Neutral sixth

Neutral Sixth

Inverse	neutral third
Name
Other names	-
Abbreviation	n6
Size
Semitones	~8½
Interval class	~3½
Just interval	18:11[1] or 13:8[2]
Cents
Equal temperament	800 or 900
24 equal temperament	850
Just intonation	853 or 841

Neutral sixth on C  Play (help·info).

A neutral sixth is a musical interval wider than a minor sixth  play (help·info) but narrower than a major sixth  play (help·info). 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.  play (help·info)

• A tridecimal neutral sixth has a ratio of 13:8 between the frequencies of the two tones, or about 840.53 cents.^[3] This is the smallest neutral sixth, and occurs infrequently in music, as little music utilizes the 13th harmonic.  play (help·info)

• An equal-tempered neutral sixth is characterized by a difference in 850 cents between the two tones, a hair narrower than the 18:11 ratio, and exactly half of an equal-tempered perfect eleventh (octave plus fourth).  play (help·info)

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 flat from 12 equal temperament minor sixths and a quarter tone sharp 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.

See also

• List of musical intervals
• Microtonal music

References

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiv. ISBN 0824747143. Undecimal neutral sixth.
2. ^ Haluska (2003), p.xxiii. Tridecimal neutral sixth.
3. ^ [1] Jan Haluska, The Mathematical Theory of Tone Systems, CRC (2004).