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Interval information
Ratio 123201/123200
Factorization 2-6 × 36 × 5-2 × 7-1 × 11-1 × 132
Monzo [-6 6 -2 -1 -1 2
Size in cents 0.014052167¢
Name chalmersia
Color name Lathotholurugugu comma
FJS name [math]\text{d1}^{13,13}_{5,5,7,11}[/math]
Special properties square superparticular,
Tenney height (log2 nd) 33.8213
Weil height (log2 max(n, d)) 33.8213
Wilson height (sopfr (nd)) 84
Harmonic entropy
(Shannon, [math]\sqrt{n\cdot d}[/math])
~2.3983 bits
Comma size unnoticeable
S-expressions S351,
S78 / S80
open this interval in xen-calc

The chalmersia is an unnoticeable 13-limit comma with a ratio of 123201/123200 and a size of approximately 0.014 ¢. It is the smallest 13-limit superparticular comma. Tempering it out equates 351/350 and 352/351, thus splitting 176/175 into two, and equates 385/351 and 351/320, thus splitting 77/64 into two – these are features highly characteristic of chalmersic temperaments. In addition, it equates a stack consisting of a 729/512 tritone plus a 169/128 grave fourth with a stack consisting of a 25/16 augmented fifth plus a 77/64 minor third.

It factors into the two smallest 17-limit superparticular ratios: 123201/123200 = (194481/194480)(336141/336140).


The chalmersia was named by Gene Ward Smith in 2003 after John Chalmers[1].

The remarkable 123201/123200 might be named the chalmersia, since John Chalmers is presumably the first to see it.

—Gene Ward Smith

See also