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]\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
Harmonic entropy (Shannon, [math]\sqrt{nd}[/math])	~3.40575 bits
Comma size	small
open this interval in xen-calc

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)^1/2 = (7/6)(99/98)^1/2 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.

See also

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