14/11: Difference between revisions
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{{Infobox Interval | {{Infobox Interval | ||
| Name = undecimal major third | | Name = undecimal major third, pentacircle major third | ||
| Color name = 1uz4, luzo 4th | | Color name = 1uz4, luzo 4th | ||
| Sound = jid_14_11_pluck_adu_dr220.mp3 | | Sound = jid_14_11_pluck_adu_dr220.mp3 | ||
}} | }} | ||
In [[11-limit]] [[just intonation]], '''14/11''' is the '''undecimal major third''', a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th | In [[11-limit]] [[just intonation]], '''14/11''' is the '''undecimal major third''' or '''pentacircle major third''', a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the [[harmonic series]]. | ||
In many notation systems (e.g. [[FJS]], [[HEJI]]), it is an imperfect fourth, as it is the [[4/3|perfect fourth (4/3)]] minus a stack consisting of an [[33/32|undecimal quartertone (33/32)]] and a [[64/63|septimal comma (64/63)]], neither of which changes the [[scale|scale degree]] or [[interval quality|quality]]. However, it is only sharp of the Pythagorean ([[3-limit]]) major third of [[81/64]] (about 407.8¢) by a [[896/891|pentacircle comma (896/891)]], which makes it function more often as a major third, hence the names. | |||
14/11 can function as a [[neogothic|neo-Gothic]] major third, as it falls between [[5/4]] and [[9/7]]. Indeed, it is the [[mediant]] ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is [[56/55]] sharp of [[5/4]], [[99/98]] flat of [[9/7]]. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = [[19/15]], about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = [[23/18]], about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why [[7/4]], the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh. | |||
It also appears in chords such as 8:11:14, the principal triad of [[orgone]] temperament. | |||
== See also == | == See also == | ||
Revision as of 08:53, 25 October 2024
| Interval information |
pentacircle major third
[sound info]
In 11-limit just intonation, 14/11 is the undecimal major third or pentacircle major third, a supermajor third of about 417.5¢. It represents the difference between the 11th and 14th harmonics of the harmonic series.
In many notation systems (e.g. FJS, HEJI), it is an imperfect fourth, as it is the perfect fourth (4/3) minus a stack consisting of an undecimal quartertone (33/32) and a septimal comma (64/63), neither of which changes the scale degree or quality. However, it is only sharp of the Pythagorean (3-limit) major third of 81/64 (about 407.8¢) by a pentacircle comma (896/891), which makes it function more often as a major third, hence the names.
14/11 can function as a neo-Gothic major third, as it falls between 5/4 and 9/7. Indeed, it is the mediant ratio between those simpler intervals, as it is (5 + 9)/(4 + 7), and is 56/55 sharp of 5/4, 99/98 flat of 9/7. Other relatively simple thirds in this region can be generated by taking the mediant between 5/4 and 14/11 (which is (5 + 14)/(4 + 11) = 19/15, about 409.2¢) and between 14/11 and 9/7 (which is (14 + 9)/(11 + 7) = 23/18, about 424.4¢. The fact that this interval functions as a type of third is one of the reasons why 7/4, the octave reduced version of the 14th harmonic, can be argued to be a type of "sinth" – a cross between a sixth and a seventh- as opposed to merely a subminor seventh.
It also appears in chords such as 8:11:14, the principal triad of orgone temperament.
See also
- 11/7 – its octave complement
- 33/28 – its fifth complement
- Gallery of just intervals
- Gentle chords
- List of root-3rd-P5 triads in JI
External links
- The Noble Mediant by Margo Schulter and David Keenan