Construct · 2 fields · 2 citations

Where does mediant collide?

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

● jingle · one word, two constructs Nearest construct by meaning·not indexed
mediant2 CONSTRUCTSMediantSTERN–BROCOT · (a+c)/(b+d)MediantTHIRD SCALE DEGREE

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2026

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Number theory

the fraction formed from two fractions by adding their numerators and their denominators separately.

In number theory the mediant of two fractions a/b and c/d is the fraction (a+c)/(b+d), formed by adding numerators and denominators separately. Graham, Knuth, and Patashnik's Concrete mathematics uses it to build the Stern–Brocot tree and the Farey sequences, where the mediant of two neighbors always lies strictly between them and is the simplest fraction in that interval. The referent is a binary operation on rationals, defined purely arithmetically, unrelated to a musical scale degree beyond the shared Latin root for middle.[1]

Unit
The fraction (a+c)/(b+d) formed from two fractions a/b and c/d
Recovery means
Not applicable
Measured by
Computed directly from the numerators and denominators and verified to fall between the two parent fractions

Music theory

The third degree, midway to the dominant

In music the mediant is the third degree of the diatonic scale and the chord built on it, so called because it sits midway between the tonic and the dominant a fifth above. Kostka, Payne, and Almén's Tonal harmony describes its weak, in-between function and its tendency to substitute for the tonic or to lead toward other chords. The referent is a scale-degree position and harmonic function within a key, fixed by its place in the scale, a different construct from an arithmetic operation on fractions, joined only by the meaning of being in the middle.[2]

Unit
The third scale degree and the chord and function built on it
Recovery means
Not applicable
Measured by
Identified by scale-degree position (the third) and its harmonic behavior within a key

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Nearby collisions

degree1 fields · 1 citationsanchor · a standalone constructbeing3 fields · 3 citationsjingle · one word, three constructschord3 fields · 3 citationsjingle · one word, three constructs

References

  1. Graham, R. L., Knuth, D. E., & Patashnik, O. (1994). Concrete mathematics: A foundation for computer science (2nd ed.). Addison-Wesley. ISBN 9780201558029
  2. Kostka, S., Payne, D., & Almén, B. (2012). Tonal harmony (7th ed.). McGraw-Hill. ISBN 9780078025143

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