Neutral sixth

Neutral Sixth
Inverse neutral third
Other names -
Abbreviation n6
Semitones ~8½
Interval class ~3½
Just interval 18:11[1] or 13:8[2]
Equal temperament 800 or 900
24 equal temperament 850
Just intonation 853 or 841
Neutral sixth on C  Play .

A neutral sixth is a musical interval wider than a minor sixth  play  but narrower than a major sixth  play . 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 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

Thirteenth harmonic on C.  Play 

13:8 (840.53 cents), the ratio of the thirteenth harmonic 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.[4]

Use of the thirteenth harmonic in the prologue to Britten's Serenade for tenor, horn and strings.

See also


  1. Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0-8247-4714-3. Undecimal neutral sixth.
  2. Haluska (2003), p.xxiii. Tridecimal neutral sixth.
  3. Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).
  4. Fauvel, John; Flood, Raymond; and Wilson, Robin J. (2006). Music And Mathematics, p.21-22. ISBN 9780199298938.
This article is issued from Wikipedia - version of the 11/3/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.