27/26: Difference between revisions

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Fredg999 (talk | contribs)
autopatrolled, Interface administrators, Sysops
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m Improved phrasing
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| Sound = jid_27_26_pluck_adu_dr220.mp3
| Sound = jid_27_26_pluck_adu_dr220.mp3
}}
}}
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 of [[13/8]]. It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].
In [[13-limit]] [[just intonation]], '''27/26''', the '''small tridecimal third tone''', appears as the interval between the Pythagorean major sixth ([[27/16]]) and the [[Octave reduction|octave-reduced]] thirteenth [[harmonic]] ([[13/8]]). It measures about 65.3{{cent}}. It is close in size to another 13-limit microtone – [[26/25]]. These intervals differ by the [[superparticular]] ratio [[676/675]], about 2.6{{cent}}, the island comma; tempering it out produces temperaments associated with [[The Archipelago]].


27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].
27/26 is significant in [[Helmholtz-Ellis notation]] as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to [[64/63]] and [[33/32]] for septimal and undecimal, respectively. However, in the [[Functional Just System]], that role is taken by [[1053/1024]].

Revision as of 13:57, 22 March 2022

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 3u1, thu unison
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 (27/16) and the octave-reduced 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 ¢, the island comma; tempering it out produces temperaments associated with The Archipelago.

27/26 is significant in Helmholtz-Ellis notation as the tridecimal formal comma which translates a Pythagorean interval to a nearby tridecimal interval, analogous to 64/63 and 33/32 for septimal and undecimal, respectively. However, in the Functional Just System, that role is taken by 1053/1024.

See also

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