Triwellisma

Interval information

Factorization	2 × 3-1 × 5-7 × 76
Monzo	[1 -1 -7 6⟩
Size in cents	6.804441¢
Name	Triwellisma
FJS name	[math]\displaystyle{ \text{6d5}^{7,7,7,7,7,7}_{5,5,5,5,5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	35.6826
Weil norm (log2 max(n, d))	35.6883
Wilson norm (sopfr(nd))	82
Comma size	small
Open this interval in xen-calc

The triwellisma is a small 7-limit comma measuring about 6.8 cents. It has the monzo [1 -1 -7 6⟩ and the ratio 235298/234375. It is the amount by which a stack of six 7/5's octave reduced exceeds 15/8, or by which a stack of seven 7/5's octave reduced exceeds 21/16. Note that two 7/5's make 49/25, which is short of the octave by 50/49, so in other words, this comma is the difference between 16/15 and a stack of three 50/49's.

Temperaments

Tempering out this comma results in the triwellismic temperament. Some edos that temper it out are 31, 99, 159, 258 and 487.

Etymology

This comma was named by Xenllium in 2021 after the triwell temperament, in which it is the second simplest comma.