22/21: Difference between revisions

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'''22/21'''
{{Infobox Interval
|1 -1 0 -1 1>
| Icon =
| Ratio = 22/21
| Monzo = 1 -1 0 -1 1
| Cents = 80.53704
| Name = small undecimal semitone
| Color name =
| Sound = jid_22_21_pluck_adu_dr220.mp3
}}


80.537 cents
'''22/21''' is a small [[superparticular]] '''semitone''' of about 80.5¢ that appears in [[11-limit]] [[Just Intonation]]. It makes the difference between the 21st and 22nd overtone. It is close in size to [[21/20]], a 7-limit [[superparticular]] interval, differing from it by [[441/440]], about 3.9¢.


[[File:jid_22_21_pluck_adu_dr220.mp3]] [[:File:jid_22_21_pluck_adu_dr220.mp3|sound sample]]
The single degree of [[88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.


22/21 is a small [[superparticular|superparticular]] semitone of about 80.5¢ that appears in [[11-limit|11-limit]] [[Just_intonation|Just Intonation]]. It makes the difference between the 21st and 22nd overtone. It is close in size to [[21/20|21/20]], a 7-limit [[superparticular|superparticular]] interval, differing from it by [[441/440|441/440]], about 3.9¢.
== See also ==
* [[Gallery of Just Intervals]]
* [[List of Superparticular Intervals]]


The single degree of [[88cET|88cET]] can function as both 21/20 and 22/21, thus tempering out 441/440.
[[Category:Semitone]]
 
[[Category:Interval]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_Superparticular_Intervals|List of Superparticular Intervals]]
[[Category:Ratio]]
[[Category:11-limit]]
[[Category:Superparticular]]

Revision as of 21:15, 23 October 2018

Interval information
Ratio 22/21
Factorization 2 × 3-1 × 7-1 × 11
Monzo [1 -1 0 -1 1⟩
Size in cents 80.53704¢
Name small undecimal semitone
FJS name [math]\displaystyle{ \text{P1}^{11}_{7} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 8.85175
Weil height (log2 max(n, d)) 8.91886
Wilson height (sopfr(nd)) 23

[sound info]
Open this interval in xen-calc

22/21 is a small superparticular semitone of about 80.5¢ that appears in 11-limit Just Intonation. It makes the difference between the 21st and 22nd overtone. It is close in size to 21/20, a 7-limit superparticular interval, differing from it by 441/440, about 3.9¢.

The single degree of 88cET can function as both 21/20 and 22/21, thus tempering out 441/440.

See also

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