Keemic chords
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- This revision was by author keenanpepper and made on 2011-10-25 22:28:33 UTC.
- The original revision id was 268608548.
- 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 //magical seventh// is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4. In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val ([[104edo]].) Hence [[magic]] (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often. Other temperaments that feature this chord prominently include 11-limit [[Keemun|keemun]], [[Superkleismic|superkleismic]], and [[Porcupine|porcupine]].
Original HTML content:
<html><head><title>magical seventh chord</title></head><body>A <em>magical seventh</em> is an 11-limit essentially tempered dyadic chord consisting of three sharp minor thirds and an 8/7, in other words a 6/5-6/5-6/5-8/7 chord, which closes at the octave since both 100/99 and 385/384 (and therefore 875/864) are tempered out. This means that in the 11-limit 4&7&15 planar temperament tempering these out, the chord is the tempering of 1-6/5-16/11-7/4.<br /> <br /> In an optimized tuning for the 4&7&15 temperament, the marvel comma 225/224 shrinks in size and may reverse direction, and adding it to the list of commas does little tuning damage; this results in 11-limit magic temperament, which has the same optimal patent val (<a class="wiki_link" href="/104edo">104edo</a>.) Hence <a class="wiki_link" href="/magic">magic</a> (19&22) temperament is practically the most accurate temperament that include this chord. Magic, however, does give it a Graham complexity of 12, so it doesn't appear that often.<br /> <br /> Other temperaments that feature this chord prominently include 11-limit <a class="wiki_link" href="/Keemun">keemun</a>, <a class="wiki_link" href="/Superkleismic">superkleismic</a>, and <a class="wiki_link" href="/Porcupine">porcupine</a>.</body></html>