Parakleisma: Difference between revisions

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{{monzo|8 14 -13}}, the '''parakleisma''', is a small [[comma]] of 5.292 cents which is the amount by which thirteen minor thirds exceed 32/3; in other words (6/5)<sup>13</sup>/(32/3). Tempering it out leads to [[Ragismic microtemperaments #Parakleismic|parakleismic temperament]].  
{{Infobox Interval
| Monzo = 8 14 -13
| Name = parakleisma
| Color name = g<sup>13</sup>3, thegu 3rd
| Comma = yes
}}
The '''parakleisma''' ([[monzo]]: {{monzo| 8 14 -13 }}), is a [[small comma]] of 5.292 [[cent]]s which is the amount by which thirteen [[6/5|classical minor thirds]] exceed 32/3; in other words (6/5)<sup>13</sup>/(32/3). Tempering it out leads to the 5-limit [[parakleismic]] temperament.
 
== Etymology ==
This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''parakleismic'', for the temperament was similar to [[kleismic]]<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064.html Yahoo! Tuning Group | Kleismic & co]</ref>. ''Parakleisma'' was back-formed from ''parakleismic'' later<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>.  
 
== Notes ==


[[Category:5-limit]]
[[Category:Small comma]]
[[Category:Parakleismic]]
[[Category:Parakleismic]]
[[Category:Commas named for their regular temperament properties]]

Latest revision as of 06:14, 17 April 2025

Interval information
Factorization 28 × 314 × 5-13
Monzo [8 14 -13
Size in cents 5.291732¢
Name parakleisma
Color name g133, thegu 3rd
FJS name [math]\displaystyle{ \text{5d3}_{5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced
Tenney height (log2 nd) 60.3745
Weil height (log2 max(n, d)) 60.379
Wilson height (sopfr(nd)) 123
Comma size small
Open this interval in xen-calc

The parakleisma (monzo: [8 14 -13), is a small comma of 5.292 cents which is the amount by which thirteen classical minor thirds exceed 32/3; in other words (6/5)13/(32/3). Tempering it out leads to the 5-limit parakleismic temperament.

Etymology

This comma was named by Gene Ward Smith in 2001 in terms of the corresponding temperament, parakleismic, for the temperament was similar to kleismic[1]. Parakleisma was back-formed from parakleismic later[2].

Notes