Kleisma: Difference between revisions

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== 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}}.

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}}

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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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 == 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}}.
+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}}
@@ Line 15: / Line 15: @@
 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]]