Parakleisma

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
Harmonic entropy (Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])	~1.45613 bits
Comma size	small
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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. Parakleisma was back-formed from parakleismic later.