# Chalmersia

(Redirected from 123201/123200)
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 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 $\text{d1}^{13,13}_{5,5,7,11}$ Special properties square superparticular,reduced Tenney height (log2 nd) 33.8213 Weil height (log2 max(n, d)) 33.8213 Wilson height (sopfr (nd)) 84 Harmonic entropy(Shannon, $\sqrt{nd}$) ~1.19982 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).

## Temperaments

Tempering out the comma in the full 13-limit gives the rank-5 chalmersic temperament.

Subgroup: 2.3.5.7.11.13

 [⟨ 1 1 2 2 2 4 ], ⟨ 0 1 0 0 0 -3 ], ⟨ 0 0 1 0 0 1 ], ⟨ 0 0 0 1 1 1 ], ⟨ 0 0 0 0 2 1 ]]
mapping generators: ~2, ~3, ~5, ~7, ~351/280
• CTE: ~2 = 1\1, ~3/2 = 701.9539, ~5/4 = 386.3145, ~7/4 = 3368.8265, ~351/280 = 391.2462
• CWE: ~2 = 1\1, ~3/2 = 701.9536, ~5/4 = 386.3140, ~7/4 = 3368.8259, ~351/280 = 391.2461

Optimal ET sequence12f, 19e, 22, 27e, 31, 46, 53, 58, 80, 104c, 111, 159, 190, 217, 224, 270, 494, 684, 764, 935, 954, 1178, 1236, 1448, 1506, 2190, 2684, 3395, 4079, 4349, 4843, 5585, 6079, 8269, 8539, …

## Etymology

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