99/98

Interval information

Ratio	99/98
Factorization	2-1 × 32 × 7-2 × 11
Monzo	[-1 2 0 -2 1⟩
Size in cents	17.57613¢
Name	mothwellsma
Color name	1orr-2, loruru negative 2nd, Loruru comma
FJS name	[math]\displaystyle{ \text{m}{-2}^{11}_{7,7} }[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	13.2441
Weil height (log2 max(n, d))	13.2587
Wilson height (sopfr(nd))	33
Comma size	small
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99/98, or the mothwellsma, is a small 11-limit comma of 17.6 cents in size. It represents the difference between the 9/7 and 14/11 supermajor thirds, or the difference between two 7/6 subminor thirds and one 11/8 semi-augmented fourth. Note that 11/8 = (7/6)²(99/98) and that 7/6 × 99/98 = 33/28, which is the fifth complement of 14/11.

Temperaments

Tempering out this comma alone in the 11-limit leads to the mothwellsmic temperament (→ Catalog of rank-4 temperaments #Mothwellsmic (99/98)) and enables mothwellsmic chords. It is related to 11-limit orwell, as a generator between 7/6 and (11/8)^1/2 is befitting of orwell.

Etymology

This comma's name comes from a contraction of mothra and orwell, the two rank-2 temperaments that temper out the comma.

See also

• 99/49 – the same interval but one octave higher
• Gallery of just intervals