Parakleisma: Difference between revisions

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Some actual history
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== Etymology ==
== Etymology ==
The parakleisma was named by [[Gene Ward Smith]] in 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>.  
The corresponding temperament was discovered first, known as ''parakleismic'' no later than early 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3481.html Yahoo! Tuning Group | ''32 best 5-limit linear temperaments redux'']</ref>. ''Parakleisma'' was back-formed from ''parakleismic'' by [[Gene Ward Smith]] in late 2002<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']</ref>.  


== Notes ==
== Notes ==


[[Category:Parakleismic]]
[[Category:Parakleismic]]

Revision as of 07:18, 14 May 2023

Interval information
Factorization 28 × 314 × 5-13
Monzo [8 14 -13
Size in cents 5.291732¢
Name parakleisma
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

The corresponding temperament was discovered first, known as parakleismic no later than early 2002[1]. Parakleisma was back-formed from parakleismic by Gene Ward Smith in late 2002[2].

Notes