Neutral second

Neutral second

Inverse	neutral seventh
Name
Other names
Abbreviation	n2
Size
Semitones	~1½
Interval class	~1½
Just interval	11:10 or 12:11[1]
Cents
Equal temperament	100 or 200
24 equal temperament	150
Just intonation	165 or 151

Neutral second on C  Play (help·info).

A neutral second or medium second is a musical interval wider than a minor second and narrower than a major second. Three distinct intervals may be termed neutral seconds:

• The intermediate neutral second, called the lesser undecimal neutral second  play (help·info), has a ratio between the higher-frequency tone to the lower-frequency tone of 12:11 and is about 150.64 cents wide, while the larger one,

• the greater undecimal neutral second  play (help·info), has a ratio of 11:10 between the two tones and is about 165.00 cents wide. The lesser undecimal neutral second may be derived from the harmonic series as the interval between the eleventh and twelfth harmonics. The greater undecimal neutral second may be derived from the harmonic series as the interval between the tenth and eleventh harmonics.

• An equal-tempered neutral second  play (help·info) is characterized by a difference in 150 cents between the two tones, a hair smaller than a ratio of frequencies between the two tones of 12:11, and exactly half of an equal-tempered minor third.

Roughly speaking, then, neutral seconds are a quarter tone sharp from minor seconds and a quarter tone flat from major seconds. The equal-tempered neutral second may be found in the quarter tone scale and in some traditional Arab music (see also Arab tone system). Because neutral seconds are essentially a semitone (minor second) plus a quarter-tone, they may be considered three-quarter tones.

In equal temperament

Approximations to the 12:11 and 11:10 neutral seconds can be found in a number of equally-tempered tuning systems. 11:10 is very closely matched by 22-ET, whereas 12:11 is matched by 24-ET, 31-ET and 41-ET. 72-ET matches both intervals closely and is also the smallest widely used equal temperament that uniquely matches both intervals. Tuning systems that temper out the comma of 121:120 do not distinguish between the two intervals.

See also

• List of musical intervals
• Microtonal music

References

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0824747143. 3/4-tone, undecimal neutral second.