243/242

Interval information

Ratio	243/242
Factorization	2-1 × 35 × 11-2
Monzo	[-1 5 0 0 -2⟩
Size in cents	7.13912¢
Names	rastma, neutral third comma
Color name	1uu1, lulu 1sn, Lulu comma
FJS name	[math]\displaystyle{ \text{A1}_{11,11} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	15.8437
Weil height (log2 max(n, d))	15.8496
Wilson height (sopfr(nd))	39
Comma size	small
S-expression	S9 / S11
Open this interval in xen-calc

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 rank-4 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.

See also

• List of superparticular intervals