22/13: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
Expansion
Address a name change; expansion
 
(5 intermediate revisions by 3 users not shown)
Line 1: Line 1:
{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = tridecimal major sixth, major minthmic major sixth
| Ratio = 22/13
| Color name = 3u1o6, thulo 6th
| Monzo = 1 0 0 0 1 -1
| Cents = 910.7903
| Name = tridecimal major sixth
| Color name =
| FJS name = M6<sup>11</sup><sub>13</sub>
| Sound = jid_22_13_pluck_adu_dr220.mp3
| Sound = jid_22_13_pluck_adu_dr220.mp3
}}
}}


'''22/13''', the '''tridecimal major sixth''', is a [[13-limit]] interval measuring about 910.8 [[Cent|cents]]. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the Pythagorean minor sixth [[27/16]] by [[352/351]].  
'''22/13''', the '''tridecimal major sixth''' or '''major minthmic major sixth''', is a [[13-limit]] [[just intonation]] interval measuring about 910.8 [[cent]]s. It is the inverse of [[13/11]], the tridecimal minor third. It is sharp of the [[27/16|Pythagorean major sixth (27/16)]] by a [[352/351|major minthma (352/351)]].
 
== Approximation ==
This interval is well approximated by [[17edo|13\17]] (917.647 cents), and even better, by [[29edo|22\29]] (910.345 cents).  


== See also ==
== See also ==
* [[13/11]] – its [[octave complement]]
* [[13/11]] – its [[octave complement]]
* [[Gallery of just intervals]]
* [[Gallery of just intervals]]
* [[17edo|13\17]] (917.647 cents)


[[Category:13-limit]]
[[Category:Interval]]
[[Category:Ratio]]
[[Category:Sixth]]
[[Category:Sixth]]
[[Category:Major sixth]]
[[Category:Major sixth]]
[[Category:Minthmic]]
[[Category:Major minthmic]]
 
[[Category:todo:expand]]

Latest revision as of 14:52, 15 January 2024

Interval information
Ratio 22/13
Factorization 2 × 11 × 13-1
Monzo [1 0 0 0 1 -1
Size in cents 910.7903¢
Names tridecimal major sixth,
major minthmic major sixth
Color name 3u1o6, thulo 6th
FJS name [math]\displaystyle{ \text{M6}^{11}_{13} }[/math]
Special properties reduced
Tenney height (log2 nd) 8.15987
Weil height (log2 max(n, d)) 8.91886
Wilson height (sopfr(nd)) 26

[sound info]
Open this interval in xen-calc

22/13, the tridecimal major sixth or major minthmic major sixth, is a 13-limit just intonation interval measuring about 910.8 cents. It is the inverse of 13/11, the tridecimal minor third. It is sharp of the Pythagorean major sixth (27/16) by a major minthma (352/351).

Approximation

This interval is well approximated by 13\17 (917.647 cents), and even better, by 22\29 (910.345 cents).

See also