512/507

Interval information

Ratio	512/507
Factorization	29 × 3-1 × 13-2
Monzo	[9 -1 0 0 0 -2⟩
Size in cents	16.98968¢
Name	tridecimal neutral thirds comma
Color name	3uu1, thuthu 1sn, Thuthu comma
FJS name	[math]\displaystyle{ \text{A1}_{13,13} }[/math]
Special properties	reduced, reduced subharmonic
Tenney height (log2 nd)	17.9858
Weil height (log2 max(n, d))	18
Wilson height (sopfr(nd))	47
Comma size	small
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512/507, the tridecimal neutral thirds comma, is a 13-limit (also 2.3.13-subgroup) comma with a value of roughly 17.0 cents. It is significant in just intonation as the amount by which the tridecimal neutral third, 16/13, differs from its fifth complement, 39/32, as well as the amount by which a stack of two 1053/1024 quartertones fall short of the apotome.

Temperaments

Tempering out this comma equates both tridecimal neutral thirds to the true neutral third sqrt(3/2), and is proposed to be called harmoneutral temperament by Vector in 2025, as it tempers the subharmonic neutral third together with its fifth complement. A possible weak extension to the 2.3.11.13.19 subgroup, deltahexacot, also tempers out 4096/3993 and 361/352.

See also

• Small comma