1000/999

Interval information

Ratio	1000/999
Subgroup monzo	2.3.5.37 [3 -3 3 -1⟩
Size in cents	1.7321¢
Name	millenisma
Color name	37uy3-2 thisutriyo negative 2nd
FJS name	[math]\displaystyle{ \text{A1}^{5,5,5}_{37} }[/math]
Special properties	superparticular, reduced
Tenney norm (log2 nd)	19.9301
Weil norm (log2 max(n, d))	19.9316
Wilson norm (sopfr(nd))	67
Comma size	unnoticeable
Open this interval in xen-calc

1000/999 is an unnoticeable 37-limit superparticular comma of about 1.73 cents. It is the difference between the intervals 27/25 and 40/37.

This comma occurs as the difference between certain 5-limit and 37-limit intervals. The octave-reduced 37th harmonic (37/32) is a semifourth about 251 ¢, while the triptolemaic augmented second (125/108), equal to a stack of three 5/3's octave reduced, is approximately 253 ¢. The difference between these intervals equals 1000/999.

This relationship demonstrates how this comma may serve as a bridge between the 5-limit and 37-limit systems, allowing for approximations of 37-limit intervals using more common 5-limit intervals. Its small size of 1.7 cents makes it practically imperceptible.

Temperaments

1000/999 is tempered out in the no-31's 37-limit extension of the superlimmal temperament. It is also useful for constructing higher-limit extensions of popular temperaments, such as kleismic and amity.

Etymology

Francium proposed the name millenisma in 2025, referring to the Latin word for thousand.

See also

• List of superparticular intervals