Editing Interval (music) (section)

== Minute intervals ==
[[File:Pythagorean comma on C.png|thumb|right|Pythagorean comma on C; the note depicted as lower on the staff (B[[semitone#Just intonation|{{music|#}}]][[syntonic comma|+++]]) is slightly higher in pitch (than C{{music|natural}}).[[File:Pythagorean comma on C.mid]]]]
{{Main | Comma (music) | Microtone}}
There are also a number of minute intervals not found in the chromatic scale or labeled with a diatonic function, which have names of their own. They may be described as [[microtone]]s, and some of them can be also classified as [[Comma (music)|comma]]s, as they describe small discrepancies, observed in some tuning systems, between [[enharmonic|enharmonically equivalent]] notes. In the following list, the interval sizes in [[cent (music)|cents]] are approximate.
* A ''[[Pythagorean comma]]'' is the difference between twelve justly tuned perfect fifths and seven octaves. It is expressed by the [[frequency]] ratio 531441:524288 (23.5 cents).
* A ''[[syntonic comma]]'' is the difference between four justly tuned perfect fifths and two octaves plus a major third. It is expressed by the ratio 81:80 (21.5 cents).
* A ''[[septimal comma]]'' is 64:63 (27.3 cents), and is the difference between the Pythagorean or 3-limit "7th" and the "harmonic 7th".
* A ''[[diesis]]'' is generally used to mean the difference between three justly tuned major thirds and one octave. It is expressed by the ratio 128:125 (41.1 cents). However, it has been used to mean other small intervals: see [[diesis]] for details.
* A ''[[diaschisma]]'' is the difference between three octaves and four justly tuned perfect fifths plus two justly tuned major thirds. It is expressed by the ratio 2048:2025 (19.6 cents).
* A ''[[schisma]]'' (also skhisma) is the difference between five octaves and eight justly tuned fifths plus one justly tuned major third. It is expressed by the ratio 32805:32768 (2.0 cents). It is also the difference between the Pythagorean and syntonic commas. (A schismic major third is a schisma different from a just major third, eight fifths down and five octaves up, F{{music|flat}} in C.)
* A ''[[kleisma]]'' is the difference between six [[minor third]]s and one ''tritave'' or ''perfect twelfth'' (an [[octave]] plus a [[perfect fifth]]), with a frequency ratio of 15625:15552 (8.1 cents) ({{Audio|Kleisma on C.mid|Play}}).
* A ''[[septimal kleisma]]'' is the amount that two major thirds of 5:4 and a septimal major third, or supermajor third, of 9:7 exceeds the octave. Ratio 225:224 (7.7 cents).
* A ''[[quarter tone]]'' is half the width of a [[semitone]], which is half the width of a [[major second|whole tone]]. It is equal to exactly 50 cents.