Neutral tones

A neutral second or medium second is a musical interval between a minor second and a major second. Three distinct intervals may be termed neutral seconds. An equal-tempered neutral second is characterized by a difference in 150. more...

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00 cents between the two tones, a hair smaller than a ratio of frequencies between the two tones of 12:11. The intermediate neutral second, called the lesser undecimal neutral second, 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, possesses a ratio of 11:10 between the two tones and is about 165.00 cents wide.

Roughly speaking, then, neutral seconds are a quarter tone sharp from minor seconds and a quarter tone flat from major seconds. The even-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.

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