Neutral interval

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Neutral third Neutral interval.png
Neutral third

In music theory, a neutral interval in 24 TET (including extensions), (but also known as a submajor interval, or as a

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superminor interval, in Just Intonation), is an interval that is neither major nor minor, but is, instead, in-between them.

In 12 TET, the major third is tuned at 400 ¢, and the minor third is 100 ¢ flatter (300 ¢). A neutral interval inverts to another

one. These intervals are a quarter tone, (50 ¢), sharper from minor intervals and 50 ¢ flatter from major intervals. In the

just intonation, as well as in tunings such as 31-ET, 41-ET, or 72-ET, which more closely approximate it with more of them, these can be closer together.

intervalsminorneutralmajor
secondsDD Llpd- 1/2 .svg D
thirdsEE Llpd- 1/2 .svg E
sixthsAA Llpd- 1/2 .svg A
seventhsBB Llpd- 1/2 .svg B

Second

Neutral second
Inverse neutral seventh
Name
Abbreviationn2
Size
Semitones ~1+12
Interval class ~1+12
Just interval 11:10 or 12:11 [1]
Cents
12-Tone equal temperament 100 or 200
24-Tone equal temperament 150
Just intonation 165 or 151
Neutral second on C Play. Neutral second on C.png
Neutral second on C Play .

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

The equal-tempered neutral is found in some traditional Arabic music (see also Arab tone system). Because the equal tempered neutral second is essentially a semitone (minor second) plus a quarter-tone, they may be considered three-quarter tones in the quarter tone scale.

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. 17-ET has a neutral second between 12:11 and 13:12, and a neutral third between 16:13 and 11:9.

Seventh

Neutral seventh
Inverse neutral second
Name
Other names-
Abbreviationn7
Size
Semitones ~10+12
Interval class ~1+12
Just interval 11:6, [1] 64:35, [2] or 24:13
Cents
12-Tone equal temperament 1000 or 1100
24-Tone equal temperament 1050
Just intonation 1049, 1045, or 1061
Neutral seventh on C Play. Neutral seventh on C.png
Neutral seventh on C Play .

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

These intervals are all within about 12 cents of each other and are difficult for most people to distinguish.

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 seventh implies a root one perfect fifth below the lower of the two notes.

See also

References

  1. 1 2 Haluska, Jan (2003). The Mathematical Theory of Tone Systems, p.xxiii. ISBN   0-8247-4714-3. 3/4-tone, undecimal neutral second and 21/4-tone, undecimal neutral seventh.
  2. Haluska (2003), p.?. Septimal neutral seventh.
  3. 1 2 Andrew Horner, Lydia Ayres (2002). Cooking with Csound: Woodwind and Brass Recipes, p.131. ISBN   0-89579-507-8.