11/8: Difference between revisions

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In [[11-limit]] [[Just Intonation]], 11/8 is an undecimal (11-based) [[superfourth]] of about 551.3[[cent|¢]]. Falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, 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 much stronger and more familiar consonances of 10 (5) and 12 (3). It 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.
In [[11-limit]] [[just intonation]], '''11/8''' is an undecimal [[superfourth]] of about 551.3[[cent|¢]]. Falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, 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 much stronger and more familiar consonances of 10 (5) and 12 (3). It 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.


:''See also [[Gallery of Just Intervals]]''
== See also ==
* [[Gallery of just intervals]]
* [[16/11]] - its [[inverse interval]]


[[Category:11-limit]]
[[Category:11-limit]]
[[Category:fourth]]
[[Category:Interval]]
[[Category:interval]]
[[Category:Ratio]]
[[Category:ratio]]
[[Category:Superfourth]]
[[Category:superfourth]]
[[Category:Fourth]]
[[Category:undecimal]]
[[Category:Undecimal]]
[[Category:untwelve]]
[[Category:Untwelve]]
 
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Revision as of 17:44, 29 October 2018

Interval information
Ratio 11/8
Factorization 2-3 × 11
Monzo [-3 0 0 0 1
Size in cents 551.3179¢
Name undecimal superfourth
Color name 1o4, ilo 4th
FJS name [math]\displaystyle{ \text{P4}^{11} }[/math]
Special properties reduced,
reduced harmonic
Tenney norm (log2 nd) 6.45943
Weil norm (log2 max(n, d)) 6.91886
Wilson norm (sopfr(nd)) 17

[sound info]
Open this interval in xen-calc

In 11-limit just intonation, 11/8 is an undecimal superfourth of about 551.3¢. Falling about halfway between 12edo's perfect fourth and tritone, it is very xenharmonic. It is the simplest superfourth in JI. As an octave-reduced overtone, 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 much stronger and more familiar consonances of 10 (5) and 12 (3). It 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.

See also