16/9: Difference between revisions

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'''16/9'''
{{Infobox Interval
|4 -2>
| Name = Pythagorean minor seventh
| Color name = w7, wa 7th
| Sound = jid_16_9_pluck_adu_dr220.mp3
}}
{{Wikipedia|Minor seventh}}


996.09000 cents
In [[3-limit]] [[just intonation]], '''16/9''' is the '''Pythagorean minor seventh''', at about 996.1 cents. It is equal to two [[4/3|perfect fourth]]s, or (4/3)×(4/3), and is thus the [[octave reduced]] form of the ninth [[subharmonic]]. It differs from the nearby [[5-limit]] minor seventh [[9/5]] (~1017.6 cents) by the syntonic comma of [[81/80]] (~21.5 cents), and the [[7-limit]] minor seventh [[7/4]] (~968.8 cents) by the septimal comma of [[64/63]] (~27.3 cents).


[[File:jid_16_9_pluck_adu_dr220.mp3]] [[:File:jid_16_9_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[9/8]] – its [[octave complement]]
* [[Ed16/9]]
* [[Gallery of just intervals]]


In [[3-limit|3-limit]] [[Just_intonation|Just Intonation]], 16/9 is the [[Pythagorean|Pythagorean]] minor seventh, at about 996.1 cents.  It is equal to two perfect fourths, or (4/3)*(4/3).  It differs from the nearby [[5-limit|5-limit]] minor seventh [[9/5|9/5]] (~1017.6 cents) by the syntonic comma of [[81/80|81/80]] (~21.5 cents).
[[Category:Seventh]]
 
[[Category:Minor seventh]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]

Latest revision as of 18:50, 30 June 2025

Interval information
Ratio 16/9
Factorization 24 × 3-2
Monzo [4 -2
Size in cents 996.09¢
Name Pythagorean minor seventh
Color name w7, wa 7th
FJS name [math]\displaystyle{ \text{m7} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 7.16993
Weil height (log2 max(n, d)) 8
Wilson height (sopfr(nd)) 14

[sound info]
Open this interval in xen-calc
English Wikipedia has an article on:

In 3-limit just intonation, 16/9 is the Pythagorean minor seventh, at about 996.1 cents. It is equal to two perfect fourths, or (4/3)×(4/3), and is thus the octave reduced form of the ninth subharmonic. It differs from the nearby 5-limit minor seventh 9/5 (~1017.6 cents) by the syntonic comma of 81/80 (~21.5 cents), and the 7-limit minor seventh 7/4 (~968.8 cents) by the septimal comma of 64/63 (~27.3 cents).

See also