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, 1uuM, luluma
FJS name	[math]\displaystyle{ \text{A1}_{11,11} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	15.8437
Weil norm (log2 max(n, d))	15.8496
Wilson norm (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 ( 2.3.11-subgroup) comma of roughly 7.1 cents. It is significant in just intonation as the difference between many 2.3.11 intervals, namely:

• 3/2 and a stack of two 11/9 – as a semiparticular comma
• 27/22 and 11/9
• an apotome (2187/2048) and a stack of two 33/32
• 45/44 and 55/54

The last difference shows the rastma as the subchroma that separates greater and lesser 11-limit chromas – a demonstration that becomes especially useful when one works extensively with high-fidelity renditions of the 11-limit.

Its square rooted value, about 3.57 cents, is also a tiny comma that is used in Neutral FJS as the formal comma of prime 11; the difference between 11/8 and the half-augmented fourth sqrt(243/128), or between 11/9 or 27/22 and the hemipythagorean neutral third sqrt(3/2).

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.

Tempering out the components of the S-expression alone (81/80 and 121/120) leads to mohaha, a structurally very clean rendition of the 2.3.5.11 subgroup combining meantone and rastmic.

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