21/16: Difference between revisions

Line 1:

~~'''~~21/16~~'''~~

{{Infobox Interval

|-4 1 0 1~~>~~

| JI glyph =

| Ratio = 21/16

470.7809 ~~cents~~

| Monzo = -4 1 0 1

| Cents = 470.7809

~~[[File:jid_21_16_pluck_adu_dr220.mp3]] [[:File:~~jid_21_16_pluck_adu_dr220.mp3|~~sound sample]]~~

| Name = septimal sub-fourth

| Sound = jid_21_16_pluck_adu_dr220.mp3

21/16~~, the septimal sub-fourth,~~ is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4/3|4/3]] by [[64/63|64/63]], 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 [[3/2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7/4|7/4]]) 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.

| Color name = z4, zo 4th

}}

21/16 is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4/3|4/3]] by [[64/63|64/63]], 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 [[3/2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7/4|7/4]]) 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.

21/16 is [[21/20|21/20]] away from [[5/4|5/4]]. 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 [[8/7|8/7]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit|11-limit]] system, [[11/8|11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22/21|22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.

@@ Line 1: / Line 1: @@
-'''21/16'''
+{{Infobox Interval
-|-4 1 0 1&gt;
+| JI glyph =
+| Ratio = 21/16
-.7809 cents
+| Monzo = -4 1 0 1
+| Cents = 470.7809
-[[File:jid_21_16_pluck_adu_dr220.mp3]] [[:File:jid_21_16_pluck_adu_dr220.mp3|sound sample]]
+| Name = septimal sub-fourth
+| Sound = jid_21_16_pluck_adu_dr220.mp3
-/16, the septimal sub-fourth, is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4/3|4/3]] by [[64/63|64/63]], 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 [[3/2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7/4|7/4]]) 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.
+| Color name = z4, zo 4th
+}}
+/16 is an interval of the [[7-limit|7 prime-limit]] measuring approximately 470.8¢. It is a narrow fourth, differing from the Pythagorean perfect fourth of [[4/3|4/3]] by [[64/63|64/63]], 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 [[3/2|3/2]] between 8 and 12 as well as between 14 and 21. There are also two harmonic sevenths ([[7/4|7/4]]) 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.
 /16 is [[21/20|21/20]] away from [[5/4|5/4]]. 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 [[8/7|8/7]], the septimal supermajor 2nd of about 231.2¢, a consonance in its own right. In an [[11-limit|11-limit]] system, [[11/8|11/8]] is also nearby, so that 21/16 can step up by the small semitone of [[22/21|22/21]] (about 80.5¢) to 11/8. These are all movements that assume an unchanging fundamental, of course, and other movements are possible.