13/12: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = tridecimal neutral second | | Name = (lesser) tridecimal neutral second | ||
| Color name = 3o2, tho 2nd | | Color name = 3o2, tho 2nd | ||
| Sound = jid_13_12_pluck_adu_dr220.mp3 | | Sound = jid_13_12_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[13-limit]] [[just intonation]], '''13/12''' is the '''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¢). | 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. | 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. | ||
Revision as of 16:15, 14 December 2023
| Interval information |
reduced
[sound info]
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.