243/242
| Interval information |
neutral third comma
Lulu comma
reduced
(Shannon, [math]\displaystyle{ \sqrt{nd} }[/math])
243/242, the rastma or the neutral third comma, is a small 11-limit (also 2.3.11-subgroup) comma with a value of roughly 7.1 cents. It is significant in just intonation as the amount by which a stack of two 11/9 neutral thirds (that is an Alpharabian narrow fifth 121/81) fall short of 3/2 just perfect fifth as well as the amount by which a stack of two 27/22 neutral thirds (that is an Alpharabian wide fifth 729/484) exceeds a 3/2 just perfect fifth, the amount by which a stack of two 33/32 quartertones falls short of an apotome (2187/2048) as well as the difference between 11/9 and 27/22, and the difference between 45/44 and 55/54. The last makes the theory where the rastma serves as the subchroma that separates greater and lesser 11-limit chromas – a theory that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.
Temperaments
Tempering out this comma in the full 11-limit leads to the rastmic temperament, or in the 2.3.11 subgroup, the neutral temperament, enabling rastmic chords in either case.
See Rastmic clan for the clan of rank-2 temperaments where it is tempered out. See Rastmic rank-3 clan for the clan of rank-3 temperaments where it is tempered out.