Neutral tetrad: Difference between revisions
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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 [[ | 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 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 | 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. | ||
The neutral tetrad is also available in [[ | The neutral tetrad is also available in [[nonoctave]] tunings which divide the [[3/2]] in half, including [[4edf]], [[6edf]] (nonoctave miracle), 8edf or [[88cET]], [[16edf]], and 20edf ([[Carlos Gamma]]). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available. | ||
[[Category:11-limit]] | [[Category:11-limit]] | ||
[[Category: | [[Category:Chords]] | ||
[[Category: | [[Category:Dyadic]] | ||
[[Category: | [[Category:Neutral]] | ||
[[Category: | [[Category:Rastma]] | ||
[[Category: | [[Category:Tetrad]] | ||
Revision as of 23:56, 30 June 2019
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 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.
The neutral tetrad is also available in nonoctave tunings which divide the 3/2 in half, including 4edf, 6edf (nonoctave miracle), 8edf or 88cET, 16edf, and 20edf (Carlos Gamma). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.