Neutral tetrad
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author genewardsmith and made on 2011-12-13 14:50:43 UTC.
- The original revision id was 285605592.
- The revision comment was:
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.
Original Wikitext content:
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%20tempered%20dyadic%20chords|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 quintad, 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 desribed 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|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.
Original HTML content:
<html><head><title>neutral tetrad</title></head><body>A <em>neutral tetrad</em> 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 class="wiki_link" href="/rastmic%20chords">rastmic</a> <a class="wiki_link" href="/Dyadic%20chord#Essentially%20tempered%20dyadic%20chords">essentially tempered dyadic chord</a> 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 quintad, 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 <a class="wiki_link" href="/24edo">24edo</a>, which does an excellent version of it.<br /> <br /> 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 desribed as the breed (2401/2400) tempering of 1-60/49-3/2-90/49. <br /> <br /> The neutral tetrad is also available in <a class="wiki_link" href="/nonoctave">nonoctave</a> tunings which divide the <a class="wiki_link" href="/3_2">3/2</a> in half, including <a class="wiki_link" href="/4edf">4edf</a>, <a class="wiki_link" href="/6edf">6edf</a> (nonoctave miracle), 8edf or <a class="wiki_link" href="/88cET">88cET</a>, <a class="wiki_link" href="/16edf">16edf</a>, and 20edf (<a class="wiki_link" href="/Carlos%20Gamma">Carlos Gamma</a>). Nonoctave scales, naturally, cannot "close at the octave," unless there is a tempered octave available.</body></html>