27/26: Difference between revisions

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'''27/26'''
{{Infobox Interval
|-1 3 0 0 0 -1>
| Icon =
| Ratio = 27/26
| Monzo = -1 3 0 0 0 -1
| Cents = 65.33734
| Name = small tridecimal third tone
| Color name = 3u2, thu 2nd
| Sound = jid_27_26_pluck_adu_dr220.mp3
}}


65.3373 cents
In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth of [[27/16]] and the thirteenth harmonic -- [[13/8]]. It measures about 65.3¢. It is close in size to another 13-limit microtone -- [[26/25]]. These intervals differ by the [[superparticular|superparticular]] ratio 676/675, about 2.6¢. This is the island comma; tempering it out produces temperaments associated with [[The Archipelago]].


[[File:jid_27_26_pluck_adu_dr220.mp3]] [[:File:jid_27_26_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[52/27]] - its [[octave complement]]
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]


In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 27/26 appears as the interval between the Pythagorean major sixth of [[27/16|27/16]] and the thirteenth harmonic -- [[13/8|13/8]]. It measures about 65.3¢. It is close in size to another 13-limit microtone -- [[26/25|26/25]]. These intervals differ by the [[superparticular|superparticular]] ratio 676/675, about 2.6¢. This is the island comma; tempering it out produces temperaments associated with [[The_Archipelago|The Archipelago]].
[[Category:13-limit]]
 
[[Category:Interval]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_Superparticular_Intervals|List of Superparticular Intervals]]
[[Category:Ratio]]
[[Category:Superparticular]]
[[Category:Listen]]

Revision as of 17:30, 1 November 2018

Interval information
Ratio 27/26
Factorization 2-1 × 33 × 13-1
Monzo [-1 3 0 0 0 -1⟩
Size in cents 65.33734¢
Name small tridecimal third tone
Color name 3u2, thu 2nd
FJS name [math]\displaystyle{ \text{A1}_{13} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 9.45533
Weil height (log2 max(n, d)) 9.50978
Wilson height (sopfr(nd)) 24

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 27/26, the small tridecimal third tone, appears as the interval between the Pythagorean major sixth of 27/16 and the thirteenth harmonic -- 13/8. It measures about 65.3¢. It is close in size to another 13-limit microtone -- 26/25. These intervals differ by the superparticular ratio 676/675, about 2.6¢. This is the island comma; tempering it out produces temperaments associated with The Archipelago.

See also

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