11/8: Difference between revisions
another table, I'm not sure if the decimal places should be reduced deltas can be very small sometimes |
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{{Infobox Interval | {{Infobox Interval | ||
| Name = undecimal superfourth, harmonic fourth, undecimal tritone, undecimal major fourth, undecimal semiaugmented fourth, harmonic semiaugmented fourth | |||
| Name = undecimal superfourth, | |||
| Color name = 1o4, ilo 4th | | Color name = 1o4, ilo 4th | ||
| Sound = jid_11_8_pluck_adu_dr220.mp3 | | Sound = jid_11_8_pluck_adu_dr220.mp3 | ||
}} | }} | ||
{{Wikipedia|Major fourth and minor fifth}} | |||
In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth]]''' of about 551.3 | In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth|semiaugmented fourth]]''' of about 551.3{{cent}}. This interval is close (~3{{cent}}) to exactly between a [[4/3|perfect fourth]] and [[729/512|augmented fourth]], the latter of which is the ''augmented'' version of the [[Pythagorean tuning|Pythagorean]] [[diatonic]] generator, therefore may be called the '''harmonic semiaugmented fourth'''. | ||
== | This interval is the simplest superfourth in JI, and as it falls about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. As an octave-reduced harmonic, it is a basis of consonance in 11-limit JI, alongside the lower odd numbers 9, 7, 5 and 3. It can be found in harmonic series chords such as 4:5:6:7:8:9:10:11:12, sitting somewhere between the stronger and more familiar consonances of 10 (prime 5) and 12 (prime 3). | ||
== Terminology == | |||
The naming pattern from [[11/9|undecimal neutral third]] and [[12/11|undecimal neutral second]] and their octave complements can be rigorously generalized and results in the somewhat unconventional '''harmonic/undecimal neutral fourth'''. This interval has also been termed the '''undecimal major fourth''' since the tempered version found in [[24edo]] was dubbed the "major fourth" by [[Ivan Wyschnegradsky]], although this may be confusing in diatonic contexts. | |||
Because it is right between the diatonic fourth and tritone, it may also be called the '''(lesser) undecimal tritone'''.<ref>Kyle Gann (1998) [https://www.kylegann.com/Octave.html ''Anatomy of an Octave'']</ref> | |||
More recently, [[Zhea Erose]] has suggested calling it something more simple: the '''harmonic fourth''' – under the idea that it is the simplest [[harmonic]] that is in the general (very) rough range of "fourths" when octave-reduced. | |||
Furthermore, as stacks of this interval form a core axis of [[Alpharabian tuning]], it has also been dubbed the '''Axirabian paramajor fourth''' or more simply the '''just paramajor fourth'''. | |||
== Potential usage == | |||
This interval is very well-represented in 24edo, making that system especially good for approximations of JI chords involving primes 3 and 11 such as 8:9:11:12. Not only that, but composers who have experience with 24edo may find it very useful not only as a fantastic addition to major chords, but also as an interesting chord root both for chord progressions within a key, and for modulations to key signatures that are not in the same chain of fifths. Furthermore, these same useful functions can carry over to higher EDOs with good 11-limit representation such as [[159edo]]. | |||
In more tonal music, 11/8 relative to the tonic ends up being used as the chord root for what amounts to a voicing variation of a 1/1-9/8-225/176-3/2 chord, which, is preceded by a variation on a 1/1-5/4-3/2-225/128 chord built on [[16/15]] relative to the tonic (basically, a type of [[Wikipedia: Neapolitan chord|Neapolitan chord]]), and, followed up by a variation on the 1/1-5/4-3/2-16/9 dominant seventh chord (or potentially even a 1/1-5/4-3/2-16/9-16/15 dominant ninth chord) built on [[3/2]] relative to the tonic for a special type of half cadence. This is a dramatic musical gesture that [[User:Aura|Aura]] has named the "simul half cadence". | |||
== Approximations by EDOs == | |||
{{Interval edo approximation|11/8}} | |||
<references group="note" /> | |||
== See also == | == See also == | ||
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* [[Gallery of just intervals]] | * [[Gallery of just intervals]] | ||
== References == | |||
[[Category: | <references /> | ||
[[Category:Fourth]] | |||
[[Category:Superfourth]] | [[Category:Superfourth]] | ||
[[Category: | [[Category:Alpharabian]] | ||