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A neutral sixth is a musical interval wider than a minor sixth ooui-php-2play but narrower than a major sixth ooui-php-3play. Three distinct intervals may be termed neutral sixths:

• The undecimal neutral sixth has a ratio of 18:11 between the frequencies of the two tones, or about 852.59 cents. ooui-php-4play

• A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the two tones, or about 840.53 cents.cite-ref-3[3] This is the smallest neutral sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic. ooui-php-5play

• An equal-tempered neutral sixth is 850 cents, a hair narrower than the 18:11 ratio. It is an equal-tempered quarter tone exactly halfway between the equal-tempered minor and major sixths, and half of an equal-tempered perfect eleventh (octave plus fourth). ooui-php-6play

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. In just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate just intonation, the intervals are closer together.

A neutral sixth can be formed by subtracting a neutral second from a minor seventh. 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.

• Thirteenth harmonic

• See also

• References

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♭. In 24-ET is approximated by A. 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.cite-ref-4[4]

• List of musical intervals

• List of pitch intervals

• Microtonal music

cite-note-11. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0-8247-4714-3. Undecimal neutral sixth.

cite-note-22. Haluska (2003), p.xxiii. Tridecimal neutral sixth.

cite-note-33. ↑ [1] Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).

cite-note-44. ↑ Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). Music And Mathematics, p.21-22. ISBN 9780199298938.