Tri-tone - Eleventh Harmonic

Known as the lesser undecimal tritone or undecimal semi-augmented fourth, 11:8 (551.318 cents), the ratio of the eleventh harmonic (F4 above C1), is found in some just tunings and on many instruments. For example, very long alphorns may reach the twelfth harmonic and transcriptions of their music usually show the eleventh harmonic sharp (F♯ above C, for example), as in Brahms's First Symphony. This note is often corrected to 4:3 on the natural horn in just intonation or Pythagorean tunings, but the pure eleventh harmonic was used in pieces including Britten's Serenade for tenor, horn and strings.

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