15625/15552: Difference between revisions

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

{{Interwiki

| en = 15625/15552

| de = 15625/15552

| es =

| ja =

}}

{{Infobox Interval

| Ratio = 15625/15552

| Name = kleisma

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

| Comma = yes

}}

[[Category:~~Stub~~]]

'''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 6/5's 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 [[tempering out|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 twelfth (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 ==

Tempering out this comma in the 5-limit leads to 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 ==

* [[Kleisma]]

== External links ==

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

[[Category:Kleismic]]

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

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-The 5-limit interval 15625/15552, which is sometimes called the "kleisma", is tempered out in [[Kleismic_family|Hanson temperament]] and the kleismic family. Tempering it equates a stack of six 6/5's and a single 3/1.
+{{Interwiki
+| en = 15625/15552
+| de = 15625/15552
+| es =
+| ja =
+}}
+{{Infobox Interval
+| Ratio = 15625/15552
+| Name = kleisma
+| Color name = y<sup>6</sup>-2, tribiyo negative 2nd,<br>Tribiyo comma
+| Comma = yes
+}}
+{{Wikipedia|Kleisma}}
-[[Category:Stub]]
+'''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 6/5's 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 [[tempering out|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 twelfth (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 ==
+Tempering out this comma in the 5-limit leads to 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 ==
+* [[Kleisma]]
+== External links ==
+* [http://tonalsoft.com/enc/k/kleisma.aspx Tonalsoft Encyclopedia | ''Kleisma'']
+[[Category:Kleismic]]
+[[Category:Commas named by translating something into another language]]