Major third - Misplaced Pages

(Redirected from Tridecimal major third) This article is about the musical interval. For the guitar tuning, see major thirds tuning. See also: Ditone

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Major third
Inverse	Minor sixth
Name
Other names	ditone
Abbreviation	M3, 3, 3, maj 3
Size
Semitones	4
Interval class	4
Just interval	5:4, 81:64, 9:7
Cents
12-Tone equal temperament	400
Just intonation	386, 408, 435

In classical music, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third (Play) is a third spanning four half steps or two whole steps. 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 E lies four semitones above C, and there are three staff positions from C to E.

The intervals from the tonic (keynote) in an upward direction to the second, to the third, to the sixth, and to the seventh scale degrees of a major scale are called "major".

Diminished and augmented thirds are shown on the musical staff the same number of lines and spaces apart, but contain of 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 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 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 (provided that the interval of a perfect fifth from the root is also present).

A major third is slightly different in different musical tunings: In just intonation it corresponds to a pitch ratio of 5:4, or ⁠ 5 / 4 ⁠ (play) (fifth harmonic in relation to the fourth) or 386.31 cents; in 12 tone equal temperament, a major third is equal to four semitones, a ratio of 2:1 (about 1.2599) or 400 cents, 13.69 cents 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 cents (play), about 22 cents sharp from the harmonic ratio of 5:4 . The septimal major third is 9:7 (435 cents), the undecimal major third is 14:11 (418 cents), and the tridecimal major third is 13:10 (452 cents).

In 12 tone equal temperament (12 TET) three major thirds in a row are equal to an octave. For example, A to C, C to E, and E to G (in 12 TET, the differently written notes G and A both represent the same pitch, but not in most other 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 (C to E, to G, to B) (⁠  B / C ⁠ $={\tfrac {\;5^{3}\ }{\;2^{6}\ }}={\tfrac {\ 125\ }{64}}\$ ). The difference between this just-tuned B and C, like the interval between G and A, is called the "enharmonic diesis", about 41 cents, or about two commas (the inversion of the interval ⁠ 125 / 64 ⁠ : $\ {\frac {\ 128\ }{125}}={\frac {\;2^{7}\ }{\;5^{3}}}\$ play)).

Consonance vs. dissonance

The major 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. In the common practice period, thirds were considered interesting and dynamic consonances along with their inverses the sixths, but in medieval times they were considered dissonances unusable in a stable final sonority.

In equal temperament, a diminished fourth is enharmonically equivalent to a major third (that is, it spans the same number of semitones). For example, B–D is a major third; but if the same pitches are spelled as the notes B and E, then the interval they represent is instead a diminished fourth. The difference in 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 occurs in the C harmonic minor scale.

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

Interval sounds

Minor thirds:

C-E