15625/15552: Difference between revisions

(11 intermediate revisions by 7 users not shown)

Line 1:

{{interwiki

| de = 15625/15552

| en = 15625/15552

| es =

| ja =

}}

{{Infobox Interval

| Ratio = 15625/15552

| Name = kleisma

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

Line 6:

Line 13:

'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six [[6/5]]'s with [[3/1]]. It is ~~tempered out in~~ [[~~Hanson|Hanson temperament~~]] and the ~~kleismic family~~. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is ~~blown up~~ to ~~a whole semitone − six~~ 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps). Its [[~~Square_superparticular~~#Glossary|S-expression]] of S252 * S26 directly implies that it is expressible as ([[25/24]])2/([[27/25]]).

'''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.

== Etymology ==

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

== See also ==

* [[Small comma]]

* [[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

* [[Kleisma]] (disambiguation page)

== External links ==

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

[[Category:Kleismic]]

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

@@ Line 1: / Line 1: @@
+{{interwiki
+| de = 15625/15552
+| en = 15625/15552
+| es =
+| ja =
+}}
 {{Infobox Interval
+| Ratio = 15625/15552
 | Name = kleisma
 | Color name = y<sup>6</sup>-2, tribiyo negative 2nd,<br>Tribiyo comma
@@ Line 6: / Line 13: @@
 {{Wikipedia|Kleisma}}
-'''15625/15552''', which is sometimes called the '''kleisma''', is the [[5-limit]] [[comma]] that separates a stack of six [[6/5]]'s with [[3/1]]. It is tempered out in [[Hanson|Hanson temperament]] and the kleismic family. Like the [[magic comma]], instead of being tempered out in [[12edo]], it is blown up to a whole semitone − six 6/5's make an augmented eleventh (18 steps), while 3/1 is a perfect tweltfth (19 steps). 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]]).
+'''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.
+== Etymology ==
+This comma was named by {{w|Shohé Tanaka}} in 1890.
 == See also ==
-* [[Small comma]]
-* [[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
 * [[Kleisma]] (disambiguation page)
+== External links ==
+* [http://tonalsoft.com/enc/k/kleisma.aspx Tonalsoft Encyclopedia | ''Kleisma'']
 [[Category:Kleismic]]
+[[Category:Commas named by translating something into another language]]