26/25: Difference between revisions

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'''26/25'''
{{Infobox Interval
|1 0 -2 0 0 1>
| Name = large tridecimal third tone
| Color name = 3ogg2, thogugu 2nd
| Sound = jid_26_25_pluck_adu_dr220.mp3
| Comma = yes
}}
In [[13-limit]] [[just intonation]], '''26/25''', the '''large tridecimal third tone''' appears as the difference between the 26th and 25th [[harmonic]]s. Thus it makes the difference between [[13/8]] and [[25/16]] (a stack of two [[5/4]]'s). If it is treated as a comma, then [[5/4]] and [[13/10]] both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.


67.9002 cents
== Approximation ==
26/25 is very well approximated in [[53edo]] as 3\53 (+0.024{{cent}}), and in [[28edt]] as 1\28edt (+0.027{{cent}}). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.


[[File:jid_26_25_pluck_adu_dr220.mp3]] [[:File:jid_26_25_pluck_adu_dr220.mp3|sound sample]]
== See also ==
* [[25/13]] - its [[octave complement]]
* [[27/26]] - the small tridecimal third tone
* [[Gallery of just intervals]]
* [[List of superparticular intervals]]


In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 26/25 appears as the difference between the 26th harmonic and the 25th. Thus it makes the difference between [[13/8|13/8]] and [[25/16|25/16]] (a stack of two [[5/4|5/4]]'s). It measures about 67.9¢.
[[Category:Third tone]]
 
[[Category:Commas named after their interval size]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]], [[List_of_Superparticular_Intervals|List of Superparticular Intervals]]

Latest revision as of 03:36, 3 August 2025

Interval information
Ratio 26/25
Factorization 2 × 5-2 × 13
Monzo [1 0 -2 0 0 1⟩
Size in cents 67.90023¢
Name large tridecimal third tone
Color name 3ogg2, thogugu 2nd
FJS name [math]\displaystyle{ \text{d2}^{13}_{5,5} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 9.3443
Weil height (log2 max(n, d)) 9.40088
Wilson height (sopfr(nd)) 25
Comma size medium

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 26/25, the large tridecimal third tone appears as the difference between the 26th and 25th harmonics. Thus it makes the difference between 13/8 and 25/16 (a stack of two 5/4's). If it is treated as a comma, then 5/4 and 13/10 both collapse to a Neogothic-flavored major third in between them representing half of 13/8. It measures about 67.9¢.

Approximation

26/25 is very well approximated in 53edo as 3\53 (+0.024 ¢), and in 28edt as 1\28edt (+0.027 ¢). Its equal multiplication - 1ed26/25 - is effectively the same thing as 28edt.

See also

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