11/8: Difference between revisions

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| Monzo = -3 0 0 0 1

| Cents = 551.31794

| Name = undecimal superfourth, major fourth

| Name = undecimal superfourth, major fourth, Alpharabian paramajor fourth, just paramajor fourth

| Color name = 1o4, ilo 4th

| FJS name = P411

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}}

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 (prime 5) and 12 (prime 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|¢]]. This interval has [https://en.wikipedia.org/wiki/Major_fourth_and_minor_fifth also been referred to] as the '''major fourth'''. Furthermore, as stacks of this interval form a core axis of Alpharabian tuning (see [[User:Aura/Aura's Ideas on Tonality #11-limit Axis Functionality]]), it can also be somewhat similarly dubbed the "'''Alpharabian paramajor fourth'''" or even the "'''just paramajor fourth'''".

This interval is the simplest superfourth in JI, and, falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic. 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 (prime 5) and 12 (prime 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.

== Approximations by EDOs ==

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[[Category:Superfourth]]

[[Category:Fourth]]

[[Category:Alpharabian]]

[[Category:Listen]]

[[Category:Untwelve]]

[[Category:Overtone]]

[[Category:Over-2]]

@@ Line 10: / Line 10: @@
 | Monzo = -3 0 0 0 1
 | Cents = 551.31794
-| Name = undecimal superfourth, <br>major fourth
+| Name = undecimal superfourth, <br>major fourth, <br>Alpharabian paramajor fourth, <br>just paramajor fourth
 | Color name = 1o4, ilo 4th
 | FJS name = P4<sup>11</sup>
@@ Line 16: / Line 16: @@
 }}
-In [[11-limit]] [[just intonation]], '''11/8''' is an '''undecimal [[superfourth]]''' of about 551.3[[cent|&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 (prime 5) and 12 (prime 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|&cent;]].  This interval has [https://en.wikipedia.org/wiki/Major_fourth_and_minor_fifth also been referred to] as the '''major fourth'''.  Furthermore, as stacks of this interval form a core axis of Alpharabian tuning (see [[User:Aura/Aura's Ideas on Tonality #11-limit Axis Functionality]]), it can also be somewhat similarly dubbed the "'''Alpharabian paramajor fourth'''" or even the "'''just paramajor fourth'''".
+This interval is the simplest superfourth in JI, and, falling about halfway between [[12edo]]'s [[perfect fourth]] and [[tritone]], it is very xenharmonic.  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 (prime 5) and 12 (prime 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.
 == Approximations by EDOs ==
@@ Line 79: / Line 82: @@
 [[Category:Superfourth]]
 [[Category:Fourth]]
+[[Category:Alpharabian]]
 [[Category:Listen]]
 [[Category:Untwelve]]
 [[Category:Overtone]]
 [[Category:Over-2]]