2058/2057

Interval information

Ratio	2058/2057
Factorization	2 × 3 × 73 × 11-2 × 17-1
Monzo	[1 1 0 3 -2 0 -1⟩
Size in cents	0.84142604¢
Name	xenisma
FJS name	[math]\text{M2}^{7,7,7}_{11,11,17}[/math]
Special properties	superparticular, reduced
Tenney height (log2 nd)	22.0134
Weil height (log2 max(n, d))	22.0141
Wilson height (sopfr (nd))	65
Harmonic entropy (Shannon, [math]\sqrt{n\cdot d}[/math])	~2.40051 bits
Comma size	unnoticeable
open this interval in xen-calc

2058/2057, the xenisma, is a 17-limit (also 2.3.7.11.17 subgroup) comma measuring about 0.84 cents. It is the amount by which a stack of two 14/11's exceed 34/21.

Commatic relations

This comma is the difference between the following superparticular pairs:

• 364/363 and 442/441
• 441/440 and 561/560
• 936/935 and 1716/1715
• 1225/1224 and 3025/3024
• 1701/1700 and 9801/9800

Not to mention some nonsuperparticular but useful relations:

• 273/272 and 1573/1568
• 1575/1573 and 1275/1274

It factors into the following superparticular pairs:

• 2401/2400 and 14400/14399
• 2080/2079 and 194481/194480

Temperaments

Tempering out this comma in the 17-limit results in the rank-6 xenismic temperament, or in the 2.3.7.11.17 subgroup, the rank-4 xenic temperament. In either case it enables xenismic chords.

Etymology

The xenisma was named by Margo Schulter in 2000.