Neutral seventh

Neutral seventh

Inverse	neutral second
Name
Other names	-
Abbreviation	n7
Size
Semitones	~10½
Interval class	~1½
Just interval	11:6[1], 64:35[2], or 24:13
Cents
Equal temperament	1000 or 1100
24 equal temperament	1050
Just intonation	1049, 1045, or 1061

Neutral seventh on C  Play (help·info).

A neutral seventh is a musical interval wider than a minor seventh  play (help·info) but narrower than a major seventh  play (help·info). Four distinct intervals may be termed neutral sevenths:

• A septimal neutral seventh  play (help·info) has a ratio of 64:35 or about 1045 cents.

• The just undecimal neutral seventh has a ratio of 11:6 between the frequencies of the two tones^[3], or about 1049 cents  play (help·info). Alternately, 13:7^[3] or about 1071.7 cents.

• A tridecimal neutral seventh  play (help·info) has a ratio of 24:13 between the frequencies of the two tones, or about 1061 cents. This is the largest neutral seventh, and occurs infrequently in music, as little music utilizes the 13th harmonic.

• An equal-tempered neutral seventh  play (help·info) is characterized by a difference in 1050 cents between the two tones, a hair larger than the 11:6 ratio, and exactly half of an equal-tempered major thirteenth (octave plus major sixth).

These intervals are all within about 12 cents and are difficult for most people to distinguish. Neutral sevenths are roughly a quarter tone sharp from 12 equal temperament minor sevenths and a quarter tone flat from 12-ET major sevenths. 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 seventh can be formed by stacking a neutral third together with a perfect fifth. Based on its positioning in the harmonic series, the undecimal neutral third implies a root one perfect fifth below the lower of the two notes.

See also

• List of musical intervals
• Microtonal music

Sources

1. ^ Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN 0824747143. 21/4-tone, undecimal neutral seventh.
2. ^ Haluska (2003), p.?. Septimal neutral seventh.
3. ^ ^{a b} Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN 0895795078.