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{{Infobox interval region
{{Wikipedia}}
|Name=Kleisma
|Cents lower=6
|Cents upper=9
|JI intervals=15625/15552, 225/224, 1029/1024, 16875/16807, 65536/65219
|Lower region=[[Unnoticeable comma]]
|Superregions=[[Small&nbsp;comma]] <br> [[Comma (interval region)|Comma]] <br> [[Comma and diesis]]
|Higher region=[[Small&nbsp;comma]]}}{{Wikipedia}}
A '''kleisma''' is an interval of about 8.1 cents, roughly the size of the interval [[15625/15552]], which is called a kleisma in just intonation.


As an interval region, the kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma. Another significance is that a lot of commas are about 3-4 kleismas in size.
The '''kleisma''' is an interval that has several related definitions. Most commonly, it refers to the [[just interval]] [[15625/15552]], but it can refer to other small comma-sized intervals or intervals with a certain function in a scale.  


Kleismas belong to the larger interval region of [[Comma (interval region)|commas]], which are part of the [[Comma and diesis|"comma and diesis"]] category.
== As an interval region ==
As an interval region, the kleisma is an interval of about 1/3 of a [[comma #As an interval region|comma]], roughly the size of the interval 15625/15552. In [[Sagittal notation]], a kleisma is specifically defined as between half of the 200-comma {{monzo| 317 -200 }} and half of the [[Pythagorean comma]] {{monzo| -19 12 }}, about 4.5{{c}} to 11.7{{c}}<ref>[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]</ref>.  


== Other definitions ==
The kleisma is significant as it is a limit of intonational fidelity when playing on some physical instruments. That is, on free-pitch instruments, there is a level of precision to which one can be expected to play a note or interval "correctly": that level of precision is the kleisma.{{cn}}


* In [[sagittal notation]], it is defined specifically as between half of the 200-comma ({{monzo| 317 -200 }}) and half of the [[Pythagorean comma]] ({{monzo| -19 12 }});
Other just intervals that may be considered kleismas include [[225/224]], [[243/242]], [[1029/1024]], [[16875/16807]], and [[65536/65219]].  
* In scale theory, the difference between a [[chroma]] and a [[Diesis (scale theory)|diesis]] is called a kleisma, or more precisely a '''moskleisma''', as used in [[extended meantone notation]].


== As a diatonic interval category ==
In the [[5L 2s|diatonic]] scale, the kleisma is the distance between the [[chroma]] and the [[diesis #As a diatonic interval category|diesis]]. This usage is most relevant in [[meantone]] tunings, where it is small and functions similarly to the diesis. It spans nineteen perfect fifths and vanishes in [[19edo]]. It is used in [[extended meantone notation]].


The [[19-comma]] is sometimes called ''Pythagorean kleisma'' for this reason.


The kleisma can be generalized to any [[mos scale]] as the '''moskleisma''', defined as |2L - 3s|, i.e. the distance between two large steps and three small steps.


{{Disambiguation}}{{Navbox intervals}}
== References ==
 
[[Category:Terms]]
[[Category:MOS scale]]
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