Parakleisma

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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
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