science

Minor third

Minor third is a science topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Minor third rather than just read about it. In short: 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).

Key takeaways

Minor 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 Minor third to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Minor third from memory before moving on to harder problems.

Reference excerpt

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.

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. 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

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 ()), 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). The 12-TET minor third (300 cents) more closely approximates the nineteenth harmonic with only 2.49 cents error. 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. 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 In music theory, a semiditone (or Pythagorean minor third) 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). 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 Musical tuning List of meantone intervals Pythagorean interval

References

Illustrations

Worked examples

Example 1 — a first encounter with Minor third

Start with the simplest possible case. Write down what Minor 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 Minor 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 Minor 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 Minor third

In research: Minor 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 Minor 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: Minor third is common in secondary-school and first-year university syllabi. It links to neighbouring topics Minor intervals, Thirds (music), so understanding it makes those chapters shorter.
In everyday life: Look for Minor 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.

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How to study Minor third in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Minor 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 Minor third out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Minor third in simple terms?

Why does Minor 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 Minor 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 Minor third.