13/12: Difference between revisions

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'''13/12'''
{{Infobox Interval
|-2 -1 0 0 0 1>
| Icon =
| Ratio = 13/12
| Monzo = -2 -1 0 0 0 1
| Cents = 138.57266
| Name = tredecimal neutral second
| Color name = 3o2, tho 2nd
| 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¢).


138.57266 cents
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.


[[File:jid_13_12_pluck_adu_dr220.mp3]] [[:File:jid_13_12_pluck_adu_dr220.mp3|sound sample]]
:''See also [[Gallery of Just Intervals]]''


In [[13-limit|13-limit]] [[Just_intonation|Just Intonation]], 13/12 is a neutral second of about 138.6¢. It is a [[superparticular|superparticular]] interval, as it is found in the harmonic series between the 13th and the 12th overtone (between [[13/8|13/8]] and [[3/2|3/2]] in the octave). It is flat of the [[11-limit|11-limit]] lesser neutral second of [[12/11|12/11]] by [[144/143|144/143]] (about 12.1¢), and sharp of the 13-limit large semitone of [[14/13|14/13]] by [[169/168|169/168]] (about 10.3¢).
[[Category:13-limit]]
 
[[Category:Interval]]
The neutral second in [[17edo|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.
[[Category:Just interval]]
 
[[Category:Neutral 2nd]]
See: [[Gallery_of_Just_Intervals|Gallery of Just Intervals]]      [[Category:13-limit]]
[[Category:Neutral second]]
[[Category:interval]]
[[Category:Ratio]]
[[Category:just_interval]]
[[Category:Second]]
[[Category:neutral_2nd]]
[[Category:Superparticular]]
[[Category:ratio]]
[[Category:second]]

Revision as of 21:58, 23 October 2018

Interval information
Ratio 13/12
Factorization 2-2 × 3-1 × 13
Monzo [-2 -1 0 0 0 1⟩
Size in cents 138.5727¢
Name tredecimal 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 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¢).

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.

See also Gallery of Just Intervals
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