science

Neutral sixth

Neutral sixth 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 Neutral sixth rather than just read about it. In short: A neutral sixth is a musical interval wider than a minor sixth but narrower than a major sixth . Three distinct intervals may be termed neutral sixths: The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents.

Key takeaways

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

Reference excerpt

A neutral sixth is a musical interval wider than a minor sixth but narrower than a major sixth . Three distinct intervals may be termed neutral sixths:

The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents. A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the two tones, or about 840.53 cents. This is the smallest neutral sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic. An equal-tempered neutral sixth is 850 cents, a hair narrower than the 18:11 ratio. It is an equal-tempered quarter tone exactly halfway between the equal-tempered minor and major sixths, and half of an equal-tempered perfect eleventh (octave plus fourth). These intervals are all within about 12 cents of each other and are difficult for most people to distinguish. Neutral sixths are roughly a quarter tone sharp from 12 equal temperament (12-ET) minor sixths and a quarter tone flat from 12-ET major sixths. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together. A neutral sixth can be formed by subtracting a neutral second from a minor seventh. Based on its positioning in the harmonic series, the undecimal neutral sixth implies a root one minor seventh above the higher of the two notes.

Thirteenth harmonic

The pitch ratio 13:8 (840.53 cents) is the ratio of the thirteenth harmonic and is notated in Ben Johnston's system as A13♭. In 24-ET is approximated by A. This note is often corrected to a just or Pythagorean ratio on the natural horn, but the pure thirteenth harmonic was used in pieces including Britten's Serenade for tenor, horn and strings.

See also List of musical intervals List of pitch intervals Microtonal music

References

Illustrations

Worked examples

Example 1 — a first encounter with Neutral sixth

Start with the simplest possible case. Write down what Neutral sixth 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 Neutral sixth 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 Neutral sixth 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 Neutral sixth

In research: Neutral sixth 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 Neutral sixth 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: Neutral sixth is common in secondary-school and first-year university syllabi. It links to neighbouring topics Neutral intervals, Quarter tones, Sixths (music), so understanding it makes those chapters shorter.
In everyday life: Look for Neutral sixth 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 Neutral sixth in 20 minutes

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

Frequently asked questions

What is Neutral sixth in simple terms?

A neutral sixth is a musical interval wider than a minor sixth but narrower than a major sixth . Three distinct intervals may be termed neutral sixths: The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents.

Why does Neutral sixth 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 Neutral sixth?

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 Neutral sixth.