Kleisma

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.

← Unnoticeable comma

Kleisma

Small comma →

Name	Kleisma
Lower bound	6¢
Upper bound	9¢
Example JI intervals
Intervals	15625/15552 (8.1¢) 243/242 (7.1¢) 225/224 (7.7¢) 1029/1024 (8.4¢) 16875/16807 (7¢) 65536/65219 (8.4¢)
Related regions
Superregion(s)	Small comma Comma Comma and diesis

English Wikipedia has an article on:

Kleisma

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.

Kleismas belong to the larger interval region of commas, which are part of the "comma and diesis" category.

Other definitions

• In sagittal notation, it is defined specifically as between half of the 200-comma ([317 -200⟩) and half of the Pythagorean comma ([-19 12⟩);
• In scale theory, the difference between a chroma and a diesis is called a kleisma, or more precisely a moskleisma, as used in extended meantone notation.

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