13/12: Difference between revisions

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{{Infobox Interval
{{Infobox Interval
| Icon =
| Name = (lesser) tridecimal neutral second
| Ratio = 13/12
| Monzo = -2 -1 0 0 0 1
| Cents = 138.57266
| Name = tridecimal neutral second
| Color name = 3o2, tho 2nd
| Color name = 3o2, tho 2nd
| FJS name = m2<sup>13</sup>
| Sound = jid_13_12_pluck_adu_dr220.mp3
| Sound = jid_13_12_pluck_adu_dr220.mp3
}}
}}


In [[13-limit]] [[Just Intonation]], '''13/12''' is a '''neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).
In [[13-limit]] [[just intonation]], '''13/12''' is the '''(lesser) tridecimal neutral second''' of about 138.6¢. It is a [[superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between [[13/8]] and [[3/2]] in the octave). It is flat of the [[11-limit]] lesser neutral second of [[12/11]] by [[144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13]] by [[169/168]] (about 10.3¢).


The neutral second in [[17edo]] is about 141.2¢, about 2.6¢ sharp of 13/12. Thus, if 10\17 (ten degrees of 17edo) is taken to approximate 3/2 and 12\17 taken to approximate 13/8, you can generate a 13-limit harmonic triad that approximates an 8:12:13 chord with a good 13/12.
== Temperaments ==
{{Todo|expand|inline=1}}
 
== Approximation ==
It is approximated to within about 0.11 [[cents]] by the 3-step interval of [[26edo]].


== See also ==
== See also ==
Line 20: Line 19:
* [[List of superparticular intervals]]
* [[List of superparticular intervals]]


[[Category:13-limit]]
[[Category:Second]]
[[Category:Interval]]
[[Category:Just interval]]
[[Category:Ratio]]
[[Category:Neutral second]]
[[Category:Neutral second]]
[[Category:Second]]
[[Category:Superparticular]]

Latest revision as of 22:37, 2 April 2025

Interval information
Ratio 13/12
Factorization 2-2 × 3-1 × 13
Monzo [-2 -1 0 0 0 1⟩
Size in cents 138.5727¢
Name (lesser) tridecimal neutral second
Color name 3o2, tho 2nd
FJS name [math]\displaystyle{ \text{m2}^{13} }[/math]
Special properties superparticular,
reduced
Tenney height (log2 nd) 7.2854
Weil height (log2 max(n, d)) 7.40088
Wilson height (sopfr(nd)) 20

[sound info]
Open this interval in xen-calc

In 13-limit just intonation, 13/12 is the (lesser) tridecimal neutral second of about 138.6¢. It is a superparticular interval, as it is found in the harmonic series between the 13th and the 12th harmonics (between 13/8 and 3/2 in the octave). It is flat of the 11-limit lesser neutral second of 12/11 by 144/143 (about 12.1¢), and sharp of the 13-limit large semitone of 14/13 by 169/168 (about 10.3¢).

Temperaments

Todo: expand

Approximation

It is approximated to within about 0.11 cents by the 3-step interval of 26edo.

See also

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