512/507
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Interval information |
Thuthu comma
reduced subharmonic
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
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.