144/143

Interval information

Ratio	144/143
Factorization	24 × 32 × 11-1 × 13-1
Monzo	[4 2 0 0 -1 -1⟩
Size in cents	12.0644¢
Name	grossma
Color name	3u1u1, thulu 1sn, Thulu comma
FJS name	[math]\displaystyle{ \text{A1}_{11,13} }[/math]
Special properties	square superparticular, reduced
Tenney norm (log2 nd)	14.3298
Weil norm (log2 max(n, d))	14.3399
Wilson norm (sopfr(nd))	38
Comma size	small
S-expression	S12
Open this interval in xen-calc

144/143, the grossma, is a 13-limit small comma. It is the difference between the 11/9 and 16/13 neutral thirds, between the 12/11 and 13/12 neutral seconds, and between the 11/8 and 18/13 superfourths/subtritones. Since it separates so many 2.3.11 and 2.3.13 intervals, the grossma is a very important interval in the 13-limit, with a function in the 2.3.11.13 subgroup akin to 36/35 in the 2.3.5.7 subgroup (7-limit), though the size of 144/143 is a quarter that of 36/35, so tempering it out is arguably more plausible.

Temperaments

A natural 2.3.11.13 temperament that extends it is namo, which sets the equated undecimal and tridecimal intervals to true neutral intervals. Namo is often used to extend temperaments with neutral thirds to the 13-limit, such as hemififths and squares.

Teff is a full 13-limit (and beyond) temperament of note that targets it, which also tempers out the syntonic comma 81/80.

Sagittal notation

In the Sagittal system, the downward version of this comma (possibly tempered) is represented by the sagittal  and is called the 143 comma, or 143C for short, because the simplest interval it notates is 143/1 = 11×13 (equiv. 143/128), as for example in C-D⁠ ⁠. The upward version is called 1/143C or 143C up and is represented by .

See also

• Small comma
• List of superparticular intervals
• Grossmisma, the difference by which a stack of seven 144/143s falls short of 21/20