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One-third octave

One-third octave 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 One-third octave rather than just read about it. In short: A one-third octave is a logarithmic unit of frequency ratio equal to either one third of an octave (1200/3 = 400 cents: major third) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade.

One-third octave — main illustration
One-third octave — illustration

Key takeaways

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

Reference excerpt

A one-third octave is a logarithmic unit of frequency ratio equal to either one third of an octave (1200/3 = 400 cents: major third) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade.

Definitions

Base 2 ISO 18405:2017 defines a "one-third octave" (or "one-third octave (base 2)") as one third of an octave, corresponding to a frequency ratio of 2 1 / 3 {\displaystyle 2^{1/3}} . A one-third octave (base 2) is precisely 400 cents.

Base 10 IEC 61260-1:2014 and ANSI S1.6-2016 define a "one-third octave" as one tenth of a decade, corresponding to a frequency ratio of 10 1 / 10 {\displaystyle 10^{1/10}} . This unit is referred to by ISO 18405 as a "decidecade" or "one-third octave (base 10)". One decidecade is equal to 100 savarts (approximately 398.631 cents).

See also Decibel Octave band Pseudo-octave Tritonic scale

References

Further reading Ainslie, Michael A.; Halvorsen, Michele B.; Robinson, Stephen P. (January 2022) [2021-11-09]. "A terminology standard for underwater acoustics and the benefits of international standardization". IEEE Journal of Oceanic Engineering. 47 (1). IEEE: 179–200. doi:10.1109/JOE.2021.3085947. eISSN 1558-1691. ISSN 0364-9059. S2CID 243948953. [1] (22 pages)

Illustrations

One-third octave: Augmented chord in the chromatic circle Playⓘ
Augmented chord in the chromatic circle Playⓘ

Worked examples

Example 1 — a first encounter with One-third octave

Start with the simplest possible case. Write down what One-third octave 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 One-third octave 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 One-third octave 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 One-third octave

In research
One-third octave 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 One-third octave 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
One-third octave is common in secondary-school and first-year university syllabi. It links to neighbouring topics Intervals (music), Units of level, so understanding it makes those chapters shorter.
In everyday life
Look for One-third octave 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 One-third octave in 20 minutes

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

Frequently asked questions

What is One-third octave in simple terms?

A one-third octave is a logarithmic unit of frequency ratio equal to either one third of an octave (1200/3 = 400 cents: major third) or one tenth of a decade (3986.31/10 = 398.631 cents: M3 ). An alternative (unambiguous) term for one tenth of a decade is a decidecade.

Why does One-third octave 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 One-third octave?

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 One-third octave.

Tags

  • Intervals (music)
  • Units of level

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