Skip to main content
Get your brand new Wikispaces Classroom now
and do "back to school" in style.
xenharmonic (microtonal wiki)
Pages and Files
XA Facebook Group
XA IRC Chat
Lists and Galleries
Backing up this wiki
|-4 1 0 1>
21/16, the septimal sub-fourth, is an interval of the
measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of
, a microtone of approximately 27.3¢. It can be treated as the 21st overtone, octave reduced. Since 21 is 3*7, 21 can be also treated as the 3rd harmonic above the 7th or the 7th harmonic above the 3rd, or both. This identity can be made clear in a chord such as 8:12:14:21, which has a just perfect fifth of
between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths (
) in this chord, between 8 and 14 and between 12 and 21. The voicing of this chord is significant, as 3/2 sounds more consonant than its inversion 4/3 and 21/8 (an octave above 21/16) sounds more consonant than 21/16.
. This is an interval of about 84.5¢, a small semitone. This introduces the possibility of treating 21/16 as a dissonance to resolve down to 5/4. It can just as easily step up to 3/2 by
, the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an
is also nearby, so that 21/16 can step up by the small semitone of
(about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.
The 7-limit is known for its subminor and supermajor 2nds, 3rds, 6ths and 7ths. 21/16 is also an essential interval of the 7-limit and worth distinguishing.
Gallery of Just Intervals
help on how to format text
Contributions to http://xenharmonic.wikispaces.com/ are licensed under a
Creative Commons Attribution Share-Alike Non-Commercial 3.0 License
Portions not contributed by visitors are Copyright 2017 Tangient LLC
TES: The largest network of teachers in the world
Turn off "Getting Started"