15625/15552: Difference between revisions

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{{interwiki

| de = 15625/15552

| en = 15625/15552

| es =

| ja =

}}

{{Infobox Interval

| Ratio = 15625/15552

~~| Monzo = -6 -5 6~~

~~| Cents = 8.10728~~

| Name = kleisma

| Color name =

| Color name = y6-2, tribiyo negative 2nd, Tribiyo comma

~~| FJS name = dd-2~~~~15625~~

| Comma = yes

| ~~Sound~~ =

}}

'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]], or a stack of three diptolemaic chromatic semitones ([[25/24]]) with the Pythagorean whole tone ([[9/8]]). It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary|S-expression]] of S252 × S26 directly implies that it is expressible as ([[25/24]])2/([[27/25]]).

== Temperaments ==

This comma is tempered out in the [[kleismic]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out and [[Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.

~~The [[5-limit]] [[~~comma~~]] '''15625/15552''', which is sometimes called the '''kleisma''', is tempered out~~ in ~~[[Hanson|Hanson temperament]] and the kleismic family. Tempering it equates a stack of six [[6/5]]'s and a single [[3/1]]~~.

== Etymology ==

This comma was named by {{w|Shohé Tanaka}} in 1890.

~~It's unique in the fact that in 12edo, instead of being tempered out, it's blown up to a whole semitone - six 6/5s make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps).~~

== See also ==

* [[~~Small comma~~]]

* [[Kleisma]] (disambiguation page)

* [[Kleismic family]], the rank-2 temperament family where it is tempered out

* [~~[Kleismic rank three family]~~]~~, the rank-3 temperament family where it is tempered out~~

== External links ==

* [http://tonalsoft.com/enc/k/kleisma.aspx Tonalsoft Encyclopedia | ''Kleisma'']

~~[[Category:5-limit]]~~

~~[[Category:Small comma]]~~

~~[[Category:Ratio]]~~

[[Category:Kleismic]]

[[Category:Commas named by translating something into another language]]

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+{{interwiki
+| de = 15625/15552
+| en = 15625/15552
+| es =
+| ja =
+}}
 {{Infobox Interval
 | Ratio = 15625/15552
-| Monzo = -6 -5 6
-| Cents = 8.10728
 | Name = kleisma
-| Color name =
+| Color name = y<sup>6</sup>-2, tribiyo negative 2nd,<br>Tribiyo comma
-| FJS name = dd-2<sup>15625</sup>
+| Comma = yes
-| Sound =
 }}
-{{Wikipedia| Kleisma }}
+{{Wikipedia|Kleisma}}
+'''15625/15552''', which is sometimes called the '''kleisma''', is the [[small comma|small]] [[5-limit]] [[comma]] that separates a stack of six classic minor thirds of [[6/5]] with [[3/1]], or a stack of five 6/5s with [[5/2]], or a stack of three diptolemaic chromatic semitones ([[25/24]]) with the Pythagorean whole tone ([[9/8]]). It is also the difference between the classic chromatic semitone ([[25/24]]) and the greater diesis ([[648/625]]), which is also known as the diminished comma. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is inflated to an entire semitone—six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps); conversely, 25/24 is mapped to a semitone while 648/625 is tempered out. Its [[square superparticular #Glossary|S-expression]] of S25<sup>2</sup> × S26 directly implies that it is expressible as ([[25/24]])<sup>2</sup>/([[27/25]]).
+== Temperaments ==
+This comma is tempered out in the [[kleismic]] temperament. See [[Kleismic family]] for the rank-2 temperament family where it is tempered out and [[Kleismic rank-3 family]] for the rank-3 temperament family where it is tempered out.
-The [[5-limit]] [[comma]] '''15625/15552''', which is sometimes called the '''kleisma''', is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Tempering it equates a stack of six [[6/5]]'s and a single [[3/1]].
+== Etymology ==
+This comma was named by {{w|Shohé Tanaka}} in 1890.
-It's unique in the fact that in 12edo, instead of being tempered out, it's blown up to a whole semitone - six 6/5s make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps).
 == See also ==
-* [[Small comma]]
+* [[Kleisma]] (disambiguation page)
-* [[Kleismic family]], the rank-2 temperament family where it is tempered out
-* [[Kleismic rank three family]], the rank-3 temperament family where it is tempered out
+== External links ==
+* [http://tonalsoft.com/enc/k/kleisma.aspx Tonalsoft Encyclopedia | ''Kleisma'']
-[[Category:5-limit]]
-[[Category:Small comma]]
-[[Category:Ratio]]
 [[Category:Kleismic]]
+[[Category:Commas named by translating something into another language]]