26/25: Difference between revisions

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Added "comma = yes" because in the body of the text it is said to be a comma
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| Color name = 3ogg2, thogugu 2nd
| Color name = 3ogg2, thogugu 2nd
| Sound = jid_26_25_pluck_adu_dr220.mp3
| 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¢.  
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¢.  

Revision as of 11:57, 17 November 2023

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, being only 0.024 ¢ flat of 3\53.

See also