2023/2000

2023/2000, the pentagoth comma, is the interval between a stack of two 20/17 minor thirds and one 7/5 tritone.

Interval information

Ratio	2023/2000
Factorization	2-4 × 5-3 × 7 × 172
Monzo	[-4 0 -3 1 0 0 2⟩
Size in cents	19.79558¢
Name	pentagoth comma
Color name	17oozg33 sosozotrigu 3rd Sosozotrigu comma
FJS name	[math]\displaystyle{ \text{ddd3}^{7,17,17}_{5,5,5} }[/math]
Special properties	reduced
Tenney norm (log2 nd)	21.9481
Weil norm (log2 max(n, d))	21.9646
Wilson norm (sopfr(nd))	64
Comma size	small
Open this interval in xen-calc

Tempering out this comma alone in the 2.5.7.17 subgroup leads to the pentagoth temperament.

Pentagoth (rank-3)

Subgroup: 2.5.7.17

Comma list: 2023/2000

Mapping: [⟨1 2 2 4], ⟨0 1 1 1], ⟨0 0 2 -1]]

mapping generators: ~2, ~5/4, ~20/17

Mapping to lattice: [⟨0 3 0 -1], ⟨0 0 1 0]]

Optimal tunings:

• WE: ~2 = 1200.566 ¢, ~5/4 = 387.475 ¢, ~20/17 = 289.545 ¢

error map: ⟨+0.566 2.294 -1.127 -4.760]

• CWE: ~2 = 1200.0000 ¢, ~5/4 = 388.049 ¢, ~5/4 = 289.369 ¢

error map: ⟨0.000 1.735 -2.038 -6.275]

Badness (Sintel): 0.509

Etymology

As of June 6, 2026, pentagoth is the name given to the rank-3 temperament 2.5.7.17[2023/2000] by groundfault. It originally referred to a temperament now called vengeance, which as a 2.5.17 temperament tempers out this comma.