Stearnsma

Interval information

Ratio	118098/117649
Factorization	2 × 310 × 7-6
Monzo	[1 10 0 -6⟩
Size in cents	6.59457¢
Name	stearnsma
Color name	latribiru negative 4th, Lr6-4, latribiru comma
FJS name	[math]\displaystyle{ \text{ddd}{-4}_{7,7,7,7,7,7} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	33.6938
Weil norm (log2 max(n, d))	33.6993
Wilson norm (sopfr(nd))	74
Comma size	small
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The stearnsma (monzo: [1 10 0 -6⟩, ratio: 118098/117649) is a small 2.3.7-subgroup comma with a width of about 6.6 cents. It is the amount by which an octave-reduced stack of six 9/7's exceeds 9/8. It is also the amount by which 343/243, equal to a stack consisting of a 7/6 and two 14/9's, falls short of its octave complement.

It is similar in size to the gamelisma, another comma in the same subgroup. Their difference is the septimal ennealimma.

It factors into (540/539)⋅(24057/24010) or (540/539)²⋅(9801/9800) in the 11-limit, which, if we take away another instance of 540/539 from the other ratio, gives rise to the identity (540/539)³/(4000/3993).

Temperaments

Tempering out this comma alone in the 7-limit leads to the rank-3 stearnsmic temperament, which splits the octave into 2 equal parts.

See Stearnsmic clan for the clan of rank-2 temperaments that temper this comma out.

Etymology

The stearnsma is likely named after Daniel Anthony Stearns.