Neutral tetrad: Difference between revisions

(2 intermediate revisions by one other user not shown)

Line 1:

A '''neutral tetrad''' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

A '''neutral tetrad''', more commonly known as a '''neutral seventh chord''', is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.

A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.

Line 6:

[[Category:11-limit]]

[[Category:Dyadic]]

[[Category:Dyadic chords]]

[[Category:Tetrad]]

[[Category:Neutral]]

[[Category:~~Rastma]]~~

[[Category:Rastmic]]

~~[[Category:Tetrad~~]]

@@ Line 1: / Line 1: @@
-A '''neutral tetrad''' is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.
+A '''neutral tetrad''', more commonly known as a '''neutral seventh chord''', is comprised of two intervals of a fifth a neutral third apart. In tunings where 243/242 is tempered out, it may be viewed as the [[rastmic chords|rastmic]] [[Dyadic chord#Essentially tempered dyadic chords|essentially tempered dyadic chord]] consisting of a stack of three 11/9 neutral third intervals followed by a 12/11, which closes at the octave since the rastma, 243/242, is tempered out. It is the 243/242-tempering of the 27-limit JI chord 18:22:27:33, or 1-11/9-3/2-11/6, and contains the neutral triad, the tempering of 18:22:27, and may be extended to the neutral pentad, 18:22:27:30:33, which is 1-11/9-3/2-5/3-11/6, a 15-limit essentially tempered chord. Equal temperaments containing neutral tetrads include 17, 24, 31, 34, 41, 55, 58, 65, 72, 89, 130, 171, 185 and 202, and it is a highly characteristic in particular of [[24edo]], which does an excellent version of it.
 A neutral triad is also a feature of temperaments tempering out 2401/2400, where the neutral third is now 49/40~60/49. It can therefore be described as the breed (2401/2400) tempering of 1-60/49-3/2-90/49.
@@ Line 6: / Line 6: @@
 [[Category:11-limit]]
-[[Category:Dyadic]]
+[[Category:Dyadic chords]]
+[[Category:Tetrad]]
 [[Category:Neutral]]
-[[Category:Rastma]]
+[[Category:Rastmic]]
-[[Category:Tetrad]]