Major third

Key takeaways

Major third belongs to science; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Major third to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Major third from memory before moving on to harder problems.

Reference excerpt

In music theory, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () 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.

As Beward and Saker explain:

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 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 ⁠ () (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 21/3:1 (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 (), 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 ⁠ = 5 3 2 6 = 125 64 {\displaystyle ={\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 ⁠ : 128 125 = 2 7 5 3 {\displaystyle \ {\frac {\ 128\ }{125}}={\frac {\;2^{7}\ }{\;5^{3}}}\ } ()).

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:

Major thirds

See also Ear training Ladder of thirds / chain of thirds List of meantone intervals Circle of thirds

References

Illustrations

Worked examples

Example 1 — a first encounter with Major third

Start with the simplest possible case. Write down what Major third claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In science, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Major third before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Major third ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Major third

In research: Major third appears in science research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Major third in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Major third is common in secondary-school and first-year university syllabi. It links to neighbouring topics Major intervals, Thirds (music), so understanding it makes those chapters shorter.
In everyday life: Look for Major third outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Major third in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Major third means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Major third out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Major third in simple terms?

In music theory, a third is a musical interval encompassing three staff positions (see Interval number for more details), and the major third () 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.

Why does Major third matter?

Because it connects several science ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Major third?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Major third.