513/512: Difference between revisions

(19 intermediate revisions by 11 users not shown)

Line 1:

{{Infobox Interval

~~| Icon =~~

| Name = undevicesimal schisma, undevicesimal formal comma, Boethius' comma

~~| Ratio = 513/512~~

| Color name = L19o1, lano 1sn, <br>Lano comma

~~| Monzo = -9 3 0 0 0 0 0 1~~

| Comma = yes

~~| Cents = 3.37802~~

| Name = undevicesimal ~~comma~~, ~~<br>~~undevicesimal ~~schisma~~, ~~<br>~~Boethius' comma

| Color name =

~~| FJS name = P1~~<~~sup>19</sup~~>

| ~~Sound~~ =

}}

'''513/512''', the '''undevicesimal schisma''', '''undevicesimal formal comma''' or '''Boethius' comma''', is an [[Unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]] and by which [[24/19]] falls short of the [[81/64|Pythagorean major third (81/64)]].

~~'''513/512''',~~ the '''~~undevicesimal comma~~''', ~~'''undevicesimal schisma'''~~ or ~~'''Boethius' comma''', is a [[19-limit]] (also~~ 2.3.19 subgroup~~) unnoticeable comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]]. By tempering it out is defined~~ the '''~~boethius~~ temperament'''~~, which enables~~ the ~~'''~~boethius chords~~'''~~. It is significant in [[Functional Just System]] and [[~~Helmholtz-Ellis~~ notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

== Temperaments ==

{{Redirect|Boethius|the medieval Roman platonist|Anicius Manlius Severinus Boethius}}

By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enable the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].

== Notation ==

This comma is significant in [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.

=== Sagittal notation ===

In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | )| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal | )| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal| )! }}.

== See also ==

* [[Unnoticeable comma]]

* [[List of superparticular intervals]]

~~[[Category:19-limit]]~~

~~[[Category:Superparticular]]~~

~~[[Category:Unnoticeable comma]]~~

[[Category:Boethius]]

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

[[Category:Commas named after polymaths]]

@@ Line 1: / Line 1: @@
 {{Infobox Interval
-| Icon =
+| Name = undevicesimal schisma, undevicesimal formal comma, Boethius' comma
-| Ratio = 513/512
+| Color name = L19o1, lano 1sn, <br>Lano comma
-| Monzo = -9 3 0 0 0 0 0 1
+| Comma = yes
-| Cents = 3.37802
-| Name = undevicesimal comma, <br>undevicesimal schisma, <br>Boethius' comma
-| Color name =
-| FJS name = P1<sup>19</sup>
-| Sound =
 }}
+'''513/512''', the '''undevicesimal schisma''', '''undevicesimal formal comma''' or '''Boethius' comma''', is an [[Unnoticeable comma|unnoticeable]] [[19-limit]] (also 2.3.19 [[subgroup]]) comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]] and by which [[24/19]] falls short of the [[81/64|Pythagorean major third (81/64)]].
-'''513/512''', the '''undevicesimal comma''', '''undevicesimal schisma''' or '''Boethius' comma''', is a [[19-limit]] (also 2.3.19 subgroup) unnoticeable comma. It is the amount by which [[19/16]] exceeds the [[32/27|Pythagorean minor third (32/27)]]. By tempering it out is defined the '''boethius temperament''', which enables the '''boethius chords'''. It is significant in [[Functional Just System]] and [[Helmholtz-Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.
+== Temperaments ==
+{{Redirect|Boethius|the medieval Roman platonist|Anicius Manlius Severinus Boethius}}
+By tempering out this comma in the 19-limit is defined the '''boethius temperament''', or in the 2.3.19 subgroup, the '''boethian temperament'''. Both enable the [[boethius chords]]. See [[No-fives subgroup temperaments #Boethian]].
+== Notation ==
+This comma is significant in [[Functional Just System]] and [[Helmholtz–Ellis notation]] as the formal comma to translate a Pythagorean interval to a nearby undevicesimal interval.
+=== Sagittal notation ===
+In the [[Sagittal]] system, this comma (possibly tempered) is represented by the sagittal {{sagittal | )| }} and is called the '''19 schisma''', or '''19s''' for short, because the simplest interval it notates is 19/1 (equiv 19/16), as for example in D-F{{nbhsp}}{{sagittal | )| }}. The downward version is called '''1/19s''' or '''19s down''' and is represented by {{sagittal| )! }}.
 == See also ==
-* [[Unnoticeable comma]]
 * [[List of superparticular intervals]]
-[[Category:19-limit]]
-[[Category:Superparticular]]
-[[Category:Unnoticeable comma]]
 [[Category:Boethius]]
+[[Category:Commas named after their interval size]]
+[[Category:Commas named after polymaths]]