Kleisma: Difference between revisions

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~~A '''kleisma''' is a kind of small [[comma]] or diesis.~~{{Wikipedia}}

~~The kleisma most commonly refers to:~~

* The interval [[15625/15552]];

* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];

* In scale theory, the difference between a [[chroma]] and a [[Diesis (scale theory)|diesis]], more precisely a '''moskleisma''', as used in [[extended meantone notation]].

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.

== 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>.

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}}

Other just intervals that may be considered kleismas include [[225/224]], [[243/242]], [[1029/1024]], [[16875/16807]], and [[65536/65219]].

== 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.

== References ==

[[Category:Terms]]

[[Category:MOS scale]]

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-A '''kleisma''' is a kind of small [[comma]] or diesis.{{Wikipedia}}
+{{Wikipedia}}
-The kleisma most commonly refers to:
-* The interval [[15625/15552]];
-* By extension, a melodic unit of about the size of 15625/15552 (≈ 8.1{{cent}}). See [[Kleisma (interval region)]];
-* In scale theory, the difference between a [[chroma]] and a [[Diesis (scale theory)|diesis]], more precisely a '''moskleisma''', as used in [[extended meantone notation]].
-{{Disambiguation}}
+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.
+== 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>.
+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}}
+Other just intervals that may be considered kleismas include [[225/224]], [[243/242]], [[1029/1024]], [[16875/16807]], and [[65536/65219]].
+== 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.
+== References ==
+[[Category:Terms]]
+[[Category:MOS scale]]