27/20: Difference between revisions

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'''27/20'''
{{Infobox Interval
|-2 3 -1>
| Icon =
| Ratio = 27/20
| Monzo = -2 3 -1
| Cents = 519.55129
| Name = wolf fourth
| Color name =
| FJS name = P4<sub>5</sub>
| Sound = jid_27_20_pluck_adu_dr220.mp3
}}


519.5513 cents
In [[5-limit]] [[just intonation]], '''27/20''' is an interval measuring about 519.6¢. It differs from the [[4/3]] perfect fourth by [[81/80]] (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3/2]] perfect fifths, or as the interval between [[10/9]] and [[3/2]]. In [[12edo]] and [[meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls," as compared to simpler intervals within the 5-limit such as [[5/4]] and [[9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.


[[File:jid_27_20_pluck_adu_dr220.mp3]] [[:File:jid_27_20_pluck_adu_dr220.mp3|sound sample]]
== See also ==


In [[5-limit|5-limit]] [[Just_intonation|Just Intonation]], 27/20 is an interval measuring about 519.6¢. It differs from the [[4/3|4/3]] perfect fourth by [[81/80|81/80]] (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five [[3/2|3/2]] perfect fifths, or as the interval between [[10/9|10/9]] and [[3/2|3/2]]. In [[12edo|12edo]] and [[Meantone|meantone]] systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls," as compared to simpler intervals within the 5-limit such as [[5/4|5/4]] and [[9/8|9/8]]. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.
* [[40/27]] – its [[octave complement]]
* [[10/9]] – its [[fifth complement]]
* [[Gallery of just intervals]]


See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]
[[Category:5-limit]]
[[Category:Fourth]]
[[Category:Listen]]

Revision as of 23:16, 27 September 2020

Interval information
Ratio 27/20
Factorization 2-2 × 33 × 5-1
Monzo [-2 3 -1⟩
Size in cents 519.5513¢
Name wolf fourth
FJS name [math]\displaystyle{ \text{P4}_{5} }[/math]
Special properties reduced
Tenney norm (log2 nd) 9.07682
Weil norm (log2 max(n, d)) 9.50978
Wilson norm (sopfr(nd)) 18

[sound info]
Open this interval in xen-calc

In 5-limit just intonation, 27/20 is an interval measuring about 519.6¢. It differs from the 4/3 perfect fourth by 81/80 (about 21.5¢), the syntonic comma. It arises naturally in JI as (for instance) the difference between a 5-limit major third and a stack of five 3/2 perfect fifths, or as the interval between 10/9 and 3/2. In 12edo and meantone systems, this interval would be no different from 4/3, as the syntonic comma is tempered out. 27/20 has been described as a "wolf" interval, implying that it "howls," as compared to simpler intervals within the 5-limit such as 5/4 and 9/8. Although in a 5-limit context it is traditionally avoided, it can be an essential interval in a harmonic context of higher complexity, where it may be admired for its bright and active character and its distinctness from 4/3.

See also

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