Construct · 2 fields · 4 citations

Where does octave collide?

One name. Different field. Different construct. One map.

● jingle · one word, two constructs Nearest construct by meaningintervalcompare the meanings
How to read this

Every construct on the map is compared with every other by the meaning of its definitions, and the closest one is surfaced here. The nearest construct to octave is interval.

Hold this as a prompt, not a verdict. Two constructs sitting close in meaning is a reason to read them side by side and decide for yourself whether they are one idea under two names. It is not proof that they are. Compare the meanings in the Collider.

octave2 CONSTRUCTSMusical octaveEUCLID · 2:1 RATIOCayley octavesCAYLEY · OCTONIONS

Spokes are fields; dashed arcs are shared lineage. Tap a field for its definition, unit, and measures.

1845Cayley octaves1964Musical octave
2026

Drag to watch the word get claimed. Each field appears at the publication date of the earliest source cited for it. Tap a year to see which.

Music theory and acoustics

The 2:1 interval between two pitches

The interval between two pitches whose frequencies stand in a 2:1 ratio, heard as the "same" note repeated higher and used as the frame within which a scale is built. The 2:1 ratio of the octave, called the diapason, is a foundational result of Pythagorean harmonic theory (sixth century BCE) and was set out mathematically in the Sectio canonis attributed to Euclid (c. 300 BCE); Shepard's 1964 study of pitch perception then showed experimentally how strongly listeners treat tones an octave apart as equivalent. Here the octave is a frequency relationship between sounds, and it has nothing to do with eight lines of a poem, eight days of a feast, or an eight-part number system.[1][2]

Unit
One 2:1 frequency doubling between two pitches
Recovery means
Not applicable
Measured by
Taken as the frequency ratio between two tones, an octave being an exact doubling, or 1200 cents

Mathematics

The octonions, an eight-dimensional algebra

The octonions, an eight-dimensional number system that extends the real, complex, and quaternion numbers and in which multiplication is neither commutative nor associative; John Graves called them the "octaves" when he found them in 1843. Cayley published the algebra in 1845, so it is also known as Cayley's octaves or Cayley numbers, and Baez's 2002 survey traces its structure and its uses in geometry and physics. Here the octave is an algebraic object with eight basis units, sharing only the root "eight" with a musical interval, a group of poetic lines, or a feast kept for eight days.[3][4]

Unit
One eight-dimensional nonassociative division algebra
Recovery means
Not applicable
Measured by
Given by eight basis elements with a fixed multiplication table

Next

Run it through the Collider, or take the citations with you.

See how octave sits against neighbouring constructs in the Collider, or export every reference on this page in one click.

Open in ColliderExport BibTeXReport this collision

Nearby collisions

interval4 fields · 5 citationsjingle · one word, four constructspitch3 fields · 4 citationsjingle · one word, three constructsfrequency4 fields · 7 citationsjingle · one word, four constructs

References

  1. Euclid. (1989). The division of the canon (Sectio canonis). In A. Barker (Ed.), Greek musical writings: Vol. 2. Harmonic and acoustic theory (pp. 190–208). Cambridge University Press. (Original work published c. 300 BCE)
  2. Shepard, R. N. (1964). Circularity in judgments of relative pitch. Journal of the Acoustical Society of America, 36(12), 2346–2353. https://doi.org/10.1121/1.1919362
  3. Cayley, A. (1845). On Jacobi's elliptic functions, in reply to the Rev. Brice Bronwin; and on quaternions. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 26(172), 208–211.
  4. Baez, J. C. (2002). The octonions. Bulletin of the American Mathematical Society, 39(2), 145–205. https://doi.org/10.1090/S0273-0979-01-00934-X

Cited on this page?

Confirm your construct, or correct us.

If your work is cited behind one of these entries, you know better than we do whether we captured the meaning right. Confirm it, suggest an edit, or dispute it, and your name goes on the entry as an author who has checked it, linked to your ORCID.

Claim your construct