Aluminium comma

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Revision as of 19:51, 5 January 2023 by Eliora (talk | contribs) (I wonder if this comma already has been given a name? given the ubiquity of 135/128 in music theory, I wonder if anyone else caught before me that it is close to 1/13th of the octave...)
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Interval information
Factorization 292 × 3-39 × 5-13
Monzo [92 -39 -13⟩
Size in cents 1.676686¢
Name aluminium comma
FJS name [math]\displaystyle{ \text{13d8}_{5,5,5,5,5,5,5,5,5,5,5,5,5} }[/math]
Special properties reduced,
reduced subharmonic
Tenney height (log2 nd) 183.999
Weil height (log2 max(n, d)) 184
Wilson height (sopfr(nd)) 366
Comma size unnoticeable
Open this interval in xen-calc

Aluminium comma is a 5-limit interval which sets the difference between a stack of thirteen major limmas and the octave. It is named after the 13th chemical element. For EDOs N up to ~2000, it is tempered if and only if 13 divides N.

Temperaments

Notable edos tempering it out are 65edo, 494edo which is a zeta edo, and 1547edo. For higher-limit extensions, see Ragismic microtemperaments#Aluminium.

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