly different in different [[musical tuning]]s: In [[just intonation]] it corresponds to a pitch ratio of 5:4, or {{small|{{math|{{sfrac| 5 | 4 }}}}}} ({{Audio|Just major third on C.mid|play}}) (fifth harmonic in relation to the fourth) or 386.31&nbsp;[[musical cents|cents]]; in [[12 equal temperament|12&nbsp;tone equal temperament]], a major third is equal to four [[semitone]]s, a ratio of 2<sup>1/3</sup>:1 (about 1.2599) or 400&nbsp;cents, 13.69&nbsp;[[cent (music)|cent]]s wider than the 5:4 ratio. The older concept of a "[[ditone]]" (two 9:8 major seconds) made a dissonant, wide major third with the ratio 81:64 (about 1.2656) or 408&nbsp;cents ({{Audio|Pythagorean major third on C.mid|play}}), about [[syntonic comma|22&nbsp;cents]] sharp from the harmonic ratio of 5:4&nbsp;. The [[septimal major third]] is 9:7 (435&nbsp;cents), the '''undecimal major third''' is 14:11 (418&nbsp;cents), and the '''tridecimal major third''' is 13:10 (452&nbsp;cents).

In 12&nbsp;tone equal temperament {{nobr|([[12 equal temperament|12&thinsp;{{sc|TET}}]])}} three major thirds in a row are equal to an octave. For example, A{{sup|{{music|flat}}}} to C, C to E, and E to G{{sup|{{music|sharp}}}} (in {{nobr|[[12 equal temperament|12&thinsp;{{sc|TET}}]],}} the differently written notes G{{sup|{{music|sharp}}}} and A{{sup|{{music|flat}}}} both represent the same pitch, but ''not'' in most other [[tuning (music)|tuning systems]]). This is sometimes called the "[[circle of thirds]]". In just intonation, however, three 5:4 major third, the 125th [[subharmonic]], is less than an octave. For example, three 5:4 major thirds from C is B{{sup|{{music|sharp}}}} (C to E, to G{{sup|{{music|sharp}}}}, to B{{sup|{{music|sharp}}}}) ({{sfrac|  B{{sup|{{music|#}}}} | C }} <math> = \tfrac{\; 5^3 \ }{\; 2^6\ } = \tfrac{\ 125\ }{ 64 }\ </math>). The difference between this just-tuned B{{sup|{{music|sharp}}}} and C, like the interval between G{{sup|{{music|sharp}}}} and A{{sup|{{music|flat}}}}, is called the "enharmonic [[diesis]]", about 41&nbsp;cents, or about two [[syntonic comma|commas]] (the [[inversion (interval)|inversion]] of the interval {{small|{{math|{{sfrac| 125 | 64 }}}} }}: <math>\ \frac{\ 128\ }{ 125 } = \frac{\; 2^7\ }{\; 5^3 }\ </math> ({{audio|5-limit limma on C.mid|play}})).

== Consonance vs. dissonance ==
The major 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 the [[common practice period]], thirds were considered interesting and dynamic consonances along with their [[inversion (interval)|inverses]] the sixths, but in [[medieval music|medieval times]] they were considered dissonances unusable in a stable final sonority.

In equal temperament, a [[diminished fourth]] is [[enharmonic]]ally equivalent to a major third (that is, it spans the same number of semitones). For example, B–D{{sup|{{music|sharp}}}} is a major third; but if the same pitches are spelled as the notes B and E{{sup|{{music|flat}}}}, then the interval they represent is instead a [[diminished fourth]]. The difference in [[pitch (music)|pitch]] is erased in [[12 tone equal temperament]], where the distinction is only nominal, but the difference between a major third and a diminished fourth is significant in almost all other [[musical tuning]] systems. B–E{{sup|{{music|flat}}}} occurs in the C&nbsp;[[harmonic minor scale]].

The major third is used in [[guitar tunings]]. For the [[guitar tunings#Standard|standard tuning]], only the interval between the 3rd and 2nd&nbsp;strings (G to B, respectively) is a major&nbsp;third; each of the intervals between the other pairs of consecutive strings is a [[perfect fourth]]. In an [[guitar tunings#Alternative|alternative tuning]], the [[major-thirds tuning]], ''each'' of the intervals are major thirds.

==Interval sounds==
* Minor thirds:
{|
|
{{Listen
| filename = Kl terz auf.ogg
| title = C-E{{sup|{{music|b}}}}
| description = Strings playing the note C then E{{sup|{{music|b}}}}
}}

|
{{Listen
| filename = Kl terz ab.ogg
| title = C-A
| description = Strings playing the note C then A
}}
|}
* Major thirds
{|
|
{{Listen|filename=Third_ET.ogg|title=Major third (equal temperament)|description=The file plays [[middle C]], followed by E (a tone 400&nbsp;cents sharper than C), followed by both tones together.}}
{{Listen
| filename = Gr terz auf.ogg
| title = C-E
| description = Strings playing the note C then E
}}

|
{{Listen
| filename = Gr terz ab.ogg
| title = C-A{{sup|{{music|b}}}}
| description = Strings playing the note C then A{{sup|{{music|b}}}}
}}
|}

==See also==
* [[Decade (log scale)]], compound just major third{{Clarify|date=April 2025}}
* [[Ear training]]
* [[Ladder of thirds|Ladder of thirds / chain of thirds]]
* [[List of meantone intervals]]
* [[Circle of thirds]]

== References ==
{{reflist|25em}}

{{Intervals}}

[[Category:Thirds (music)]]
[[Category:Major intervals]]

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