Kleisma (interval region)

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Revision as of 00:35, 25 April 2026 by Dave Keenan (talk | contribs) (Added approximate cents for the Sagittal bounds.)
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← Unnoticeable comma Kleisma Small comma →
Name Kleisma
Lower bound
Upper bound
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

A kleisma is an interval of about 8.1 cents, roughly the size of the interval 15625/15552, which is called the kleisma in just intonation. In Sagittal notation, a kleisma is specifically defined as between half of the Pythagorean 200-fifths kleisma [317 -200 and half of the Pythagorean comma [-19 12, about 4.5 ¢ to 11.7 ¢.

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.

See also



ViewTalkEditInterval classification
Interval regions
Unison and octave UnisonComma and diesisOctave
Seconds Minor secondNeutral secondMajor second
Thirds Minor thirdNeutral thirdMajor third
Fourths and fifths Perfect fourthSuperfourthTritoneSubfifthPerfect fifth
Sixths Minor sixthNeutral sixthMajor sixth
Sevenths Minor seventhNeutral seventhMajor seventh
Interseptimal intervals Interseptimal 2nd-3rd • Interseptimal 3rd-4th • Interseptimal 5th-6th • Interseptimal 6th-7th
Interval qualities
Diatonic qualities DiminishedMinorPerfectMajorAugmented
Tuning ranges Neutral (interval quality)Submajor and supraminorPental major and minorNovamajor and novaminorNeogothic major and minorSupermajor and subminorUltramajor and inframinor