Parakleisma
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Factorization | 2^{8} × 3^{14} × 5^{-13} |
Monzo | [8 14 -13⟩ |
Size in cents | 5.2917319¢ |
Name | parakleisma |
FJS name | [math]\text{5d3}_{5,5,5,5,5,5,5,5,5,5,5,5,5}[/math] |
Special properties | reduced |
Tenney height (log_{2} nd) | 60.3745 |
Weil height (log_{2} max(n, d)) | 60.379 |
Wilson height (sopfr (nd)) | 123 |
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math]) |
~2.51848 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
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]}.