Kleisma: Difference between revisions
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{{Wikipedia}} | |||
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]] | |||