Kleisma: Difference between revisions
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== As an interval region == | == 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}} | 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 [[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. | 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:Terms]] | ||
[[Category:MOS scale]] | [[Category:MOS scale]] | ||
Latest revision as of 14:57, 14 July 2026
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, roughly the size of the interval 15625/15552. In Sagittal notation, a kleisma is specifically defined as between half of the 200-comma [317 -200⟩ and half of the Pythagorean comma [-19 12⟩, about 4.5 ¢ to 11.7 ¢[1].
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.[citation needed]
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 diatonic scale, the kleisma is the distance between the chroma and the 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.