Neutral tetrad

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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 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.