Neutral sixth

Three distinct intervals may be termed neutral sixths: 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.

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.

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♭.

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.