Quectisma

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

Interval information

Factorization	2554 × 3-351 × 5
Monzo	[554 -351 1⟩
Size in cents	0.1084101¢
Name	quectisma
FJS name	[math]\displaystyle{ \text{49d34}^{5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	1112.64
Weil norm (log2 max(n, d))	1112.64
Wilson norm (sopfr(nd))	2166
Comma size	unnoticeable
Open this interval in xen-calc

The quectisma, [554 -351 1⟩, is an unnoticeable 5-limit comma measuring about 0.108 cents in size. It is the tiny interval between a stack of 351 3/2's and 5/4, octave reduced.

Temperaments

Tempering out this comma leads to the quectismic temperament. Edos with very accurate fifths such as 665edo temper out this comma. This temperament, with its ultra-long chain of fifths, has been used to stress test the Temperament Evaluator.

Etymology

This comma was named by CompactStar in 2023, most likely after the SI prefix quecto-.