729/704: Difference between revisions

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{{Infobox Interval

~~| Icon =~~

| Name = Alpharabian infra-augmented prime, Alpharabian infra-apotomic quartertone, undecimal major diesis

~~| Ratio = 729/704~~

| Color name = L1u1, lalu 1sn, Lalu comma

~~| Monzo = -6 6 0 0 -1~~

| Comma = yes

~~| Cents = 60.41206~~

| Name = Alpharabian ~~infraaugmented~~ prime, ~~<br>~~Alpharabian ~~infraapotomic~~ quartertone, ~~<br>~~ undecimal major diesis

| Color name =

| ~~FJS name =~~

~~| Sound~~ =

}}

'''729/704''', the '''Alpharabian ~~infraaugmented~~ prime''' or '''Alpharabian ~~infraapotomic~~ quartertone''' is a type of quartertone that differs from [[33/32]] by [[243/242]], and is itself the interval left over after subtracting 33/32 from [[2187/2048]]. While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out. This interval differs from the simpler [[28/27]] by the [[symbiotic comma]]. ~~This~~ interval is ~~referred to~~ in the [~~http:~~//~~www.huygens~~-~~fokker~~.~~org~~/~~docs/intervals.html Huygens-Fokker Foundation~~'~~s interval list] as the~~ '''~~undecimal major diesis~~'''.

'''729/704''', conventionally named the '''undecimal major diesis'''<ref>[http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]</ref>, is a [[medium comma]] measuring about 60.4{{cent}}. In [[Alpharabian tuning]], it is called the '''Alpharabian infra-augmented prime''' or '''Alpharabian infra-apotomic quartertone'''.

It is a type of quartertone that differs from [[33/32]] by [[243/242]], and is itself the interval left over after subtracting 33/32 from [[2187/2048]]. While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out. This interval differs from the simpler [[28/27]] by the [[symbiotic comma]]. Furthermore, three instances of this interval fall short of [[10/9]] by a comma that is only a little over a cent in size.

== Sagittal notation ==

In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | (!) }} and is called the '''11 large diesis''', or '''11L''' for short, because the simplest interval it notates is 11/1 (equiv. 11/8), as for example in F-B{{nbhsp}}{{sagittal | (!) }}. The upward version is called '''1/11L''' or '''11L up''' and is represented by {{sagittal| (|) }}.

== See also ==

* [[1408/729]] – its [[octave complement]]

* [[Alpharabian tuning]]

* [[Gallery of just intervals]]

~~[[Category:11-limit]]~~

== References ==

[[Category:~~Interval ratio~~]]

[[Category:Quartertone]]

[[Category:Alpharabian]]

[[Category:Commas named after their interval size]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = Alpharabian infra-augmented prime, Alpharabian infra-apotomic quartertone, undecimal major diesis
-| Ratio = 729/704
+| Color name = L1u1, lalu 1sn, Lalu comma
-| Monzo = -6 6 0 0 -1
+| Comma = yes
-| Cents = 60.41206
-| Name = Alpharabian infraaugmented prime, <br>Alpharabian infraapotomic quartertone, <br> undecimal major diesis
-| Color name =
-| FJS name =
-| Sound =
 }}
-'''729/704''', the '''Alpharabian infraaugmented prime''' or '''Alpharabian infraapotomic quartertone''' is a type of quartertone that differs from [[33/32]] by [[243/242]], and is itself the interval left over after subtracting 33/32 from [[2187/2048]].  While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out.  This interval differs from the simpler [[28/27]] by the [[symbiotic comma]].  This interval is referred to in the [http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list] as the '''undecimal major diesis'''.
+'''729/704''', conventionally named the '''undecimal major diesis'''<ref>[http://www.huygens-fokker.org/docs/intervals.html Huygens-Fokker Foundation's interval list]</ref>, is a [[medium comma]] measuring about 60.4{{cent}}. In [[Alpharabian tuning]], it is called the '''Alpharabian infra-augmented prime''' or '''Alpharabian infra-apotomic quartertone'''.
+It is a type of quartertone that differs from [[33/32]] by [[243/242]], and is itself the interval left over after subtracting 33/32 from [[2187/2048]].  While many may be accustomed to thinking of 33/32 and 729/704 as "semiaugmented primes", this analysis is only completely accurate when 243/242 is tempered out.  This interval differs from the simpler [[28/27]] by the [[symbiotic comma]].  Furthermore, three instances of this interval fall short of [[10/9]] by a comma that is only a little over a cent in size.
+== Sagittal notation ==
+In the [[Sagittal]] system, the downward version of this comma (possibly tempered) is represented by the sagittal {{sagittal | (!) }} and is called the '''11 large diesis''', or '''11L''' for short, because the simplest interval it notates is 11/1 (equiv. 11/8), as for example in F-B{{nbhsp}}{{sagittal | (!) }}. The upward version is called '''1/11L''' or '''11L up''' and is represented by {{sagittal| (|) }}.
 == See also ==
 * [[1408/729]] – its [[octave complement]]
-* [[Alpharabian tuning]]
 * [[Gallery of just intervals]]
-[[Category:11-limit]]
+== References ==
-[[Category:Interval ratio]]
+<references/>
+[[Category:Quartertone]]
 [[Category:Alpharabian]]
+[[Category:Commas named after their interval size]]