14/11: Difference between revisions
CompactStar (talk | contribs) It is a perfect fourth, even if it is not 4/3. there is no "imperfect fourth" in pyth spine JI systems. |
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In [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''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 [[11-limit]] [[just intonation]], '''14/11''' is an '''undecimal major third''', specifically the '''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 a perfect fourth, as it is [[4/3]] divided by [[22/21]], which is 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. | In many notation systems based on the [[3-limit]] with commatic alterations (e.g. [[FJS]], [[HEJI]]), it is classified as a perfect fourth, as it is [[4/3]] (just perfect fourth) divided by [[22/21]], which is 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. | 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. | ||
Revision as of 22:03, 8 November 2024
| Interval information |
pentacircle major third
[sound info]
In 11-limit just intonation, 14/11 is an undecimal major third, specifically the 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 based on the 3-limit with commatic alterations (e.g. FJS, HEJI), it is classified as a perfect fourth, as it is 4/3 (just perfect fourth) divided by 22/21, which is 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